112
Pass Your Grade 7 Maths Examination Skills m ORRY PROJECTS M BUSttM
Pass Your Grade 7 Maths
Examination Skills
mORRY PROJECTS MBUSttM
Priority Projects Consultancy (Pvt) Ltd w PRIORITY PROJECTS PUBLISHING
Suite 9, Highfield Junction Complex, Southerton P O Box 66856, Kopje, Harare
Tele/Fax: 263-4-775968/781669 Cell: Oil 604 996 0912 313 682 011 716 961
Website: www.ppp.co.zw E-mail: [email protected]
©Priority Projects Publishing 2008
Reprinted 2009, twice
ISBN: 978 0 797436107
EDITOR: Zabron M. Mponda & S.T. Moyo
LAYOUT AND DESIGN: Zenzele Ncube
COVER DESIGN: Zenzele Ncube
PRINTING: South Africa
ALL DIAGRAMS: Zenzele Ncube
All rights reserved. Reproduction of this publication in part or full is strictly prohibited.No mechanical or electrical recording/transmission in any form or by any means,
photocopying or otherwise, without the prior consent and permission of the copyrightowner in writing.
The publisher uses recyclable paper
AcknowledgementsSpecial thanks are extended to the Ministry of Education, Sports and Culture (Curriculum Development Unit) for providing guidance through the Primary Mathematics Syllabus.
CONTENTS
Sail Bite EarnUnit 1 Numbers.......... ...............................................................................................5
Unit 2 Addition: Whole numbers and Decimal numbers............. .......................... 10
Unit 3 Subtraction: Whole numbers and Decimal numbers............... J.................. 12
Unit 4 Multiplication: Whole numbers and Decimal numbers................................ 14
Unit 5 Division: Whole numbers and Decimal numbers................ .......................... 17
Unit 6 Common Fractions: Proper fractions, Improper and Mixed numbers........... 20
Unit 7 Fractions: Addition and Subtraction........ .......................................................23
Unit 8 Fractions: Division and Multiplication....... ............................................ .........28
Unit 9 Decimals: Tenths, Hundredths and Thousandths.,........ ............... ................31
Unit 10 The Highest Common Factor (HCF) and Lowest Common Multiple (LCM) 36
Unit 11 Percentages...................................................................................................39
Unit 12 Averages......... .....................*.................................. ............................... ....... 43
Unit 13 Ratio and Proportions............. ....................... ...............................................45
Unit 14 Areas and Perimeters.......... .........................................................................47
Unit 15 Speed, Distance and Tim e.............. .............................................................53
Unit 16 Angles and Direction.................................. .......................................... ........ 56
Unit 17 Polygons and Solid Shapes................................................................... ....... 61
Unit 18 Savings and Interest........................................ ...................... .................... ....67
Unit 19 Volume, Capacity and Mass....................... ................ .................................. 72
Unit 20 Time and Timetables........................... ............................... ..........................75
Unit 21 Graphs..,....................................................................... ...................... ........... 80
Unit 22 Paper 1 Tests................................................................................................ 82Test 1 ......... ................................................................. ............... .................83Test 2.......... ........ ............................. -...... ............... - ............................... .88Test 3 ..... .................................. ........................................ ...........................92Test 4 ....... ...............wr.................................. ...................................... ...........97Test 5 .... ...................................................................... ...............................101
Unit 23 Paper 2 Tests..............................................................................................106Test 1 ........................................................ ..................................................107Test 2 ........................................................................................................... 109Test 3 ...... ............................................. ..................................... -................111
V _ _______________________ :......................... .......................... ............................)
HOW TO USE THIS BOOK
Pass Your Grade 7 Mathematics is a revision practice book written for the p ilo s e of helping ^rade 7 pupils with Mathematical skills that are required to cop© with the demands of the Grade 7 Paths syllabus, and to enable them to pass their ZIMSEC Examination.
It is a book that can be taken as a pre-requisite for both understanding and acquisition of skills in Mathematics. Pupils can tackle the exercises individually, with parents, or in class. Where the exercises are done Individually, pupils should refer to the Pass Your Grade 7 Maths Answer Book for answers to the questions. The answers to the questions may be given to teachers for marking.
• The topics have been introduced sequentially, logically and systematically.
• Examples have been given on how to tackle problems under each topic.
• The book has a self-teaching aspect in that methods and instructions on how to work out problems have been outlined to promote a quick grasp of concepts.
• Adequate work is given under each topic for practice purposes.
• Typical Paper 1 and Paper 2 examination questions are provided at the end of the book for examination preparation purposes.
• Answers to each exercise are provided for the pupil or anybody providing assistance to the child in a separate answer booklet
V
UNIT 1
NUMBERS
A place value indicates the position of each digit in a given IIUII.IVBI.In a decimal number, the comma separates the whole number from the fraction.
WHOLE NUMBERSBelow is an abacus picture to show place value. Read the number shown on the abacus picture.
M HTh TTh TH H U
The number shown on the abacus picture in words is five million three hundred and seventy-eight thousand two hundred and ninety-four.
Therefore: M - stands for millionsHTh - stands for hundred thousandsTTh - stands for ten thousandsTh - stands for thousandsH - stands for hundredsT - stands for tensU - stands for units
Exercise ARead the numbers below and then draw abacus pictures to show the numbers:a) 1 602 453 b) 5 184 329c) 2 938119 d) 7 456201e) 9373 475 f) 3 893 5469) 6 074 013 h) 4 748 9610 5 884 268 i) 3 904 481
Exercise BWrite the numbers in exercise A in words.
DECIMAL NUMBERSDecimal numbers haw a comma which separates the whole number from the fraction. Any number to the right of the decimal comma is a fraction.
5
Below is an abacus picture to show a decimal number.
Read the number shown on the abacus picture below:
The number shown on the abacus picture in words is eighty-seven thousand three hundred and sixty-two comma seven four nine.Therefore: HTh - stands for hundred thousands
Th - stands for thousands H - stands for hundreds T - stands for tens U - stands for units t - stands for tenths h - stands for hundredths th - stands for thousandths The sign (,) is known as a comma.
Exercise CRead the decimal numbers below and draw the abacus pictures to show the decimal numbers:
a) 8 163,203 b) 53,466c) 971,64 d) 263,47e) 78,21 f) 676,484g) 4 861,725 h) 3 882,360 92 845,2 j) 148,943
Exercise DWrite the numbers in exercise C in words.
Exercise EWhat is the value of the underlined digit?
a) 246,293 b) 1,677c) 467,301 d) 2,72617e) 578,927 f) 8 675,216g) ^4814,564 h) 1 §76,2740 3.925,821 i) 8 381,443
6
ROUNDING OFF NUMBERS TO THE NEAREST TEN, HUNDRED, THOUSAND, TEN THOUSAND, HUNDRED THOUSAND AND MILLION
Rounding off numbers to the nearest tenExplanation: When rounding off numbers to the nearest ten, look at the unite column. If the number under units is below 5, the number will change to the original ten. If the number under units column is 5 or above 5, the number will change to the next ten.
The number to be rounded off will move steps back to the original ten.
The number to be rounded off will move steps forward to the next ten.
Example a): Round off 74 to the nearest ton.
Method:• Use the place value chart T U
7 4• Look at the units column. 4 is below half of 10, so 7 will not change and 4 becomes a 0.
I....+ I I I.....I I I I I I70 71 72 73 74 75 76 77 78 79 80 i------------------ v ----------------1 i---------------v -------------------------1
• Move 4 steps back to 70.• 74 is nearer 70 than 80.• Therefore 74 to the nearest ten is 70.
Example b): Round off 49 to the nearest ten.
Method:• Use the place value chart T U
4 9• Look at the units column. 9 is above half of 10. Therefore 4 tens will change to 5 tens and 0
units.• You move one step forward to 50 as illustrated below:
40 41 42 43 44 45 46 47 48 49 50
I - ----------------------
7
49 is nearer 50 than 40,Therefore 49 to the nearest ten is 50.
Exercise FRound off Vie numbers below to the nearest ten.a) 26 *b) 72c) 543 d) 4 285e) 655 468 f) 57349) 156 587 h) 84 614 9360 973 274 i) 967248
ROUNDING OFF NUMBERS TO THE NEAREST HUNDRED
Example: Round off 584 273 to the nearest hundred
Method:• Use the place value chart HTh TTh Th H T U
5 8 4 2 7 3• Look at the tens column. 7 tens is above half of one hundred. Therefore 2 hundred will change
to 3 hundred and 7 and 3 will become zeros.• 273 is nearer 300 than 200 as illustrated below:
200 210 220 230 240 250 260 270 280 290 300
Therefore: 584 273 to the nearest hundred is 584 300.
Exercise GRound off the numbers below to the nearest: a) hundred b) thousand c) ten thousandd) hundred thousand.
a) 467 245 d) 945 847b) 590 673 e) 7 869 786 C) 823434 f) 4 644 324
Exercise HRound off We numbers below to the nearest unit, tenth and hundredth.
a) 638,726 b) 471,375c) 365,546 d) 582,913e) 637,678 f) 148,477g)0
247,411 h) 317,623835,745 i) 927,461
POWERS
A power is a result we get by multiplying a number by itself a certain number of times.
8
Example: 53 (five to the power of 3). The 5 is called base.. The small raised 3 is called the index. It means 5 must be multiplied 3 times.
Method:• To find the answer. the base multiplies itself by the number of times shown by the index.• 53 = 5 x 5 x 5
= 125Always remember, any number to the power of 0 is 1 as shown in the example below:
4°=1
Exercise IWhat is the value of each of the numbers given below?
a) 35 b) 43e) 83 d) 74e) 64 f) 5A§) 92 h) 1030 55 j) 4 7
Exercise JCompare using >, = or < where: > means bigger than
= means equal to < means smaller than
a) 56 0 4 4 b) lO4 ? ^
c) 10° □ 100 d)
e) 92 08 1 f) 103x 4 D 5 0 0 0
9) 104 □ 40 000 h) 144 P 1 2 2
0 54 + 43 0 ^ X 4 j) 34 + 93O l0 3
V9
UNIT 2
ADDITION: W H O LE N UM BER S AND DECIM AL N UM BERS
Addition is an operation which involves putting two or more numbers or sets of things together so as to find the total.
Example: 769 243 + 3 905 + 47167 = 820 315
Method:• The place value will give guidance on how to arrange the numbers.• Arrange digits of the same value under the same column.• Write figures sterling from the right.• Add figures starting from the right.• Remember to carry tens to the next column and so on.
H ThTTh Th H T U7 6 9 2 4 3
4 7 1 6 73 9 0 5
8 2 0 3 1 52 i i 1
Exercise AWork out the following:
a) 3472 + 29 + 463 b) 7 527 + 6 094 + 429c) 6248 + 308+764 d) 38 796 + 46384e) 96 048+15 186 f> 83 261 + 219 + 40779) 772 462 + 334 909 h) 648 596 + 557434 + 346i) 85 692 + 93+ 347 i) 1 438151 +60415 + 38
DECIMAL NUMBERS
Decimal numbers have a comma placed between units and tenths.
Example: 748,56 + 9,7 + 81,421
Method:• The place value will give guidance on how to arrange the decimal numbers.• Arrange digits of the same value under the same column.• Write the figures from the right observing the position of the comma.• The position of the comma should not be changed.• Add starting from the right.• Remember to put the decimal comma on its correct position on the answer.
Th H T U , t h th7 4 8 , 5 6
8 1 , 4 2 1+ 9 . 7
8 3 9 . 6 8 11 1 1
NB: Watch the position of 9,7. 9 units has been written under the unit column and 7 under the tenths column.
10
Exercise BFind the sum of each of the following:
a) 347,19 + 5,3 + 78,8 b) 53,21 + 8,37 + 94,623c) 86,58 + 8 + 3,9 d) 713,3 + 3,54 + 6e) 137,6 + 4,63 + 32,8 f) 648 + 32,4 + 19,212g) 279 + 3,1+0,007 h) 8,211 +47,3 + 5280 726,41 + 95,24 + 7,6 j) 927,7 + 5,32 + 4,719
Exercise C
Number stories
1 . In a school, there were 19 453 textbooks at the beginning of the year. In September the same year, 5 686 books were donated to the school. How many books were there by the end of the year?
2. In Murehwa North constituency, 13 729 people voted on the first day of the elections and 6 492 voted on the second day. How many people voted altogether?
3 . Find the sum of 279 496; 34 807 and 361 014.
4. 6 027 boxes of chalk were packed on Monday, 5 936 on Tuesday and 4 685 on Wednesday. How many boxes of chalk were packed altogether?
5. At a Sen/ice Station, 34 750 litres of petrol were sold in January, 28 500 litres in February and19 950 litres in March. How many litres were sold altogether?
6 . The heights of three boys are 1,61m, t,57m and 1,49m. What is their total height?
7. At a garage, a Mazda pick-up was marked $750 550 and a Datsun pick-up was marked $459 750. How much are'the two vehicles worth?
8. A boarding school used $979 208,90 in January, $883 769,45 in February and $937 264,87 in March. How much was spent in the three months?
11
UNIT 3
S U B TR A C TIO N : W H O LE N UM BER S AND DECIM AL NUM BERS
Subtraction is an operation which involves taking away a part from a given quantity or set of things.
Example: 53 208 - 4 579 = 48 629
Method:* The place value will give guidance on how to arrange numbers.■ The digits of the same value should be in the same column.■ The bigger number should be written on top.■ When subtracting, start from the right* When the digit on top is smaller than the digit at the bottom, remember to borrow from the next
column.■ If you give at the top, don’t forget to give at the bottom digit to the left of that being subtracted.
Working: TTh Th H T U5 ’3 12 10 ’8
- 1 54 65 87 94 8 6 2 9
* 8 minus 9 is not possible. So borrow one ten from the tens column to make a total of 18. Therefore 18 - 9 is equal to 9.
■ Give 1{ten) to 7 to make it 8.0 minus 8 is not possible. So borrow 1 (hundred) from the hundreids column which is 10 tens. 10 minus 8 is equal to 2.
■ Give 1 hundred (10 tens) to 5 to make it 6 hundred. 2 minus 6 is not possible. So again borrow1 thousand from the thousands column which is 10 hundreds. 10 Hundreds plus 2 hundreds equals 12 hundreds.Then 12 hundreds minus 6 hundreds equals 6 hundreds.
■ Give 1 thousand to 4 to make it 5. 3 minus 5 is not possible. So we borrow 1 ten thousand from the ten thousand column which is 10 thousands. 10 thousands plus 3 thousands equals13 thousands. Then 13 thousands minus 5 thousands equals 8 thousands.
■ Lastly, give 1 ten thousand under 5. Subtract 1 from 5 and the answer is 4. This gives us 48 629 as the answer.
Exercise AWork out the answers to the problems below:a) 34 051 — 9 764 b) 75 264-36176c) 84 467 - 35576 d) 20 475 -1 9 586e) 246 903-184 726 f) 435 7 1 5 - 266 967g) 500 207 - 179 828 h) 661 341 -1 7 3 235i) 460 584 - 74 676 j) 334 217-125 358
DECIMAL NUMBERS
Example: 571,03 - 83,456 = 487,574
Method:* The place value will give guidance on the arrangement of numbers.
Arrange digits of the same value under the same column.
IS
Write figures starting from the right.The position of the comma should not be changed.When subtracting, start from the right.When the digit on top is smaller than the digit at the bottom, remember!© borrow from the next column.If you give at the top, don’t forget to give at the bottom digit to the left of that being subtracted.
Working:H T U , t h th5 17 *1 , ’0 13 10i 98 43 54 e5 6
4 8 7 . 5 7 4
Exercise BWork out the answers to the problems given below:a) 42,7-31,93 b) 73,5-51,47c) 543,263 - 78,61 d> 655,3-147,85e) 603,271 -95,48 f) 7 534,2-83,6759) 901-2,37 h) 268,3 - 70 356,3 - 74,56 j) 754,436 - 366,74
Exercise C
Number Stories
1. Mr Munaiwa bought a lounge suite for $27 500. How much more did it exist if Mr Chemunhikwi bought the same lounge suite for $193 249?
2. The Zimbabwe National Sports Stadium has enough space to accommodate 60 000 people.At a Castle Cup final, 57 217 entered the stadium to watch a match. How many more people were needed to fill up the stadium?
3. 875 207 tonnes of maize were stored at a grain silo. If 387 419 tonnes of maize were sold, how many were left?
4. A farmer had 70 005 herd of cattle. 6 677 were attacked by a disease and died. How many cattle were left?
5. The Zimbabwe Sugar Refinery produced 307 815 tonnes of sugar, 218 606 tonnes of the sugar were exported. How many tonnes of sugar were left?
6. Find the difference between 27,4 and 3,652.
7. Decrease 412,3 by 57,785.
8 The sum of two numbers is 346,204. One of the numbers is 97,479. What is the other number?
9. Stanley has a mass of 71,875kg. Taurai’s mass is 6,9 kg less. What is Taurai’s mass?
10. A motorist travelling from Nyamapanda to Harare had 55 litres of petrol in the tank. When he arrived in Harare, he had used 38,250 litres. How many litres were left in the tank?
13
UNIT 4
M U LTIPLICATIO N : W H O LE N UM BER S AND DECIM AL NUM BER S
Multiplication is defined,as repeated addition of the same number, if you add 7+7+T+7, the answer is 28. Because there are four 7s, in multiplication we write it as 7 x 4 = 28.
For a person to be in a position to work out problems involving multiplication, there is need to know the multiplication facts.
Study the multiplication chart below:
X 1 2 3 4 5 6 7 8 9 10 11 121 1 2 3 4 5 6 7 8 9 10 11 122 2 4 6 ' 8 10 12 14 16 18 20 22 243 3 6 9 12 15 18 21 24 27 30 33 364 4 8 12 16 20 24 28 32 36 40 44 485 5 10 15 20 25 30 35 40 45 50 55 606 6 12 18 24 30 36 42 48 54 60 66 727 7 14 21 28 35 42 49 56 63 70 77 848 8 16 24 32 40 48 56 64 72 80 88 969 9 18 27 36 45 54 63 72 81 90 99 .10810 10 20 30 40 50 60 70 80 90 100 110 12011 11 22 33 44 55 66 77 88 99 110 121 13212 12 24 36 48 m 72 84 96 108 120 132 144
How to use the multiplication chart
Example: 9 X 7
• Look at 9 on the column.« Look at 7 on the row.« Go down the column under 9 and then go across the row of 7. Where the column meets the
row is the answer.■ Therefore 9 x 7 = 63.• NB. If you multiply any number by 0 the answer is O.» Any number multiplied by 1 remains the same.
WORKING WITH WHOLE NUMBERS
Example: 786 x 37786 is called the multiplicand.37 is called the multiplier.The answer is called the product.Therefore, finding the product means multiply.
Working: 786X 3723580 =786 x 30
+ 5502 ------► =786 x 729082 ------► = 786 x 37
The multiplicand and the multiplier should be arranged vertically to facilitate easy working.■ First multiply 786 by 30. Write 0 down for 30 and then multiply by 3. Multiply 3 by 6 to get 18.
Write 8 and then carry 1. Multiply 3 by 8 and then add 1 to get 25. Write 5 and carry 2. Multiply3 by 7 and then add 2 Jo get 23.The product for the first part 786 x 3lfc 23 580.
■ Second, multiply 786 by 7. Multiply 7 by 6 to get 42. Write 2 and carry 4. Multiply 7 by 8 to get 56. Add 4 to make it 60.Write 0 and carry 6. Multiply 7 by 7 to get 49. Add 6 to get 55. Write 55. The product of the second part, 786 x 7 = 5 502
- Add 23 580 and 5 502 to get 29 082■ Therefore 786 x 37 = 29 082
Now find the products of the problems given in Exercise A.
Exercise A
a) 273 x9 b) 348 x 8c) 579 x 6 d) 648 x5e) 943 x7 f) 709 x3g) 512x39 h) 769 x 48i) 867 x 65 i) 607 x 93
k) 704 x 28 0 572 x 38m) 947 x4 O) 495 x47
n) 675 x 89
DECIMAL NUMBERS
A decimal number has a comma which separates the whole number from the fraction. The comma may be on the multiplicand or multiplier or both. The product will have the total number of decimal places from both the multiplicand and the multiplier counted from right to left,
WORKING WITH WHOLE NUMBERS
Example; 63,5 x 2.912 700 ------► =63,5x20
+ 5715 — ► =63,5x9184.15 ------► =63,5x2,9
Working:• Multiply as if multiplying whole numbers. No decimal commas in the working.■ The product will have two places of decimal, that is, one from the multiplicand and the other on
the multiplier.■ The product will be 184,15.■ NB. If the multiplicand has 3 places of decimal and the multiplier has 1, the product will have 4
places of decimal.
Exercise B
Find the products of the following:
a) 4,9 x 3,7 b) 7,4 x 0,3c) 24,8x6,5 d) 93,2 x 5,4e) 0,003 x 0,4 f) 7,56 x 0,029) 843x2,6 h) 373 x 0,78
V 0 0,009 x5 i) 6,243 x 0,8
15
Exercise C
Number stories1. Find the product of 493 and 85.
2. An oil company can produce 849 drums of oil per day. If it can operate for 23 days a month, how many drums does it produce per month?
3. A company had 737 workers. Each worker was paid $86 per hour. How much money was required for all workers per hour?
4. A lorry carried 200 x 50kg bags of cement. If the lorry made 5 trips, how many kilograms did Jt carry?
5. A bicycle tyre costs $765. Mr Mutinhiri bought 38 tyres to resell at his shop. How much did he pay for all the tyres?
6. A motorist bought 93,5 litres of petrol at $67,30 per litre. How much did he pay altogether?
7. If rice cost $98,50 per kilogram, what is the cost of 7,8kg of rice?
8. 16 passengers boarded a bus from Marondera to Harare. Each passenger paid $450,50. How much did they pay altogether?
16
UNITS
Division is repeated subtraction of the divisor from the dividend. The answer Is called a quotient.
Example: 27 * 9 = 3
Therefore: 27- 9 1*918
- 9 2nd 99
- 9 3rd 90
Division is the method used instead of subtracting continuously. It will be tiresome and time- consuming to do so when dealing with 3 or 4 digit dividends.
NB: Knowing multiplication facts plays a vital role when working out problems of division.
Example: 81 divided by 9 = 9 9 x 9 = 81
LONG DIVISION
Example: 4 968 divided by 9
Working: 552
=_45r 18
-1 8 __ 0
Method:■ Start by dividing 9 into 4. It cannot go into 4.■ Divide 9 into 49. It goes 5 times, remainder 4. Write 5 directly above 9.■ Multiply the 5 by 9 and write your answer below 49 as shown.■ Subtract 45 from 49. The answer is 4.■ Bring down 6 and it becomes 46. Divide 46 by 9. It gives 5. Write 5 directly above 6.■ Multiply the 5 by 9 and write your answer below 46.■ Subtract 45 from 46. The answer is 1 .■ Bring 8 down to form 18 and divide 18 by 9.■ Write 2 directly above 8.■ Multiply 2 by 9. Write your answer below 18.
Subtract 18 from 18. The answer is 0.________________________________________
27 is the dividend,9 is the divisor.3 is the quotient.
NB: Some division problems have remainders.
Example: 838 +7
119 remainder 5J j r
13
Exercise AWork out the problems below:a) 735 + 35 b) 182 + 7e) 272 + 17 f) 3842 + 34i) 429 + 13 j) 8 944 + 43
C) 768 + 16 g) 3 255 + 31
d) 322 + 23 h) 2 310 + 55
Exercise B
Work out the problems below. They have remainders:
a) 215 + 14e) 442 + 19i) f 913 + 42
b) 820+19f) 937+43 j) 4 749 + 36
c) 631+16g) 1663 + 28 k) 5 859 + 39
d) 946 + 25h) 2 243 + 29I ) 8 745 + 54
DECIMAL NUMBERS
Example: 33,84 +1,2
Method:• Make the divisor a whole number by moving the decimal comma as many places to the right
as necessary, in the problem above, move one decimal place to make the divisor 12.■ Balance the dividend by moving the decimal comma the same number of places to the right.• Start dividing.■ The decimal comma on the quotient must be exactly above the decimal comma in the
dividend.
NB: If the divisor is a whole number, divide without moving the decimal comma on the dividend.
Working: 33,84 + 1 ,2. Move the decimal comma 1 place to the right on the divisor first and then 1place to the right again on the dividend to make it 338,4 +12.
28,212| 338,4
-24.9!
_96 24
__ Q
18
Exercise CWork oat the problems below:
a) 8,76-5-2 b) 49,92 -r 3,2 d) 31,2*48c) 11,70 -r 1,8
e) 0,492 -f 12g) 164,58 -r 6,2i) 1,770 -r 0,06
k) 1,355-5-5
h) 15,375-5-1,25 j) 70,38 -5- 2,3 I) 57,024-r 0,6
f) 6,93 + 7
Exercise D
Number Stories
1. How many pieces of cloth, each 4,5m long, can be cut from a roll that is 94,5m long?
{2- The area of a garden is 2 425,5m2. If the width is 38,5m, calculate the length of the garden.
3. The perimeter of a square is 82,4cm. What is the length of one side?
4. A sheet of metal is 0,5cm thick. How many sheets are there in a pile 0,85m high?
5v How many pieces of cloth, each 5,5m long, can be cut from a length of 126,5m?
6, The distance from Harare to Chemhondoro Primary is 62,5km. A peg was placed every 0,5km along the road. How many pegs were placed along the road?
7. A vendor bought a 49,5kg bag of salt. He packed the salt into 0,25kg packets. How many packets did he pack?
J19
UNIT 6
COMMON FRACTIONS: PROPER FRACTIONS, IMPROPER AND MIXED NUMBERS
FRACTIONSi) A fraction is a number that is not a whole number.ii) A fraction is part of a whole number.
Below is a diagram to show that a fraction is part of a whole number:
Answer the questions below:a) What fraction of the shape is shaded?
b) How many quarters ( — ) are in one whole number?
PROPER FRACTIONSA proper fraction has two numbers written one on top of the other. The number on top of the other is called a numerator and the number at the bottom is tailed a denominator,: The numerator on a proper fraction is smaller than the denominator.
4. - (numerator)9 - (denominator)
Exercise A
a) Learn to read the fractions below:
1 2 1 3 4 7 7 9 7 132 3 4 5 6 9 12 20 30 1000
b) Write the fractions below in words
1 11 1 11 ® 1 —3 5 7 9 13 » 20 6 4 12
Study the fraction chart below:
1 whole
/ / / / /1n
123
i4
m15 W //A
1
J.10
20
NB: Try to remember that:
2 halves make a whole
— Is bigger than — 2 3
— is bigger than — 2 10
2 . , 1 — is equal to — 4 2 — is equivalent to —
10 2
Exercise B
Compare the fractions below using >, = or <,
e)
0
1 □ - 2
b ) - O - 2 5
± □ - .6 3
f l l D i10 5
^ □ 1 4 2
j) - □ - 3 5
k )i □5 100
<)) — □ — S 2
4 r-. 8h ) - O —
5 10
i) ? □ - «5 100
IMPROPER FRACTIONS AND MIXED NUMBERS
Improper FractionsAn improper fraction is a fraction that has a numerator which is bigger than the denominator as shown below:19 15 27
644
9
Mixed NumbersA mixed fraction has a whole number and a proper fraction put together as shown below:
n i iChange the mixed numbers below to improper fractions:
Example: 3|
Method:• Multiply the denominator by the whole number.- Add the answer to the numerator.■ Write the answer over the denominator.
3 + | = 3 x 5 = 1 5
= 15 + 4 = 1 9
19
5
21
NB:■ To check whether your answer is correct, divide the numerator by the denominator.
a 19■ The equal sign between means 3| has an equal value to —
Exercise CWork out the fractions below into improper fractions:
a) 4| b) 5 f C> 3g d )7 § e>3§
f) 8|
©IN
CM3
h) 6| i) 9| i) 4|
k )7 | ') 3 13 m )1 3 f n )19| ° )17|
Exercise DChange the improper fraction below to mixed numbers.
Example: 22 = j |P3
Method:■ Divide the numerator by the denominator.■ Write the whole number first.■ Write the remainder over the denominator.
22 1 — = 22 -f 3 = 7 remainder 1 = —3 3
• nNB: To check whether the answer is correct, multiply the denominator by the whole number and then add the numerator to the answer.
Work out die fractions below into mixed fractions:
« 7
237 - 7
^27 e) — 6
- f • ?
* 7 * ?
22
r UNIT 7 A
ADDITION: PROPER FRACTIONS
. 1 5 Example: — + —2 7
Method■ Find the common denominator of 2 and 7. (This is the smallest number into which 2 and 7
enter without leaving a remainder).
■ Find — of the common denominator.
■ Add the two answers and write the total over the common denominator.■ If the numerator is bigger than the denominator, divide the numerator by the denominator.■ Writer the answer as a mixed number.■ Reduce the answer (fraction) to the lowest terms.■ Keep the equal signs directly under each other.
2 7 2 7 = 7+10
14 common denominator
= 17 divide 17 by 1414
25■ Rnd — of the common denominator.
1 5 1 5 Woriang: — + — = — + —
Exercise A
Work out the fractions below:
+ 45
+23 J
23
•s 7 5 9 2 » 11 5j) — + — k) — + — I) — + —8 12 13 3 14 7
ADDITION: MIXED NUMBERS
Example: 3| + 1| =
Method:■ Add the whole numbers first. Write the answer besides the division line.■ Find the common denominator for 7 and 4.
4■ Find — of the common denominator and write the answer above the division line.
73
■ Find — of the common denominator.4
■ Add the answers for the two fractions and write the total over the common denominator.■ The whole number should be written at each step.■ If the numerator is bigger than the denominator divide the numerator, by the denominator. The
answer should be added to the whole number.■ The remainder should be written over the denominator.■ Reduce the answer(fraction) to the lowest terms if it can be reduced.■ Keep equal signs directly under each other.
4 .13 ±21 28
_ ■ SZ * 1-S 28 ’ 28 28
Add the 1 whole to 4 to make it 5
5-928
Exercise B
Work out the answers of the following mixed numbers:
CMICO04 + «# +
1 7
5 49
+ 2§ d ) 5 ?+ 4
4 58
+ 2i f) 6J + 1f +2 1 S
20
3? +’ I h ) 2! + 1I
24
i) 21 + 35 " \
k) 4 6 + 2 9 + 1 12
Exercise C
Number Stories
1. A teacher bought 5| kilograms of meat in January and 3| in February. What was the total mass of meat she bought in the two months?
2. At a school, a boy spent 5 ^ hours in the classroom and 2^ hours at the football pitch. How many hours is this altogether?
3. Find the sum of 3| and 4 | .
4. Jack spent | of his money in one shop, 1 in another shop and | in the third shop. What was
the total fraction he spent?
5. Two parcels weigh 2| kg and 7|kg respectively. What is the total weight of the parcels’ .;
SUBTRACTION: PROPER FRACTIONS
7 2Example: ----------- =8 3
Method:■ Find the common denominator (the smallest number in which 8 and 3 enter without leaving a
remainder).
7• Find — of the common denominator.
■ Find — of the common denominator.3
• Subtract the two numbers and write the answer over the common denominator.* Reduce the answer to the lowest terms if it can be reduced.■ Keep the equal signs directly under each other.
82
Working: 7 2— - — (Common denominator of 8 and 3 is 24)8 3
21-16 24 common denominator
5_24
J25
Exercise DWork out the problems below:
a) b)1_3
c)8 4
d)67
35
e)11
1223 f) 10
23 g) 12
36
13
15
56
49 j) 8
47
k)15 _7 18 12
11 1 16 8
SUBTRACTION: MIXED NUMBERS
Example 1: 2| - 1|
Method:■ Subtract whole numbers first.■ Find the common denominator for the fractions.
■ Find — of the common denominator.41
■ Find — of the common denominator.2
■ Subtract the two numbers and write the answer over the common denominator.■ If the first number cannot subtract the second number, borrow 1 whole from the whole number.■ The whole number is determined by the common denominator. Add the whole to the first
number and then subtract.■ Reduce the answer to the lowest terms if it can be reduced.■ Keep the equality signs directly under each other.
Working: 2| -
= I 3 ' 24 common denominator
Example 2 : 4^ - 1|
_ 3 4 - 2 124 common denominator
_ 2 28 - 21 NB: the whole number is 24- Add 24 + 4= 28. Subtract 21 from 2824 24
V ■ _____ ________ J26
Exercise EWork out the problems below:
a) 3§ -11 b) 4f -3§ 0) 7I
CO1 d) 6| -n
e) 5| - 21 f) 81 ■ H g) H ■q h) 41 ■ * *
i) 7§ -5 f D 4$ ■ H k) 2$ ■ i§ 1) 4| ■ 1 *
Exercise FNumber Stories
X ‘A car takes 2| hours to travel from Harare to Rusape and a bus takes 3| hours for the samejourney. How much shorter time does the car take?
>JL ■35'
What is left from a roll of cloth 1 0 i metres long after cutting 3| metres off?
g The difference between two mixed numbers is 2gL. If the greater number is 7 | , what is the smaller number?
4 From a piece of steel 3 f metres long, a piece measuring 3| was cut off. What fraction wasleft?
& A farmer planted maize on | of his arable land. ^ had tobacco. The rest was left for grazing
pastures. What fraction was left for grazing?
J
UNIT 8
FRACTIONS: DIVISION AND MULTIPLICATION
DIVISION
3 2 Exam piel: — -r —
10 5Method?* To divide fractions, invert the divisor of the second fraction and muftiply.■ By Inverting, the numerator becomes the denominator and the denominator becomes the
numerator.■ Change the division sign to muffiplcation sign.■ Cancel the fractions using a factor which will get into the number at the top and bottom.* Multiply the numbers left after caRse®t§ a lii© bottom and wit© the answer,■ Multiply the numbers left after cancelling on top and write the answer over the denominator.■ Reduce the answer to the fewest terms if it ran be reduced.
Working:3
10
25
3 3— x —W 2234
Example 2: 3| -r |
Method: Before using the method above* change the mixed number to an improper fraction.
Working:_ 11 5- 6
211=• --- X ——zt 5
_ 225
II
Exercise AWork out the problems below:
3
e)to
35
1213
4
2124 ' 3
d»
ft)
8 29 3
15 527 9
m
\
Exercise B
Work out the problems below:
E’ 1l * 16 b> 2f * 12 c> 2| ^ ^ to <9 3 f *■ f
e) 3 j + I f I) 3 i ♦ I f 8! 21 *1| h) I f - 4§
i) 8| , 6 | i! 6 f , 3|
Exercise €Number Stories1. Four-fifths of a sum of money was shared equally among 8 children. What fraction did each
from the big bottle. What fraction of a litre was in each bottle?
5, A man bought 17^kg of rice. He packed the lice m -^kg packets. How nasny packets did fie psck?
6, A sheet of hardboard had an area of 2| m2, 5 equal pieces were cut from fee sheet What is the area of one piece?
M U LTIP LICA TIO N
Exampie: — x —tG 7
Method:* Divide using a factors! which wflf get lnto a raimbsrat the top and at the feolom.■ Multiply the numbers left after dividing at the bottom and wnte your denominator.■ Multiply tiie numbers left at the top after dividing and write the answer over the denominator.* If the numerator is bigger te n the denominator, divide the numerator by the denominator and
write the answer as a mixe«f number.■ Reduce the answer to the lowest terms if it can be reduced.
child get?
Sl 6|kgof rice was repacked Into 3 equal packets. What was the weigh! of each packet?
3. Share 1 ~ kg of sweets among 1G children. What fraction will each child receive?
4, A big bottle had litres of poisonous chemical 4sraaifer bottles-of the same size were tilted
V
22
29
Example2: 3^ x l|
Method:Before using the method suggested above, change the mixed number to an improper fraction.
Exercise DWork out the fractions below:
, 9 2a ) -------x —
10 3K* 1 4b) — x —
2 5x 3 5c) — x —
4 6„ 3 8d) — x —
4 9
V 1 4e) — x — 4 5
, 18 9 g) — x —
27 10. , 35 5h) — x -
40 7
21 4 i) — x —28 7
Exercise E
12 5
* « x i
Work out the problems below:
a) ? 2 x § b) - x - 21 14
« ) *s x 2 2
I) 2 f x 2 i
f) 3| x 2 l
i) 31 « 1 |
18 17k) — x —
51 21
c) 3* x 3 j
g) 1| x l J j
« 5 19 I) — x —38 20
d) 6§ x 2J
h) x 5 l
Exercise F
Number Stories1. Five-eights of a bag had green maize. Two-thirds of the maize had gone bad. What fraction of
mealies had gone bad?
2. Five-sevenths of a class entered an essay-writing competition. Two-fifths of these won prizes. What fraction of the class won prizes?
3. A tractor travelled at an average speed of 42^ km an hour for 2^ hours. How many kilometres did it travel?
4. Jonathan got 18 marks in a Maths test. He got 2 j times more marks in Shona. How many marks did he get in Shona?
5. A clinic is 2 f km from the shops. A school is 11 times as far from the shops. How far is the5 ^school from the shops?
JU A small pot holds 6J litres of water. A big pot holds 2| litres as much water. How many litres
does the big pot hold?
30
UNIT 9
DECIMALS: TENTHS, HUNDREDTHS AND THOUSANDTHS
A decimal fraction is any number which is less than 1. A decimal number has a decimal comma. In cases where there is a whole number, the whole number will be to the left of the decimal comma.
Below is an abacus picture to show the decimal notation.
The number shown on the abacus picture is nine thousand four hundred and seventy-one comma three two eight.
Th - stands for thousands.H - stands for hundred.T - stands for tens.U - stands for units.1 - is the decimal comma.t - stands for tenths.h - stands for hundredths.th - stands for thousandths.
NB: The comma separates the whole number from the fraction.Any number to the right of the decimal is less than 1. Therefore 0,328 is less than 1.
Tenths
— as a decimal is 0,1. — as a decimal is 0,4.10 10
1A as a decimal is 1,4.
31
Changing a common fraction to a decimal fraction.
Explanation:■ Because — has one zero, this means there must be one number to the right of the decimal.
10■ Because the tenth column is the first column to the right of the decimal comma, therefore there
must be one number to the right of the decimal comma.■ To put it mathematically, you divide the numerator by the denominator as shown below:
4Working: — as a decimal is 0,4
10
Divide 10 into 4. It is not possible. So write 0 and put a comma. Add 0 to 4 and divide 10 into 40. The answer is 4.The final answer is 0,4.
4So — as a decimal number is 0,4.
10
Exercise A
Write the common fractions as decimals.
a)3 , 6
c)9
b) — —10 10 10
2-4*10 *> H g) 4-310
4-2H10 i> 3 io
7_10d)
h> 2 £10
Exercise B
Write the following as decimals.
a) 8 tenths b) 2 tenths
36e) 56 tenths f) ------
100
c) 47 tenths
93g) 100
d) 71 tenths
h) —10
064
10j)
49100
32
Hundredths
1------ is written as 0,01.100
------ is written as 0,07 as a decimal.100
Explanations:
■ Because------ has two zeros, this means we must have two numbers to the riqht of the100
decimal.■ The hundredth column is the second to the right of the decimal comma. This means there must
be two numbers to the right of the decimal comma.■ Mathematically, divide the denominator into the numerator as shown below:
Working:100
0, 09 100| 9
^0 90
- _Q 900
- _aoo 0
■ Divide 100 into 9. It’s not possible, so write 0 and put a comma.■ Add a zero (0) to make it 90.■ Divide 100 into 90. It can’t go into 90, so write 0 and add another 0 to make it 900.■ Divide 100 into 900, the answer is 9.■ Therefore, the final answer is 0,09.
90• S o ------ as a decimal number is 0,09.
100
Exercise CExpress the fractions below as decimals:
X 15 M 28 . 3 ^ 85a) ------ b) ------ c) --- d ) 100 100 100 100
, 7 7 _ 723 . 451 913e) f) ------ g) --- h) ------
100 100 100 100
343 c 2 Q 23 «\ a 59* ^ " 100 k' 100 0 100
Exercise DExpress the decimals as common fractions.
27 b) 0,04 c) 0,01 d) 0,59
33
e) 7, 35 f) 9,78 g) 5,18 h) 22,19
i) 4,05 j) 8,64
Thousandths: -------1000
When dealing with thousandths, there must be three numbers to the right of the comma.
■ Divide 1 000 into 39. It can’t. Write 0 and put a comma.• Add 0 to make it 390. \■ Divide 1 000 into 390. It can’t. Write 0. Add another 0 to make it 3 900.■ Divide 1 000 into 3 900. Write 3. Multiply 3 by 1 000 to get 3 000.■ Subtract 3000 from 3 900. The answer is 900.• Add 0 to make it 9 000.■ Divide 1000 into 9 000. The answer is 9.■ Therefore the final answer is 0,039.
39• S o ------- as a decimal is 0,039.
1000
Exercise EWrite the fractions below as decimals.
93 7 v 519 ^ 827a\ b) -------- c) --------- d) -------
1000 1 000 1 000 1000
39Example: ------- as a decimal is 0,039.1000
1000 390.039
390- __Q
3900- 3000
90009000
Q
x 5 216e) ----------
1000f)
1 0009) ---------
1 000 1000
492i) ---------
1 0007 341 1000
Express the decimals as common fractions.
a) 0,003 b) 0,008 C) 0,037 d) 0,056
J
e) 0,750
i) 7,583
f) 0,275
j) 6,025
g) 0,825 h) 4,125
COMMON FRACTIONS
5Example: Change — to a decimal.8
Method:■ Divide the denominator into the numerator.■ Because the numerator is smaller than the denominator, write 0. Put a comma.■ Add zero and divide.■ If there is a remainder, continue adding a zero until the divisor gets into the dividend without
leaving a remainder.■ NB. If the numerator is bigger them the denominator, write the answer you get after dividing.
First write zero, then put a comma.
Working: f = 0,6258 _ 8 j5 —
rQ50
-4820
-1640
-4Q
Exercise FExpress the fractions as decimals.
X 7 ^ 3 , 5 ^ 9a) — b) — c) — d) —8 4 16 8
5 3 74 40 20
Exercise G Number Stories
A. Express the sum of 2^ and 11 as a decimal.
^ Express 3| and 1 as decimals and find their difference.
3. Mr Jonga spent 0,3 of his money in one shop, 0,05 in another and 0,025 in a third shop. What fraction of his money was left? Express the answer as a decimal.
4. Two parcels of meat weigh 2^ kg and 3| kg respectively. Find the total mass of the parcels
and express the answer as a decimal. ,
35
UNIT 10
THE HIGHEST COMMON FACTOR (HCF) AND _ LOW EST COMMON MULTIPLE (LCM) M
FACTORA factor is a number which divides into another number without leaving a remainder.
Example: What are the factors of 18?
18 =18 18 = 9 18 =61 2 3
1 8 = 4 reminder 2 18. = 3 remainder 3 1 8 = 34 5 6
18 = 2 remainder 4 18 =2 18 = 1 remainder 87 9 10
AW the remaining numbers from 10 up to 17 will leave a remainder.
IfL = 1 18
To find the factors of 18, select all the answers without a remainder. So, the factors of 18 are 1,2,3,6,9 and 18.
Exercise A
What are the factors of the numbers below?
a) 12 b) 20 C) 24 d) 28
e) 30 f) 36 9) 42 h) 48
i) 72 j) 84
PRIME NUMBER■ A prime number has only 1 as a factor.■ A prime number cannot be divided by any other number without leaving a remainder except 1.- NB: 1 is not a prime number.■ The only even number which is a prime number is 2.■ All prime numbers are odd. Odd numbers cannot be evenly divided by 2.
Exercise B
a) From the grid on page 37 identity all prime numbers from 1 up to 100:____
1 2 3 4 5 6 7 8 9 1011 12 13 14 15 16 17 18 19 2021 22 23 24 25 26 27 28 29 3031 32 33 34 35 36 37 38 39 4041 42 43 44 45 46 47 48 49 5051 52 53 54 55 56 57 58 59 6061 62 63 64 65 66 67 68 69 7071 12 73 74 75 76 77 78 79 8081 82 83 84 85 86 87 88 89 9091 92 93 94 95 96 97 98 99 100
b) List 10 prime numbers above 100.
TH E HIGHEST COMMON FACTOR (HCF)
The Highest Common Factor is the biggest number which will get into two or more numbers without-leaving a remainder.
Example: Find the Highest Common Factor (HCF) of 16, 20 and 24.
Method:■ Find the factors of 16,20 and 24.■ Find the factors appearing on all numbers.■ Multiply the factors to find the HCF.■ NB: 4 cannot be written as a factor. 4 will be written as 2x2.■ 6 cannot be written as a factor. It will be written as 2x3.■ When writing factors, start with the smallest e.g. 2 x 3 x 5 (not 5 x 2 x 3).
Working: 16 = 2 x 2 x 2 x 220 = 2 x 2 x 524 = 2 x 2 x 2 x3
To find the factor, 2 is appearing twice on all numbers. Leave out all other factors. Therefore, the HCF is 2 x 2 =4.This means 4 can be divided into 16,20 and 24 without leaving a remainder.
Exercise C
Find the Highest Common Factor of:
a) 21,28, and 42 b) 14,28 and 42
c) 32,48 and 72 d) 36,72 and 96
e) 63,72 and 81 f) 25, 75 and 125
9) 18,27 and 54 h) 16,64 and 96
V__________________ :....................... ...37
TH E LOW EST COMMON MULTIPLE (LCM)The Lowest Common Multiple is a number into which two or more numbers can go without leaving a remainder.
Explanation:Given two numbers 3 and 7, the multiples of 3 are 3,6,9,12,15,18,21,24,27,30. The multiples of 7 are 7,14, 21,28,35,42,49, 56, 63, 70.The smallest multiple of 3 which is also a multiple of 7 is 21. Therefore, 21 is the Lowest Common Multiple of 3 and 7.
NB: 42 is a multiple of 3 and 7 but it is NOT the lowest.
Example: Calculate the Lowest Common Multiple of 16,20 and 24.
Method:■ Rnd the factors of 16,20 and 24.■ Write the factors taking note that each factor in ail numbers is represented once when
calculating LCM.■ Multiply the factors to find the LCM.
Working: Calculate the LCM of 16,20 and 24.
1 6 = 2 x 2 x 2 x 220 = 2 x 2 x 524 = 2 x 2 x 2 x3
To find LCM, the four 2s on 16 will represent the 2s in 20 and 24. Multiply the factors of 16 by 3 because 3 is appearing once and then by 5 as shown below:
Therefore, theLCM = 2 x 2 x 2 x 2 x 3 x 5 = 240.This means 16,20 and 24 can get into 240 without leaving a remainder.
Exercise D
Find the LCM of the following:a) 21, 28 and 56b) 20,28 and 30c) 16, 24 and 27d) 25 and 30e) 54 and 72f) What is the smallest number exactly divisible by 15,35 and 60?g) Rnd the smallest number which when divided by 63 and 84 will leave no remainder.h) Fencing posts are placed 4,5 metres apart along a road on one side of the road and 5,4
metres apart on the other side. The first posts are exactly opposite each other. What will be the distance along the road before two posts are exactly opposite each other again?
i) Find the HCF and LCM of 54, 72 and 108. j) Calculate the HCF and LCM of 60 and 75.
38
UNIT 11
PERCENTAGES
Percent means out of 100. A percentage is a special kind of fraction whose denominator is always 100. The symbol for percent is %.
Because percentage is always given out of 100, the symbol % is thought of as a re-arrangement of
the numerals 1,0 and 0 of 100. Therefore, instead of writing 9 percent or you simply use the symbol as indicated, 9%.
Below is a large rectangle. Study it and then answer questions.
Questionsa) How many small rectangles are there in the large rectangle altogether?b) How many rectangles are shaded?c) Write the number of shaded rectangles as a common fraction of the large rectangle.d) Write the number of shaded rectangles as a percentage.
43■ You got it correct if your answers to the questions above are: (a) 100; (b) 43; (c) — and
(d) 43%. 100■ Did you notice that fractions can be changed to percentages?
Changing fractions to percentages
3Example: Change— to percentage.5
Method:■ The secret behind changing fractions to percentages is that of equivalent fractions.■ Multiply the denominator of a given fraction by a number which will give the denominator 100.* Multiply the numerator using the same number used for the denominator.■ Write the answer as a percentage.
Working: — = = 60% (5 x 20 = 100; so 3 is also multipled by 20 = 60,5 5 x 20 100
60 . . . . ,giving ------ which is 60%).a a 100
39
/^Exercise AChange the fractions below to percentages:
3 h\ 1 2 rl\ 13a) s } 2 c) ? d) 20
e) 2 * 5 9) J h) I25 50 4 tO
•x 17 _ 20 i i J) 2
Changing decimals to percentages
Example: Change 0,4 to a percentage.
Method:■ Change the decimal number to a common fraction.■ Multiply the denominator of the fraction by a number which will give a denominator hundred- Multiply the numerator of the fraction using the same number that multiplied the denominator.■ Write the answer as a percentage.
4Working: 0,4 = —
10
4 x 10 4010 X 10 100 (10 multiplied by 10 gives 100.4 multiplied by 10 gives 40. V
This means ^ = 40%.) /
Exercise BChange the decimals below to percentages:
a) 0,5 b) 0,35 c) 0,7 d) 0,2
e) 0,97 f) 0,81 g) 0,1 h) 0,69
Changing percentages to decimals
Example: Change 6 7 ^% to a decimal.
Method:
■ Change 6 7 - % to a common fraction by multiplying 67 by 2 which is equal to 134. Add 1 to
make it 135, over 200 and NOT over 2, i.e.
• Divide 135 by 200 using the long division method.
■ Start by dividing 200 into 135. It cannot go in. So put a zero, followed by a comma.
40
f ^ m Add 0 to the dividend to make it 1 350. ..■ Divide 1 350 by 200. It goes 6 times. Multiply 6 by 200. The answer is 1 200.■ Subtract 1 200 from 1 350 then you get 150.■ Add 0 to 150 to make it 1 500.■ Divide 1 500 by 200. It goes 7 times.• Multiply 7 by 200 and the answer is 1 400.■ Subtract 1 400 from 1 500 and the remainder is 100.■ Add 0 to 100 to make it 1000.■ Divide 1 000 by 200 and it goes 5 times..■ Multiply 5 by 200 and the answer is 1 000.» Finally subtract 1 000 from 1 000 and the answer is zero (nil).
Working: Change 6 7 l% to a decimal: (67 x 2 = 134 + 1= 135).
0,675 200fl3 5
- 0 1350
-1200 1500
- .1400 1000
-.1000
Exercise CChange the percentages to decimals:
a) 4 2 j% b) 821% c) 651% d) 721%
e)
■HCM
h«o> f) 581% 9) 371% h) 671%
«) 85|% j) 321%
CALCULATING PERCENTAGES
Example: Calculate 35% of 80.
Method:35
■ Write the problem as - — of 80.. ■ 100
35 ,» Divide by 10 so that it becomes — of 8.
10
■ Divide by 5 so that it becomes — of 8.2
■ Divide by 2 so that it becomes — of 4.
■ Multiply 7 by 4 and the answer is 28.
41
Working: 35% of 80 = 7M x £€fWO
= 28
Exercise DWork out the problems below:a) 40% of 240 b) 18% Of 350 c) 65% of 280 d) 45% of 620e) 75% of 300 f) 95% of 880 g) 16% of 75 h) 25% of 540i) 90% of 950 j) 80% of 320
Writing numbers to a percentage
Example: Write 18 out of 25 as a percentage.
Method:■ Write the problem as 18 x 100.
25 1■ To change to a percentage, multiply by 100.■ Cancel by 25 so that it becomes 18 x 4
1 1■ Multiply 18 by 4.
Working: 18 x±0O = 18x425 x 11 = 72%
Exercise E
a) 17 out of 25 b) 19 out of 25 c) 15 out of 30 d) 18 out of 30e) 45 out 50 f) 35 out of 70 g) 22outof40 h) 72 out of 90
i) 39 out of 50 j) 28 out of 40
Exercise F Number Stories1 ? Mr Nyandoro bought 60 litres of petrol. He used 54 litres on a journey. What percentage o f'
petrol was used?2. In the year 2002, Zimunya Primary School had a total enrolment of 1500.780 of the pupils
were boys and 720 were girls. What percentage of pupils were (a) boys and (b) gids?3. A farmer planted 220 orange trees. Thirty-three of the trees were eaten by termites. What
percentage of the trees were (a) destroyed by the termites and (b) not destroyed?60 pupils in Murewa District competed at provincial level in athletics. Out of these, 18 pupils managed to compete at national level. What percentage competed at national level?
5, In a grade one class, 55% of the pupils attended pre-school. What percent did not attend preschool?
a 60 000 people attended a rally at the National Sports Stadium. 45% of these were women and 35% were men. The rest were children. How many children attended the rally?
Tj, Mr Matope estms $35 000 a month. 35% of it is spent on food, 25% on school fees, and 15% on clothes. He banks the rest. How much money does he bank a month?
42
UNIT 12
AVERAGES
To get an average, calculate the total of given numbers and then divide the total by the number of numbers or items given.
Example: Find the average of the following numbers: 327,216 and 330.
Method:• Add the three numbers to find the total.■ Divide the total of the three numbers given by 3 because we are given three numbers.
Working: 327 216
+ 330 873 divided by 3
= 291
Exercise A1. Find the average of
a) 23,4; 22,8; 24,6; 16,3 and 18,4.b) 187,5; 163,29; 174,3 and 62,54.c) 126; 50; 168; 254 and 192.d) 48,5; 62,37; 72,1 and 35,47.e) Three men weighed 72kg, 83kg and 97kg respectively. What was their average weight?f) If the average weight of 7 boxes of nails is 49,8kg, what is the total weight of the 7boxes?
g) If the average salary of five men was $15 250, what was thefr total earnings?
Number stories
Example: The average weight of three pockets of potatoes is 4,9kg. If two of the pockets weigh5,2 kg and 4,8kg respectively, what is the weight of the third pocket?
Method:■ Multiply 4,9kg by 3 to find the total weight of 3 pockets.■ Add 5,2kg and 4,8kg to find the mass of 2 pockets.■ Subtract the mass of 2 pockets from the total mass of 3 pockets. The answer is the weight of
the third pocket.
Working: Average weight of 3 pockets = 4,9kgTotal weight of 3 pockets = 4,9kg x 3
= 14,7kg
Total weight of 2 pockets = 5,2kg + 4,8 kg= 10kg
Therefore, the mass of the third pocket = 14,7kg -10kg= 4,7kg.
V ________ J43
Exercise B ANumber Stories
t, John’s average mark for four Maths test was 36,5. If his marks for the thr®B tests were 38,30 and 34, what was his mark in the fourth test?
Z. The average cost of three suits was $9 547. If two of the suits cost $8 600 and $7 341, what was the cost of the third suit?
3. The average daily attendance at a school for one week was 716. if the average attendance for3 days was 718, what was the average attendance for the other two days?
4. The class average for 40 pupils (25 boys and 15 girls) in an English test was 44,5. if the average of the 25 boys was 43, what was the average for the girls?
5. The average of four numbers is 18,75 and the average of another 2 numbers is 46,5. What is the average of the 6 numbers?
J
44
UNIT 13
RATIO AND PROPORTIONS
RatioRatio is used when comparing quantities of the same kind. Both quantities in comparison should be in the same units of measurement.
Ratio can be written in two ways e.g 3:1 or |
Example: Mrs Nyungurutapi had 75 sweets. She shared the sweets between Chenai and Ruzivo such that Chenai got twice as much as Ruzivo. How many sweets did each get?
Method:■ Find the total ratio by adding 2 and 1 to get 3.
2■ Write 2 over total ratio 3 i.e. — and then multiply by the total number of sweets (75) to be
32 75
shared to get the first share i.e. — x — .3 1
2■ Divide by 3 and the answer will become j x 25
■ Multiply 2 by 25 to get 50.
■ To find the second share write 1 over the total ratio 3 i.e. — and then multiply by the total3
1 75number of sweets (75) to be shared i.e. — x — .
3 1I 25
■ Divide by 3 to get - x —I I
■ Multiply 1 by 25 to get 25.
Working: Number of sweets to be shared = 75 Ratio = 2:1Total ratio . = 2 + 1 = 3
u 2 75Chenai s share = — x —3 1
= 50 sweets
1 75Ruzivo’s share = — x —
3 1= 25 sweets
NB: If you add Ghenai’s share and Ruzivo’s share, the answer should be equal to the total number of sweets being shared ( he; 75).
45
Exercise AWork out the problems below:a) Divide 918 in the ratio 2:7. b) Share 783 textbooks between two tosses in the ratio 4:5.c) Divide 784 in the ratio 1:2:5. d) Share 864 in the ratio 7:8:9.e) A piece of cloth 63 metres long is cut into two pieces so that one piece is twice as long as the
other. What is the length of each piece?f) Three paddocks were to be fenced. The first paddock needed a 3-strand fence, the second a 5-
strand fence. 9 432m of wire were used altogether. How much wire was used on each paddock?g) $873 was shared between Tinotenda and Takudzwa so that Tinotenda got 3| times as much as
. Takudzwa. How much did each get?h) Divide $869 between Giv6more, Godfrey and Kenneth so that Givemore gets $35 more than
Godfrey and Godfrey gets $15 more than Kenneth.
PROPORTION
Example: An aeroplane flying at 600km/h takes 7 hours to complete a journey. How long would it take to complete the same journey if it travelled at 840km/h?
Method:■ Draw a simple proportion box.» In the top box write the speed 600km/hr.■ Opposite in the box write the time 7hrs.■ In the bottom box write the speed in question 840km/h.■ Opposite the box write a question mark.■ Inside the box with a question mark, answer the question by writing more if the aeroplane is
going to take more time, less if the aeroplane is going to take less time.■ If the time is going to be more, the bigger number goes on top and then multiply by the time
(that is 7hrs).■ If the time is going to be less, the smaller number goes on top and then multiply by the time (7hrs).■ Divide the numbers to get the answer.NB: If the speed increases, the time will decrease.
Working:600km/h 7hrs
840km/h ? [less]
= 6Q0km/h x 7 840km/h x 1
= 60x7 84x1
= 5 x 7 7x1
divide by 10
divide by 12
= 5 hours
The aeroplane will take 5 hours to cover the same journey.
Exercise B
Number Stories
a) 8 men can dig a trench in 48 days. Working at the same rate, how long would it take 12 men to do the same job?
b) Travelling at 120km/h, a car can travel from Harare to Mutare in 3 hours. How long will it take to complete the journey if it travels at 90km/h?
c) A bus travels 540km in 6 hours. How many kilometers will it cover in 4 hours?'d) A car can travel 247km on 19 litres of petrol. How many kilometres will it travel on 13 litres of petrole) Jimmy takes 49 minutes to ride to the shops at 5km/h. How long would he take if he rode at
7km/h ?f) A car travelling at 72km/h covers a distance from a bus stop to a lay-bye in 5 seconds. What is
the distance from the bus stop to the lay-bye?_______ _________________________________
46
UNIT 14
AREAS AND PERIMETERS
A R EA
Area is a measure of surface, it is measured in square units.When calculating areas, all measurements must be in the same units of measurement.
The standard units of measurement are:■ square millimetres = mm2■ square centimetres = cm2■ square metres = m2• square kilometres = km2
Conversions100m2 = 1are10000m2 = hectare100 ares = 1 hectare
Calculating area of a rectangle
Method:• When calculating the area of a rectangle, the formular is length x width• Length is the longer side.• Width is the shorter side.• The opposite sides are equal to either length or the width.• When calculating area, the answer should be written in square units.
Example:
Length 9cm
width4cm
Length of a rectangle = 9cmWidth of the rectangle = 4cm Area of the rectangle = 9cm x 4cm
= 36cm2
NB: The number of rectangles in the shape abdve is 36
CALCULATING THE AREA O F A SQUARE
Area of a square is also side x side.
3cm
3cm
CALCULATING THE AREA OF A TRIANGLE
Method:
■ Formula for finding area of a triangle is ^ base x perpendicular height.
■ The base is the bottom line of the triangle.■ The height is measurement from the bottom line to the top of the triangle. The line should be
90° to the base of the triangle.
Example: Work out the area of a right-angled triangle.
Perpendicular height 5cm
base 10cm
Working:
Area of a triangle
Height - 5cm; Base =10fiii
1= — basex
2
(divide 2 into 10 and you get 5)
(multiply 5cm by 5cm)
10x5cm
2
= 25cm2
40
Exercise ACalculate the area of the shapes below:
a) ______ 13m________
9m
b )
19mc)
d>
19m 12cm
f)
Calculating area of the shaded part
8cm
6cm
29mMethod:■ Calculate the area of the whole shape by■ Calculate the unshaded.part by multiplying 23m x 8m.■ To find area of the shaded part, subtract area of the unshaded part from the area of whole
shape._______________________- _____________________ ____________
49
Working:Area of the whole shape
Area of the unshaded part
Therefore, area of the shaded part
29m x 14m 406m2
23m x 8m 184m2
406m2- 184. i i
222m2
Exercise BCalculate the area of the shaded part:
33m
49m
17m
c) Calculate the area of the path:
\
Exercise C " \Number Stories
1. A workshop measures 27m by 19m. What is the area of the floor?
2. A storeroom measures 17m long, 9m wide and 4m high. There is only one door measuring 1 m by 2m. What is the area of the four walls?
3. A piece of manila sheet measures 78cm by 48cm. A boardermeasuring 5cm is marked inside the edge of the paper. What is the area of the border?
4. A paddock measures 245m by 90m and is fenced. Just outside the paddock is a fireguard 2m wide right round the paddock. What is the area of the fireguard?
PERIMETERSPerimeter is the distance right round an object.
Calculating the perimeter of a rectangle
The formula for calculating perimeter of a rectangle is length + width x 2 Other shapes may requirethat you simply add up all given measurements.
Method:
■ Add length and width.■ Multiply the answer by 2.■ Write your answer using the given units of rneasuj ement
Exercise DCalculate the perimeter of the shapes below:
8cm
14cm
17ma)
19cm 11m
26cm
V51
C)
e) 8lti 2cm 2cm
Exercise E1) The perimeter of a square is 76m. What is the area of the square?Of The perimeter of a rectangle is 138 metres. If the width is 27 metres, what is the area of the
rectangle?3) The length of a rectangle is 2 times the width. If the perimeter is 222 metres, what is the area
of the rectangle?4) The perimeter of a rectangular field is 548m If the field is 3 times as long as it is wide, what is
the area?§)* The perimeter of a rectangular field is 488m. If the width is 92m, what is the length of the field?
V .
52
U N I I 1i>
SPEED, DISTANCE AND TIMESpeed, distance and time are inseparable. To calculate speed, there must be distance travelled and time taken to cover the distance. To calculate distance, speed and time should be given and similarly to calculate time, distance and speed should be given.
A. SPEED
Speed is defined as distance travelled in a given time, usually in an hour or in a second.
Speed is calculated using the formula:
Speed - Distance =(distance divided by time).Time
Example! Calculate the average speed of a car which travelled 420km in 7 hours. .
Method: Divide the distance (420km) by the time (7 hours).Write your answer in kilometres per hour.
Working: Speed = Distance /D \Time T '
= 420km 7 hours
60km/h
Exercise A
Work out the following:
V Calculate the average speed of a bus which travelled 360km in 4 hours.
2- Calculate the average speed of a cyclist who travelled 60km m 4 hours.
3 Calculate the speed of an aeroplane which travelled 3 200km in 4 hours.
4 A bus started a journey from Harare to Chirundu, a distance of 440km at 0630 hours. It completed the journey at 1200 hours. What was its average speed7
A train left Bulawayo at 1600 hours. It arrived in Gweru at 2100 hours.The distance travelled was 275km. What was the average speed of the train?
a A boy ran 100m in 10 seconds. What was his speed in kilometres per hour?
1: A car travelled a distance o f 108km from Murehwa to Marondera in 1 J, hours. What was its average speed7
53
/ b . U l b l A N U t
The formula for calculating distance is speed x time.
Therefore, Distance = Speed x Time
Example: Travelling at 71 km/h, a bus took 2 hours to travel from Mutoko to Harare.What is the distance from Mutoko to Harare?
Method: Multiply speed by time;i.e. 71 km/h x 2 hours = 142km
Exercise B
Work out the following:
1 A lorry travelled at 90km/h and covered a certain distance in 5 hours. What was the distance travelled?
% An aeroplane flying at 100km/h took 7 ^ hours to cover a certain distance. What distance was covered?
3 Cycling at 18km/h, Mr Shava took 3 hours to cover the distance from Kwekwe to Gweru. How long is it from Kwekwe to Gweru?
V
4 Travelling at 40km/h, a tractor took 2± hours to cover a certain distance. How long was the distance it covered?
5 A motorist travelled from Mutare to Kadoma at 80km/h. It took him 5 | hours to complete the journey. How long was the distance he travelled?
C. TIM E
To calculate time divide distance by speed.
Time = Distance = (distance divided by speed)Speed
Example: A motorist travelled from Nyanga to Harare, a distance of 270km at 90km/h.How long did the journey take?
Method: Divide distance by speed;i.e. 270km -f 90km/h
= 270 90
Distance is calculated by multiplying speed and time.
= 3 hours
54
Work out the following problems:
% How long would the journey take if a bus travelled 360km at 90km/h?/ '(2 The distance from Harare to Beitbridge is 580km. How long would the journey take if a motorist
travelled at 1OOkm/h?
(& A cyclist travelled from Rusape to Mutare, a distance of 90km at 40km/h. How long did the journey take?
4, An athlete ran 48km in a marathon competition at 16km/h. How much time did he take to cover the distance?
S' An aeroplane travelling at 900km/h between Frankfurt and Johannesburg covered a distance of 7 200km. How long did the journey take?
cxercise v*
um i 10
A. AN G LES
An angle is a measure of a rotation.An angle is measured in degrees.The sign for degrees is 0.
Types of angles■ A right angle is 90°.
An angle less than 90° is called an acute angle.■ An angle which is more than 90° but less than 180° is called an obtuse angle.
A straight angle is always 180°.■ A reflex angle is more than 180° but less than 360°.* A complete rotation, that is a circle, is 360°.
(i) Right angle (ii) Acute ang!le
90°
(iii) Obtuse angle (iv) Straight angle
90° 90°
(v) Reflex angle (vi) Rotation
90°
c x e r c is e m
Complete the following:
a jS 'i right angle has □ 0
1b)/ An acute angle which is — a right angle has □ °.
7c)/" An acute angle which is — of a right angle has □ °.
92
dy An acute angle which is — of a right angle has □ °.5
e y 270° has □ right angles.
.,fy One complete rotation has □ right angles which gives us □ '
g) Name the angles below:
("O'
A N G LES AND TR IA N G LES
Calculate the angles marked with letters.
Example: Calculate angle q.
Y
/ Metnoa:Line XY is a straight line i.e. 180°.The angle given is 130°.To find angle q, subtract 130° from 180°.The answer is 50°.
Exercise B
Calculate the angles shown as letters below:
(iii) (iv)
\
(v) (Vi)
C A LC U LA TIN G A N G LES ON TR IAN G LES
Every triangle always has 3 angles.The sum of the 3 angles of any triangle is 180°.
58
59
I B. DIRECTION
A compass is used to show direction
The Compass
\
NORTH
NE stands for North East. NW stands for North West. SE stands for South East. SW stands for South West.
Exercise D
Copy and complete the table below. All turns are in a clockwise direction.
FROM TO NO. OF RIGHT ANGLES
NO. OF DEGREES
North SouthEast NorthSouth East North EastSouth North WestWest South East
60
/ UNIT 17
POLYGONS AND SOLID SHAPES
POLYGONS
Shapes with more than two sides are called polygons.
Explanation:A shape with 3 sides is called a triangle.A triangle with 3 equal sides is called an equilateral triangle.A triangle with 2 equal sides is an isosceles triangle.A triangle with no equal sides is called a scalene.
■ A shape with 4 equal sides is called a square.■ A shape with 4 different sides is called a quadrilateral.
A shape with 4 sides but 2 opposite sides being equal is called a rectangle. « A shape with 5 sides is called a pentagon.
A shape with 6 sides is called a hexagon.■ -A shape with 7 sides is called a heptagon.• A shape with 8 sides is called an octagon.■ A shape with 9 sides is}called a nonagon.■ A shape with 10 sides is called a decagon.■ A round shape is called a circle.
Exercise A
Name the shapes below:
a)
c)
b)
d)
f)
61
Parts of a circle
D
a) The line making the boundary of a circle is called the circumference.b) Line AB is the diameter. It divides the circle into two equal halves.c) Line CD is the radius.d) Line AD is the arc.e) Line EF is the chord.f) Point C is the centre of the circle.
62
ounu snapes
Solid shapes have three dimensions that is length, width and height.
Solid shapes or prisms are terms used mostly to mean shapes with three dimensions.
The opposite faces of prisms are equal.
Prisms
Cuboid
The shape below is a rectangular prism or cuboid.
top
Cube
All measurements of a cube are equal All faces are equal in size
' Exercise B
Answer questions below:
A cube has____________faces.A cube has____________edges.It h a s________ vertices.The opposite sides a re ________
Cylinder
A cylinder has It h a s________
____________faces.circular faces and
curved faces.HEINZBAKEDBEANS
circular face
curved face
Sphere
Ball
The ball is spherical in shape
Cone
A cone has . Its base is
vertexin shape.
vertex
base
64
k A C I U IO C V/
Below is a diagram of a round hut. Study it and then answer the questions that follow.
a) What shape is the wall of the hut?b) What shape is the roof of the hut?c) What other shapes can you identify on the building?
Triangular prism
Exercise D
a) The 2 opposite sides of this prism are____________ in shape.b) How many rectangular faces does a triangular prism have?
65
' pyramids
Basically we have two types of pyramids:a) square-based pyramids andb) triangular pyramids.
The square based pyramid
Exercise E
a) The square pyramid has a _________ base.b) It has____________equal triangular faces.c) It has_____________ edges.d) It has i ________ vertices.
The triangular pyramid
Exercise F
a) The triangular prism has a _____b) It h a s______________ edges.c) It has_________ triangular faces.
base.
Unit 18
SAVINGS AND INTEREST
You can save money by opening a savings account at a bank or Building Society.
Below are terms used at a bank:
Deposit: is the money that you put into your bank account.
Withdrawal: is the term used when you take money from your bank account.
Balance: is the money left in your account after a withdrawal.
Deposit form
Study the picture of a deposit form and withdrawal form and then answer the questions that follow.
P.O.t.B. DEPOSIT FORMName of Mr.
S.8.7 CLASS 3
depositor -Mre. ^ , , „ ■ „ .and Mi&s................................................ $ 1.$ *&ddr6ss
.......... M .
... ..........................................'......
Identification particulars....... b3...:..2.S..‘M . s z ...t f . J ?(where applicable)
Account Number
0 * 0
Amount in ■
figures
Amount of depositm
....................... cents
of which $ .............................. U ~ . ................ ....................................(d«tatts of <d*|g3Ntoba:4i*tedover!Mrf)
R a id in g (T Q l \Signature ......................................................................................
........ r l ' f c / . o f c / o j t . ..................................Data
OFFICIAL USE Date stamp and initials
RaeuKant balance
Symbol Code
a) What is the account number?b) How much was deposited in the account?c) On what date was the amount deposited?
67
( Withdrawal Form
PEOPI E’S OW N SAVINGS BANK WITHDRAWAL FORM
| NAMEMRMRSMISS
SB 12CLASS 4
/ 15 I t \ f ML' I C T T f O C \
ACCOUNT No.
(BLOCK LETTERS)
_____ _►ENTITY PARTICULARS 6 l ^ f+ (t7 AMOUN1
I ACKNOWLEDGE RECEIPT OE THE SUM I WISH TO FIGURES I WITHDRAW' BY CHEQUE (MINIMUM SIOO)TO THE UNDER MENTIONED SUM IN FAVOUR O F :_______________________
i n ].-pa H ' 9 ..."ic |g' i. . i.i i i ... o
A-y,
a m o u n t JH c1 (IN WORDS)
dollars
SIGNATURE
cents
UJLt.(T onesigncd in the presence o f the Paying Officer)
I DATE / \ O ci f t , l CHEQUE No.
I AUTHORITY
PAYING O FFIC ER MUST COMPLETE IDENTIFICATION CERTIFICATION (where applicable) ON REVERSE OF FORM
OFFICIAL USE 1) VI! STAMP & INITIALS
IRESULTANT BALANCF.
0WARRANT No.
a) How much was withdrawn from the account?b) On what date was the amount withdrawn?
NB. Withdrawal can be done using an Automated Teller Machine (ATM) card. No form is filled.
Below is a specimen of an A TM card: Pin 0006.To withdraw money, insert the card into the A T M and punch the pin 0006 on the ATM .Follow A T M instructions.
68
I Study the picture of a page in Post Office savings account book and then answer questions y below:
DATE COOE DEMAND2 A3
DEPOSIT0 0 4 3 0
BALANCE OFFICtffv^iNrriAts IDENTITY /" -
*1|
1 18 WoW __ 9COO= ~ n q t/1V_ {
BALANCE BROUGHT FORWARD s \o
2 in g.--- 5*. <------- ( = = -< U < V 2 ^ )'
ic
3(M f (A *a> - ^ © 6 © = " Ih ; > rv)PLP'J5
t-“ v a2 ^
4 •JOG'S CU ■=» M-l<Cf 2. *wnBk.’L£ 1 k J Q )
b(O; ?rt7 l l
I .■___ !
5 to 'ft h ~3-i c\~L "^1i
? V s h »-2Q02 r
6 — S t:—
t
7 •^u)‘ I*—.!• ov * —
• rI
■?/gfe5 ;
\. J J CD ... " ... .— ..................... .... ....... .........
8L ’•V 'V V*~ '
—-
9 O—-v-ri'rrv
1. What was the balance carried forward before the 18/06/02?2. How much money was deposited on the 18/06/02?3. How much money was deposited on the 28/08/02?4. When was the last transaction done?5. Was the last transaction a deposit or a withdrawal?
IN TER EST
Interest is the extra money we get from the bank after depositing money in savings account over a period of time. Interest is calculated using given rate e.g. 8% p.a. (per annum)..
Below are terms used when calculating interest.
Principal : is the amount deposited in a bank account.Rate : the figure usually given as a percentage used when calculating interest.Tim® : is the period from the day the money was deposited in a bank to the date
when interest is calculated.Total Amount: refers to the amount obtained after adding principal and interest.
69
Calculating Interest
Example: Calculate the interest on $15 000 for 1 year at 7% interest per annum. (Per annum means per year.)
Method. Interest Principal x Rate x Time
Working.
Therefore:
PrincipalRateTime
Interest
$15 0007%1 year
$15 000 x 7 x 1 1 x 100 x 1
$ 1 5 0 x7
$1 050
(7% = 7_) 100
Exercise A
Work out the following interest:
a)' $5 000 at 8% p.a for 4 years
o^/ $30 000 at 8% p.a for 5 years
e y $14 2fD0 at 5~% p.a for 3 years
g) $10 0 0 0 a t6 l% p.a for 6 years
i) $48 000 at 3~% p.a for 3^ years
ti}- $25 000 at 5% p.a for 2 years
$18 000 at 5% p.a for years
$60 000 at 7% p.a for 1 a year
$35 000 at 4% p.a for 7 years
j^ $84 000 at 8 ^% p.a for 9 years
Calculating the total amount
Example: Calculate the total amount on $3 500 for 3 years at 6% interest p.a.
Method:
Working:
Therefore:
Calculate the interest first.Add interest to principal get the total amount.
PrincipalRateTimeInterest
$3 5006%3 years$3 500 x 6 x 3
1 x 100 x 1 $630
Total Amount Principal + Interest $3 500 + $630 $4 130
70
Calculate the total amount on:
a) $13 000 in 1 i years at p.a. for 8% b) $27 000 in 5 years at p.a. for 9%
c) $46 000 in 2 l years at pa . for 6% d) $7 800 in 9 years at p.a. for 7%
e) $14 200 in years at p.a. for 6% f) $60 000 in 8 years at p.a. for 42 % 4
g) $10 000 in 6 years at p.a. for 7% h) $35 000 in 4 yearS at p.a. for 11%
i) $48 000 in 5 years at p.a. for 15% j) $84 000 in 3 years at p.a. for 9%
Calculating time
Example: Calculate the number of years in which a principal of $24 000 will grow to $28 500
at 3 |% interest per annum.
Method: Calculate total interest by subtracting principal from amount.Calculate interest per annum on the principal.To find time, divide total interest by interest per annum.
Working: Total Amount = $28 500 Principal = - $24 000 Total Interest = $ 4 500
Interest per annum on $24 000 at 3 |%
24 000x 15 x 11 x 400 x 1
$900
Therefore, the number of years = $ 4 500 (4 500 divided by 900)$ 900
= 5 years
Exercise C
In how many years will:
a) $ 8 000 grow to $9 400 at 3 |% p.a? b) $ 30 000 grow to $33 150 at 3^% p.a?
c) $ 10 000 grow to $11 800 at 4% p.a? d) $ 35 000 grow to $41 300 at 4% p.a?
e) $15 000 grow to $15 9,00 at 6% p.a?. f) $ 5 000 grow to $9 900 at 7% p.a?
g) $ 32 000 grow to $38 400 at 5% p.a? h). $ 10 000 grow to $16 300 at 6% p.a?
i) $ 10 000 grow to $20 000 at 5% p.a? j) $ 70 000 grow to $75 600 at 8% p.a?
71
VOLUME, CAPACITY AND MASS
Volume: is a measurement of space that an object takes up. is measured in cubic units.
Capacity: is usually used to refer to how much a container can hold.
Mass: the amount of matter a body contains. This is called weight in non-technical terms.
Below are standard units of measurement:
Volume and Capacity
1000 millilitres = 1 litre1 millilitre = 1 cubic centimetre1000 cubic centimetres = 1 litre1000 litres = 1 cubic metre1 000 000 cubic centimetres = 1 cubic metre
Cubic centimetres is written in short as cm3.Cubic metres is written in short as m3.A small 3 is written to show that three dimensions have been used in the calculation.
V
The standard units for measuring mass are grams, kilograms and tonnes.
1000 grams = 1 kilogram1000 kilograms = 1 tonne
Volume
The formula for finding the volume of a rectangular prism is length x width x height. The answer is written in cubic units.
Changing millilitres to litres and litres to millilitres
Example: 2 150ml = 2,1501
Method:To change millilitres to litres, divide 2 150ml by 1 000 because there are 1 000ml in 1 litre.N.B. There should be three numbers to the right of the decimal comma.
To change litres to millilitres multiply by 1 000.N.B. The decimal comma will move three places to the right.
72
1. Write in millilitres:a) 4,350/ b) 6, 725/ c) 9,050/ d) 1, 975/
e) 5,125/ f) 2,645/ g) 8,100/ h) 0,550/
1/ , 1.4 53 4
i) 3,002/ j) 0.087/ k) - / I ) - /
2. Write the numbers below in litres.a) 250ml b) 47ml c) 4 215ml d) 3 270ml
e) 9ml f) — m3 g) ^ m 3 h) -^-m35 4 10
.. 1 „ 3 3i) - m 3 j) — m32 5
Exercise B
Work out the problems below:1. A bottle of medicine holds 225ml. How many 5ml can be measured from the bottle?2. A concrete block measures 0,75m x 0,23m x 10cm. What is its volume?3. Calculate the volume of the shape below:
4. If 3m3 of soil weigh 1 tonne, what is the weight of soil removed from a rectangular pit measuring 14m by 10m by 6m?
5. The area of the base of a swimming pool is 875m2. What is its capacity if its height is 3 metres?
6. A lorry trailer measuring 17m long by 2m wide by 0,5m high carried a full load of pit sand. How many cubic metres of pit sand did it carry?
MASS
Changing grams to kilograms and kilograms to grams.
Exercise C
Change these grams to kilograms.a) 3 912g b) 7 048g c) 8 685g d) 352g
73
• / ~ o
i) 43g j) 115g k) 27 641 g I) 43 042g
Change kilograms to grams.
a) 5,641kg b) 1,329kg c) 0,486kg d) 4,927kg
e) 0,038kg f) 0,006kg
4j)
10
Exercise D
Number Stories.
1. A lorry had a mass of 29,255t after carrying bags of maize. The bags had a mass of 15,625t. What was the mass of the empty lorry?
2. The gross mass of a tin of baked beans is 925g. The mass of the (empty tin is 45g. What is the net mass of beans?
3. How many 50kg bags of cement can be carried in a 30-tonne truck?4. Two railway wagons were loaded with coal weighing 48,575t and 43,798t respectively. What
was their difference in weight?5. How many 250gram packets can be packed from 25kg of flour?6. The mass of a loaded lorry was 76 tonnes. The load had a mass of 40 tonnes. What was the
mass oHhe lorry?
74
I U I 1 I I C - \J
• Time can be written using either the 12-hour clock system or the 24-hour clock system.• The 12-hour clock is characterised by the use of am, (ante-meridian) meaning morning and
pm (post-meridian) meaning afternoon.The 24 hour clock system is characterised by thea) use of four figuresb) continuation of hour reading after 12 noon right up to 24.
The standard units of time
1 minute = 60 seconds1 hour = 60 minutes24 hours = 1 day7 days = 1 week28/29/30/31 days = 1 month12 months . 1 year365 days = 1 year366 days = 1 leap year
The 12-hour clock system
The longer hand of a clock is called the minute hand. The shorter one is the hour hand.
Below is a clock face with hands.
The minute hand will go round the clock once in 60 minutes for the hour hand to move from one Dur to another.
75
O’Clock
25 minutes to 25 minutes past
Half past
Exercise A
What is the time shown on the clock faces below?
a) b) c) d)
76
How many hours and minutes are there between:
6:17 am to 2.19 pm b) 4.47 am to 5.39 pm11,05am to 8.51 pm d) 10.43am to 3.27 pm1.03 pm to 11.26 pm f) 2.48 pm to 10.57 pm8.44 am to 10.37 pm h) 11.29 am to 8.49 pm5.25pm to 7.15 am the next day i) 10.33 pm to 5.45 am the next day
The Digital Watch System
The digital watch system is characterised by minutes, which are recorded continuously up to the next hour.Minutes are recorded from 1 to 59. The next minute after 59 will change the present hour to the next since there are 60 minutes in one hour.
Below is a diagram to show the digital watch system.
The time shown above is 11:23:05 or 23 minutes and 05 seconds past 11.
Exercise CWrite the times below in short using the digital watch system.
a) 5 minutes past 7 am b) 26 minutes past 3 pmc) 19 minutes past 3 pm d) 11 minutes past 1 pme) 10 minutes to 6 am f) 25 minutes to 10 amg) 3 minutes to 11 pm h) 20 minutes to 8 pm') 13 minutes to 2 am j) 29 minutes to 9 am
The 24-hour clock system or International Notation.
• In the 24-hour clock system, time is expressed in hours and minutes.Four digits are used when writing time.
• N.B: There is continuity when writing hours i.e. 1,00pm in the 24 hour clQck system will be 1300 hours.
• In the 24-hour clock notation, am or pm is not used.• The reading of time is always in hours.
• Example: 5.00 am is 0500 hours and is read as zero 5 zero zero hours.
5.00 pm is 1700 hours, read as 17 hours (or 17 hundred hours).5.07 pm is 1707 hours read as seventeen zero seven hours.
77
Write the time in 24 hours clock notation.
a) am b) c) d)
Exercise E
Complete the table below:
12-hour clock 24-hour clock notation3.16 am 0316 hours (Example)5.29 am8.56 am
0941 hours7.33 am4.22 pm 1622 hours1.19 pm8.47 pm10.31 pm
2353 hours12.03 am
TIMETABLES
Exercise F
Study the bus timetable below and then answer questions based on it.
Harare Departure 0645Banket . Arrival 0730
Departure 0735Chinhoyi Arrival 0850
Departure 0910Karoi Arrival 1005
Departure 1025Chirundu Arrival 1145
a) At what time does the bus arrive in Banket?
c) At what time does the bus leave Karoi?d) What is the total stopping time?e) What is the actual travelling time?
Exercise G
Below is a distance table. Study it and then answer some questions that follow:
MACHEKE
33 MARONDERA78 47 CHITUNGWIZA
107 73 25 HARARE
59 89 112 87
a) What is the distance from Harare to Macheke?b) What is the distance from Harare to Mrewa?c) What is the distance from Harare to Macheke via Mrewa?d) What is the difference in distance between travelling from Harare to Macheke by direct route
and from Harare to Macheke via Mrewa?
79
A graph shows the relationship between two members of a set.
Types of Graphs
• A pie graph or pie chart is often used to show proportions of various quantities rather than the quantities themselves.
• A pictograph or an iso-type graph uses a picture to record information.• A line graph is a diagram consisting of a line or lines, straight or curved, showing the variation
of two quantities.
Pie ChartA pie chart shows fractions of the whole.
Exercise A
Study the pie chart showing the sporting activities done at Boys High School with 960 pupils and then answer the questions below:
1. How many boys enjoy playing soccer in the school?2. How many boys enjoy playing basketball in the school?3. How many boys play tennis in the school?4. What is the difference between the boys who play soccer and those who do not?
Bar Graph or Column Graph
Exercise B
Study the column graph showing the levies collected at Kandava Primary School during the second week of the term and the questions below it.
25 000
M T W T P
2. On which day was the least amount collected?3. How much was collected on Tuesday?4. What is the difference between the amount collected on Wednesday and that collected on
Friday?5. What is the average daily collection for the week?
The Line Graphs
Exercise C
The graph below describes a journey by a motorist. Study the graph and then answer questions.
Time
(i) What distance was covered in 1 hour?(ii) The motorist rested after travelling how many kilometres?(iii) How much time did-the motorist spend resting?(iv) How many hours did the whole journey take?(v) What was the actual travelling time?
Exercise DThe jagged line graph below shows the number of patients who went to Harare Central Hospital one Friday. Study the graph and then answer questions below it.
ca>aja
o2
(i) How many patients went to Harare Central Hospital between 6am and 8.00am?
(ii) What time recorded the highest number of patients?
(iii) At what time were fewer patients attended?
(iv) What do you think might have caused a sharp rise of patients being attended to at the hospital between 6pm and 8pm?
81
Paper 1Time: 2 hours
Instructions to Candidates:
1. Read all instructions carefully.
2. Choose one correct answer from the suggested answers
3. Answer all questions.
82
Answer all questions.
Time: 2 hours
1. What is the value of digit 9 in 792 131 ?A. ten thousand B. thousand C. hundred D. tens
2. Calculate the sum of $263,49; $532,05 and $7,55.A. $803,09 B. $783,09 C. $792,99 D. $903,t9
873. Write — as a mixed number.9
A- 89 B 8| c 9| D' 9§
44. The total marks in an English test are 100. Takudzwa got — of the total marks. How many
marks did he get? 5A. 65 B. 80 C. 70 D. 90
5. Mr Mhlanga and Mr Chara bought new cars in January. In March the odometer for Mr Mhlanga read 7 403,7km and that of Mr Chara read 6 816,9km. What is the difference in the distance travelled?A. 497,9km B. 585,7km C. 413,2km D. 586,8km
6. Use >; =; < to compare the fractions 8| I I 8,75.A. >v B. < C. = D. not equal
7. Round off 157 064 to the nearest ten thousand.A. 160 000 B. 157 070 C. 157 000 D. 158 000
8 7i + 1§ - □A.8f2 B.8* c.9| D.8|
9. The average mass of 4 bags of rice is 88kg. If three of the bags weigh 89kg, 82kg and 91 kg, what is the mass of the fourth bag?A.87kg B. 90kg C. 89kg . D. 93kg
10. Fill in the missing number. 0,500 0,625 t I 0,875.A. 0,125 B. 0,750 C. 0,725 D. 0,650
11. 67,121 +24,33 + 8 =A. 99,451 B. 69,562 C. 99,154 D. 70,354
12. 65% of the children in a school can speak English fluently. If 663 children can speak fluently, how many children are in the school?A. 993 B. 650 C. 1020 D. 728
13. 0,096 x 100 = Q A. 0,0096 B. 9,6 C. 0,960 D. 96,00
83
15. 6 men can mould twenty thousand bricks in 30 days. How many men would be needed to mould the bricks in 20 days?A. 4 B. 8 C. 12 D. 9
16. Find the 30, .45 and 20.A. 160 B. 120
17. Calculate the volume of the triangular prism.
C. 180 D. 5
C. 108cm3 D. 108cm2
0 <J ' I' I18. (100 000 x 4) + (10 000 x 7) + (10 000 x 9) + (1 000 x 3) + (100 x 0) + (10 x 5) + (1 x 2) =
A. 4*>93 052 * B. 497 352 C. 479 352 D. 470 352
19. A rectangular tank holds 432m3 of water; its base measures 12m by 6m. How deep is the tank?A. 5m B. 6m C. 4,32m D. 72m
20. Mr Shava travelled in his car from Harare to Nyazura a distance of 195km. He travelled at 75km/h. How many hours did the journey take?A. 3hrs B. 2hrs 20 min C. 2hrs 45min D. 2hrs 36min
21. 683 + 454 A. 44 B. 37 C .1137 D. 625
22. Calculate the interest on $24 000 for 6 months at 7 ^% interest per annum.
A. $1 680 B. $900 C. $400 D. $1 960
23. Mrs Munaiwa’s mass is 72kg. Mr Munaiwa’s mass is 9kg more than Mrs Munaiwa’s mass. What is the ratio of Mrs Munaiwa’a mass to Mr Munaiwa’a mass?A 9:8 B. 7:6 C. 4:3 D. 8:9
24. How many degrees is the part removed from the circle?
A. 45° B. 60° C. 30° D. 35°
25. Tendai bought a.camera for $25 440. He sold it for $31 800. What percent profit did he make? A. 20% B. 25% C. 15% ' D. 10%
26 4§ - 2§ = □
A .2Z B .2 1 C .1 § D .1 ;Z
27. A sheet of paper measures 30cm by 20cm. It is cut into pieces measuring 4cm by 3cm. How many pieces can be cut?A. 50 B. 30 C. 60 D. 12
28. Calculate the area of the shaded part.
A. 437m2 B. 75m2 C. 512m2 D. 362m2
29. 15,375 -f 1,25 to two places of decimal isA. 22,22. B. 12,22. C. 22,32. D. 12,3.
30. Write 2105hrs in 12-hour clock notation.A. 21.05pm B. 9.05pm C. 10.05pm D. 9.55pm
431. A school received a grant of $84 000 from the government. — of the money was used to
purchase stationery. How much was used to purchase stationery?A. $48 000 B. $12 000 C. $36 000 D. $64 000
32. What is the value of four $500 notes, two $100 notes, seven $10 notes and six $2,00 coins? A. $612.00 B. $2 282 C. $776 D. $4 272
33. Calculate 70% of 29,480/.A. 2948/ B. 20,628/ C. 18,846/ D. 20,636/
( 34. There were 185 spoons in each box. How many spoons were in 37 boxes?A. 5550 B. 6935 C. 6845 D. 6937
35. Write 4§ as an improper fraction.
A. — B. — C . “ D. —9 9 9 9
36. A bus left Harare at 8.30am and arrived at Beitbridge boarder post at five minutes past four in the afternoon. How long did the journey take?
A. 8 ^ hrs B. 7 l hrs C. 4 | hrs D. 7 hrs 35min
37. A rectangular plot is twice as long as it is wide. If the width is 70m, what is the area? A. 440m2 B. 9800m2 C. 140m2 D. 420m2
38. Find the cost of painting a wall of a room 26m by 18m at $40 per square metre.A. $18 720 B. $1 040 C. $720 D. $468
39. Share $783 between Farai and Roy in the ratio of 4:5. What is Roy’s share?A .$720
40. 6 1 * 3 1
A. 21
B .$435
B. 3 i
41. Write — as a decimal fractions. 40
A. 3,40 B. 0,075
C. $391,50
C. 0,340
D. $368
D .11
D. 4,30
42. Write three million four hundred and sixty seven thousand and twenty-one in number'symbols. A. 3 476 210 B. 3 467 201 C. 3 467 021 D. 346 721
43. Seven ninths of a pole is above the ground. If 4,9m is above the ground, what is the whole length of the pole?A. 4,5m B. 6,3m C. 4,9m
44. The graph below shows Mr Kaunza’s daily sales.
7 000
D. 7,2m
| 4 000
Q 4 000
Which day had the highest sales?A. Monday. B. Saturday. C. Friday. D. Thursday.
45. A bursar at a secondary sphool got a 15% increase in salary. He now earns $23 000. How much money did he earn before the increase?A. $20 000 B. $24 000 C. $25 500 D. 26 450
46. Calculate 5,25% of $9 600.A. $9 904 B. $48 000 C. $504
47. How many lines of symmetry does the shape have?
D .$625
C. 2 D. 4
48. Bernard got 18 marks in a Maths test. He wrote another Maths test and got 2 ^ times more marks. How many marks did he get in the second test?A. 36 B. 27 C. 22 D. 45
49. The difference between — of a number and — of it is 27. What is the number?8 11
A. 270
50.(13 + 2 l ) x f = Q
B. 792
B. 2\O
C. 88
C .1 1
D. 781
D. 2;
Answer all questions.
Time: 2 hours
1. Six million four hundred thousand and forty can be written asA, 640040. B. 6 400 040. C. 60 400 40. D. 6 000 000 440.
2. In 4 568 the value of the 4 is A. 1 000. B.B. 40. C. 4000. D. 40 000.
3. — as a mixed number is 3
' ■ f D. 8§.
4. 3,4034 rounded off to 2 decimal places isA. 3,44. B. 3,40. C. 3,040. D. 3,41.
5. The other way of writing 3,675 tonnes isA. 3 000kg +600kg + 70kg + 15kg.B. 3 OOOt + 670kg + 50kg + 5kg.C. 3 000kg + 600kg + 70kg + 5kg.D. 3 000kg + 600kg + 7kg + 5kg.
6. In the 24-hour notation 12.02 am isA. 1202hfs. B. 1402hrs. C. 0002hrs. D. 0200hrs.
7. I have 1 x $5 note, 2 x $2 notes, 3 x $1 coins, 2 x 20c coins. How much money do I have inall?A. $8,20 B. $12,40 C. $9,40 D. $10,40
8. In 3,769 the value of 7 isA. tens. B. hundreds. C. tenths. D. units.
9. What fraction of an hour is 42 minutes?
A . - B. — C. — D. —4 30 10 10
10. The area of the shape below is 48cm2. What is its height?
10cm12cm B. 8cm C. 21,237cm D. 29,237cm
88
11. 7 + 21,367 + 0,07 + 0,8 A. 2778. B. 292,32. C. 21,237. D. 29,237.
12. If mangoes are sold at 20c for 3, how much will 12 mangoes cost?A. $3,00 B. $0,90 C. $0,80 D. $2,40
13. I gave the shopkeeper 2 x $20 notes for purchasing three items costing $17,20; $12 and $6.40. My change wasA. $4,40. B. $4,25. C. $2,25. D. $2,00.
14. " '
The figure shown is aA. cuboid. B. cylinder. C. pyramid. D. prism.
15. 6 men take 2 days to paint a house. How long would 2 men take to do the same job?A. 2 days B. 4 days C. 6 days D. 10 days
16. The volume of a cube whose sides are 5cm long isA. 25cm3. B. 50cm3. C. 100cm3. D. 125cm3.
17. How many hours and minutes are there from 8.20am to 11.10pm?A. 2 hrs 50mins B. 3hrs 50mins C. 14hrs50mins D. 7hrs 52mins
18. Chipo is facing South-East of the school. She turns to face West in a clockwise direction. Through how many degrees has she turned?A. 135° B. 105° C. 90° D. 45°
19. The number of bottles holding 750ml which can be filled from a container holding 18 litres are A. 24. B. 40. C. 18. D. 30.
20. The length of line AB in the diagram below isA. 18cm. B. 13cm. C. 15cm. D. 7cm.
1cm
13cm
21. 3 6 -5 0 + 24 = A. 36.
B
2cm
5cm
B. 110. C. 24. D. 10.
22. — of a number is 36. Therefore, the number is4
A. 18. B. 27. C. 48. D. 28.
23. What is the mass of the tin when the gross mass is 950g and the net mass is 827g? A. 27g B. 123g C. 230g D. 1777g
24. How many 50-cent pieces can be got from $17,50?A. 30 B. 35 C. 1750 D. 25
25. A man bought a shirt at a wholesale for $60 and later sold it for $69. His percentage profit was A. 15%. B. 13%. C. 87%. D. 115%.
26. The average of 5 tests is 50 and four of the marks are as follows: 38; 49; 68 and 41. The fifth value isA. 46. B. 48. C. 50. D. 54.
27. 13 books cost $52,00. What would I pay for 52 books?A. $20,08 B. $310 C. $180 D. $208
28. The value of three $10 notes, two five dollar notes and five 5c coins isA. $30,25. B. $35,25. C. $40,25. D. $40,00.
29. How many degrees is right angles?A. 190° B. 135° C. 75° D. 180°
30. The area of a square piece of land is 144m2. Its perimeter isA. 48m. B. 40m. C. 100m. D. 60m.
31. Bako School starts at 0745 hours. Peter was 23 minutes late. He arrived atA. 0808hrs. B. 0818hrs. C. 0708hrs. 1 D. 0722hrs.
32. A box which measures 7cm long, 5cm wide and 2cm deep has a volume ofA. 14cm3. B. 70cm3. C. 10cm3. D. 24cm3.
33. A helicopter flew from Harare to Botswana at a speed of 715km/h and it took 3 hours, From Harare to Botswana it isA. 715km. B. 2 055km. C. 795km. D. 2 145km.
34. What is the H.C.F of 30, 36 and 72?A. 2 B. 4 C. 6 D. 9
35. Divide the sum of 4 | and 2 jo by their difference.
A. 30 B. 3 C. 3jq D. 7 |
36. This triangle has............................lines of symmetry.A. 1 B. 2 C. 3 D. 4
10cm
37. If the product of 259 and 29 is 7 511, then the product of 2,59 and 2,9 isA. 75,11. B. 751,1. C. 7,511. D. 7511.
2 5 3
39. $520 is shared among the pupils X, Y, 2 in the ratio 3:4:6 respectively. What is Y’s share?A. $120 B .$135 C. $160 D .$260
40. 0.007kg in grammes isA. 7g. B. 70g. C. 700g. D. 0.7g.
41. Which year is not a leap year?A . 1844 B. 1972 C. 2000 D. 1975
42. Tatambura had $65 in his bank account. He made a withdrawal of $25 and then a deposit of $10. What was his new balance?A. $40 B. $50 C. $75 D. $90
Use the pie chart to answer questions 43 and 44. It shows the proportion of different books in a library.
43. There are 730 books in the library altogether. How many are Maths books?A. 146 B. 219 C. 292 D. 365
44. The proportion of Shona books to Science books to Maths books i$A. 2:3:1. B. 1:3:2. C. 3:2:1. D. f-:-2^3r
45. — as a decimal fraction is 8A. 0,75. B. 0,87. C. 0,625. D. 0,875.
1 1 346. A man spends — of his salary on rent, — on food and — on clothes. The rest he saves.8 i 4 8
Calculate his salary if he saves $50 monthly.A. $200 B. $300 C. $100 D. $760
47. What number is 30 less than 100?A. 130 B. 120 C. 70 D. 150
48. A car travelling from Kariba to Chiredzi took 8 hours. The distance covered was 864km. Its average speed for the whole journey wasA. 108km/h. ,B. 80km/h. C. 108km. D. 80km.
49. Rufaro ran 500m in 5 minutes. What was her speed in km/h?A. 56km/h B. 36km/h C. 2500km/h D. 6km/h
50. XCIX written in Arabic numerals isA.110. B. 109. C. 99. D. 19.
Answer all questions.
Time: 2 hours
1. One way of writing 376 isA. 3 + 76. B. 3 + 70. C. 3 + 70 + 6.
2. Two thousand and two isA. 2 200. B. 2 020. C. 2 002.
243. Write — in the lowest terms.
363 n 2 4
A. - B. - C. -2 3 9
4. 5 | has the same value as
A . H . B. — . C * .20 4 4
5. 0.65 as a common fraction is. 13 6 _ 3A. — . B. — . C.
20 10 7
6. 915 cents in dollars and cents isA. $91,50. B. $91,05. C. $915.
7. A is the centre of the circle. What fraction of the circle is not shaded?
8. A line hasA. volume. B. mass. C. area.
D. 300 + 70 + 6.
D. 20 002.
7D. — .
20
D. $9,15.
D. —10
D. length.
D. equilateral
92
A. $9025,25. B. $3425. C. $34,25. D. $54,00.
11. In the 24-hour notation 15 minutes past 12 midnight isA. 1215hrs. B. 0015hrs. C. 2415hrs. D. 1512hrs.
12. The sum of 4 hundreds, 3 tens and 9 units isA. 16. B. 124. C. 4,39. D. 439.
13. Idah sent a telegram which cost 24c a word. The cost of a telegram of 13 words was A. $,037. B. $3,12. C. $3,70. ' D. $31,20.
14. What is the area of the given triangle?
A. 18cm2 B. 27cm2 C. 13,5cm2 D. 9cm2
15. A big carton measuring 36cm x 12cm x 10cm contains small boxes 5cm x 6cm x 9cm. How many, boxes are in the big carton?A. 16 B. 27 C. 30 D. 270
16. The volume of a cube is 125cm3. One side is 5cm long. What is the area of one face?A. 50,cm2 B. 15cm2 C. 25cm2 D. 125cm2
17. The net mass of a tin of jam was 0.05kg. The jam had a mass of 1,5kg. What was the gross mass?A. 1,55kg B. 2,0kg C. 1,45kg D. 1,0kg
18. How much time is there from 0830 hrs to 1415hrs?A. 6 hours 45mins B. 5 hours 45mins C. 6 hours 25mins D. 5 hours 15mins
19. Adonis banked $300 for a period of 2 ^ years. The interest he got at 3% p.a. wasA. $22,50. B. $45,00. C. $225. D. $4,50.
20. Agnes is 40 years old. Farai is 18 years old and Bianca is 14 years. Their average age is A. 16. B. 24. C. 27. D. 18.
21. The diagram shows the timetable for a bus from Gweru to Gutu.
Gweru Departure 1000Mvuma Arrival 1045
Departure 1110Chartsworth Arrival 1158
Departure 1221Gutu Arrival 1410
What is the total time taken for the whole journey?A. 7 hrs 50 mins B. 3 hrs 10 mins C. 2 hrs 50 mins D. 4 hrs 10 mins
93
94
A. 6cm
33. 342,1 x 10 = | |. A. 342,1
B. 7cm C. 3cm D. 21cm
B. 3 421 C. 3,421 D. 34,26
34. Tawanda’s pace is — of a metre. He takes 20 paces to cross a road. How wide is the road? A. 5m 4 B. 500m C. 50m D. 0.5m
35. Find 0.1 of 30.A. 0,30 B. 3 C. 0,03 D. 30
36. What is the H.C.F of 36; 54; 81?A. 12 B. 9 C. 6 D. 3
37. When a number is shared in the ratio of 3:5, the smaller number is 36. What is the larger number?A. 60 B. 36 C. 21 D. 96
38. 9 000 plus 4 540 minus 4 460 isA. 4-460. B. 9 048 C. tS-G©& D. 13 460.
39. Mrs Dube bought 3kg'of sugar and got 25c change from $4,60. What was the price per kg?A. $1,45 B. $2,30 • C. $1,54 D. $1,64
40. A car uses 1 litre of petrol to travel 9 kilometers. How many litres of petrol does it use to travel279 km? A. 30 B. 9 C. 27 D. 31
42. How many A. 575
5ml spoons of cough mixture can be taken from a 115ml bottle?B. 23 C. 0,23 D. 5,75
43. What percentage does Tariro put aside for accounts?
A. 20% B. 85% C. 80% D. 60%
45. The perimeter of a square room is 24m. A. 48m2 B. 36m2
A. 5kgB. 4,5kgC. 4kgD. 9kg
What is the area of the room?C. 24m2 D. 96m2
46. How many faces does this shape have?
47. How many weeks are in 175 days?A. 27 B. 25 C. 5 D. 7
48. A delivery van makes 4 return journeys everyday between two places which are 9,35km from each other. What distance does it cover each day?A. 74,8Km B. 37,4km C. 18,7km D. 65,45km
Use the graph to answer questions 49 and 50.
soccer netball swimming volley ball
49. How many children choose swimming as their favourite sport?A. 3 B. 4 C. 5 D. 6
50. How many more children like soccer than volleyball?A. 2 B. 3 C. 7 D. 5
96
1
Answer all questions.
Time: 2 hours
1. 6 + 17 + 3 =A. 27. B. 36. C. 26. D. 16.
2. 6 - 4 2 + 70 =
A. 106. B. 36. C. 22. D. 34.
3. 23 x 7 =A. 91. B. 106. C. 81. D. 161.
4. How many weeks are there in 630 days?A. 12 B. 80 C. 45 D. 90
5. 3 - 0,255 =
A. 1,542. B. 2,745. C. 0,355. D. 2,521.
6. 2,4 x 0,7 =
A. 168. B. 16,8. C. 44. D. 1,68.
7. 0,125 of 88 peaches is
A. 0,22. B. 11. C. 22. D. 44.V
8. Write $1,20 as a decimal fraction of $4,80.A. 0,25 B. 0,125 C. 0,5 D. 0,05
a 8 39. - x - =9 4
A. 11. B.11. C. 1. D. §.
10. The H.C.F. of 21 and 49 isA. 3. B. 9. C. 7. D. 21.
11-21 + 1| =
A. 3 B. C. 312. D. 3 ^ .
12. 50 oranges at 5 for 10 cents costA. $4,00. B. $3,00. O r ^ t e D. 25,00.
13. Calculate time between 7.00 am and 10.30pm‘.A. 17,30 B. 3,30 C. 15,30 D. 12,30
14. Share 144 marbles in the ratio of 5:7. The larger share isA. 12. B. 84. C. 96. D. 60.
15. 4 2 x 3 = 4 0 x 2 + .. . .A. 40. B. 42. C. 33. D. 46.
97
A. 2 B. 12 C. 6 D. 9
317. — of my money is $96. How much money do I have?
4A .$128 B .$100 C. 72 D. 99
i s . ®6 8 '— '
A. 31 B.11 C. 11 D. I
19. The volume of a cuboid 10cm long by 8cm wide and 2cm thick isA. 140cm3. B. 160cm3. C. 80cm3. D. 160cm.
20. The area of a square piece of land is 64cm2. The side of the ground isA. 4m. B. 5m. C. 16m. D. 8m.
21. The difference between 7 842 and 4 941 isA. 2 901. B. 96. C. 2 881. D. 3 564.
22. 2 & - 1 J . Q
A 1 r2 c 3 i23. The area of a triangle where the base is 31cm and the height is 12cm is
A. 186ft'm2. B. 43cm2. ' C. 186cm. D. 2 1 ^ cm2.
24. Express as a common fraction in the lowest terms 8^% .
. 8 _ 9 33 1A. ----- B. ----- C. ----- D.400 400 400 2
3-25. Express — as a decimal.
5B. 0,6 C. 0,15 D. 0,56
Angle ABC isA. 100°. B. 45°. C. 90°. D. 75°.
27. 4 | kg of flour is the same as
A. 4,125kg. B. 4,750kg. C. 4,250kg. D. 4,500kg.
28. Write 1 225 to the nearest thousand.A. 100 B. 1 200 C. 1 220 D. 2 000
98
29.
30.
Write 2245 hours of the day as 12-hour time.A. 10:45 B. 10:45 am C. 45:10 D. 10:45 pm
8 men can build a wall in 24 days. How many mete men are needed to build the wall in 32 days?A. 9 B. 3 C. 6
31. How many cent stamps can I buy with $3,50?
A. 140 B. 200 C. 60
32. A jersey ball costs $700. The cost of 12 such balls is A. $7 200. B. $712. C.$8 600.
33. The least number into which both 16 and 18 can divide is
34.
35.
36.
37.
38.
39.
40.
41.
42.
43.
44.
A. 36.
32,76 t 3,6
A. 91
B. 144.
B. 0,091
Find the product of 145 and 5.A .150 B. 725
The number ten million and ten is A. 10 000 001. B. 10 000 010.
Which one of these is a prime number? A. 48 B. 17
C. 120.
C. 0,91
C. 29
C. 10 000 10.
C. 39
How many days were there in January, February and March 19809 A. 92 B. 89 C 90
A. 3* B.2 C.21
D. 10
D 322
D. $$ 400.
D. 288.
D 9,1
D. 275
D. 10 000 100
D. 33
D. 91
D. 560
The average of three numbers is 40. if one of them is 50 and the other is 45, what is the third? A. 35 B. 25 C 45 D. 55
Find the perimeter of a rectangular paddock 300m long by 250m wide A. 1100m B. 550m C. 75 000 D .7 500
A concert started at 9.00am and ended at 7.00pm. There was an hour break in between. How long did the concert activities take?A. 9 hours B. 10 hours C. 8 hours
The distance around a regular octagon of sides 20cm is A. 80cm. B. 160cm. C. 120cm.
D. 7 hours
D. 140cm.
5 , 1 .— of — IS6 3
A . — . B . l C. 10.18 2
D .2±.
99
45. The simple interest on $500 at 5% for 2 years isA. $100. 6. $80. C. $50. D. $4.
46. A storekeeper bought 12 pairs of shoes for $60;00 and sold them for $70,00 each What % profit did he make?A. 10% B. 40% C. 30% D 20%
47. The cost of tiling a floor 8m long and 5m wide at $3 per rn isA. $120. B. $40. G $24 D. $50.
48. A lorry can carry 4 500kg. How many pockets of potatoes each 15kg can it carry?A. 3 B. 300 C. 30 D.25
49. If you share $11,06 between Peter and John so thft John gets 38 cents moasnhan Peter, John getsA. $5,61. B. $5,72. C.$5,77. D. $5,34.
50. Area of the wall below isA. 35m2. B 28m2. C. 46m2. D. 8m2.
4m
7m
too
Answer all questions. Time: 2 hours
1.
HTh Th H U —
The number shown isA. 40 153,623. B. 40 135,632.
2. 9° plus 33 is A. 15 B. 28.
110 100 1000
C. 40 153,263.
C. 10.
D. 40 153,362.
D. 36.
3. — as a decimal fraction is 25A. 0 16. B 0,04-
4. 5,067 to the nearest tenth is A. 5,11. B. 5,07.
-2 0 + 1 6 = 0 .5. 11A. 31 B. 36
C. 2,54.
C. 5,6.
C. 25
6. Arrange the following fractions in descending order.
2 7_ 33 12 4
5 . 5 — and —6 8
A.5. 3. 2. 5. 5_ i . j _ i T"« M6 4 3 8 6
■■7 5 5 3 2 12' 8 ' 6 ' 4 ' 3
7. 506 cents in dollars is A. $506,00.
1
D 3 2 5 5 7 B. - r ; —
4 3 6 8 12
ri 2 . 3. 5 . 5 . _7 * 3 : 4 ’ 6 ’ 8 ’ 12
B $5 06.
8. — past 12 midnight in 24 hour notation is 4A. 0015. B. 1215.
C. $5,60.
C. 2215.
D. 4,25.
D. 5,1.
D. 7
D. 50,06.
D. 0124.
101
9. If there are 800 pupils in a school and | are boys, how many girls are there?A. 500 B. 300 C. 450 D. 580
10. 51 +11 - Q
A. I 2
B.21 c 4 io D .4 l
11 A piece of string 3,60 metres was cut into three pieces in the ratio 1:2:3. The length of the largest piece wasA. 1,6cm. B. 1,8m. C. 1,9m. D. 1,8cm.
V12. A farmer took 48 head of cattle to the Cold Storage Company. This was 25% of his herd. How
many cattle did the farmer have?A. 96 B. 73 C. 12 D. 192
13. The difference between the sum of 14 and 19 and the product of 3 and 11 is A. 33. B O. C. 66. D. 20.
14. A suit was marked $95,00. It was reduced by 20%. How much was it sold for?A. $19,00 B. $114,00 C $76,00 D. $75,00
15. How much time is there between 3:07 am and 6:58 pm?A. 3 hours 51 minutesB. 6 hours 59 minutesC. 8 hours 53 minutesD. 15 hours 51 minutes
161 The area of the triangle isA. 25cm2.B. 15cm?.C. 23cm2.D. 30cm2.
17. The mass of an empty tin of jam is 65g. The jam is 1,663kg. What is the gross mass? A. 9,360kg B. 1,728kg C. 7,634kg D. 6,094kg.
18. Rudo is facing West. She turns 2| right angles in an anti-clockwise direction. She is now facingA. East. B. North. C. North-east. D. South-east.
19. Find the Highest Common Factor (H.C.F) OF 24,36 and 90.A. 2 B. 3 C. 8 0 :6
20; O is the centre of the circle. Triangle OXY is a, or a n .....A. scalene.B. equilateral.C. right-angled.D. quadrilateral.
21. A match box is 5 # n long, 3,5cm wide and 2cm deep. How many of these match boxes fit into a box 10cm long, 7cm wideband 6cm deep?A. 12 B. 10 C. 8 D. 20
102
- 59,75 = D 1,25
23. Bulawayo
22. 100 A. 51,25 B. 59,75 C. SO,25 D. 159,75
164 Gweru437 273 Harare679 515 369 Kariba581 478 263 632 Mutare
The distance between Bulawayo and Kariba shown in the table above is A. 164. B. 679. C.369. D. 533.
24. 6,5cm
4cm
What is the difference between the perimeter of the rectangle and the square?A. 13cm B. 8cmC. 21cm D. 13cm2
25. Referring to the diagram for Question 24 above, the area of the shaded part is A. 22cm2. B. 22cm. C. 26cm2. D. 16cm2.
26. A plane flies 200km in 15 minutes. Its speed in km/h is A. 800km. B. 1500 km. C. 3 000km. 0.600km.
27.35
8. — 15
28. Mr Moyo bought 25 chickens at $4,00 each. Five of them died and he sold the remainder at $6,00 each. The profit he made wasA. $100. B. $20. C. 120. D. 40.
1 129. Jane read — of her book on Monday, — on Tuesday and the remaining 140 pages on
3 . 2Wednesday. The book had....................... . pages.A. 200 B. 120 C. 840 D. 240
30. There were 72 people on a bus. There were 4 men to every 3 women and 3 women to every 1 child. The total number of women and children was A. 27. B 36.
31. What is the product of 4,10 and 25?A. 10 B .1000
C. 9.
C. 100
D. 18.
D. 165
32. as a percentage is 8
A. 50%
33. a -59 - 59 = 79; a is * A. 59.
B 1 0 i%
B 79
C.
e. 118.
D. 12%.
103
34. 6 | + 2 | =
A. 9 f2 B. 8 f C . 9 f D. 81
35. — =3
A. 0,23. B. 0,67. C. 0,32. D. 0,33.
36. How much is 1 x $10 note, 2 x $20 note, 3 x $5 notes, and 2 x $1 coins?A. 66 B. 68 C. 67 D. 65
37. If I was 14 in 1963, when was I bom?A. 1949 B. 1947 C. 1946 D. 1950
38.
The perimeter of the largest face isA. 42cm. B. 32cm. C. 50cm. D. 31cm.
39. Three quarters of a number is 27. The number is A. 45. B. 81. C. 54. D. 36.
40. 2 - - =5
A . - B. 11 C.1J D . |5 5 4 3
41. The Lowest Common Multiple of 18 and 54 isA. 36. B 18 C. 108. D. 54.
42. 50 metres of cloth is needed to make 20 shirts. How much cloth is needed to make 8 shirts? A. 20m B. 16m C. 80m D. 145m
43. It costs $1,20 per word to send a telegram and a surcharge of 12% is added to the total cost How much will be paid for 20 words?A. $24 B. $2,88 C. $22,12 D. $26,88
44. Mr Moyo had a balance of $72,00 in his bank account. He deposited $18,00 and made a withdrawal of $40,00. His new balance wasA. $112,00. B. $58,00. C. $90,00. D. $50,00.
45. 0}065of$73 <A. $72 C. $56,80 D. $66,08
46. Mr Tembo drove from Bmdura to Zvishavane, a distance of 480km, at an average speed of 90km/h. How lorig did the joumey take in hours and minutes?A.5h30min B.4h10min C.ShJtomin D.5h40min
104
105
Paper 2
Instructions to candidates:
1. Answer all questions in Section A.
2. Answer any three questions from Section B.
3. Section A carries 25 marks.
4. Section B carries 15 marks.
5. To obtain full marks for any question, all working must be shown.
6. Do not measure from given diagrams.
7. Electronic calculators and cd slide rules must not be used in the examinations.
8. Underline answers and rule off after each answer.
V106
/
Answer all questions in this section.
1. Find the difference between 211 and 78.
2. A tank has a length of 4m, a width of 3m and a depth of 2m. Calculate the capacity of water in the tank when it is three quarters full.
Section A (25 marks)
3. Find the value ofa) 0,638 x 100 b) 0 ,3 -0 ,2 5
3 14 In a baq of beans — was rotten and — of the remainder was sold. What fraction of the bag of8 2
beans was (a) sold (b) remained?
5. Betty invested $540 000 at 9% interest per annum for 2 years.a) Calculate the interest she earned.b) Find the total amount received.
6. A Grade 6 class saved money to start a garden for the first term. Study the graph and answer questions that follow.
40
Amount 35
in 30
dollars 2520
15
10
5
0Jan Feb Mar
Months
April
a) How many months did the class save more than $20?b) What was the class average savings from January to April?
7. An aeroplane travels 4 800km in 12 hours.a) Calculate the average speed in kilometers per hour.b) If the aeroplane travels at the same average speed, how far would it travel in 15 hours?
107.
Answer any three questions from this sections.
8. Mrs Gumbo bought a 150ml bottle full of cough syrup for her baby. The baby took 5ml of syrup3 times per day for a week.a) How many millilitres of the syrup did the baby take in one week?b) Express as a fraction in its lowest terms the amount of the syrup that remained in the
bottle after one week.
9. Here is a plan of Rudo’s bedroom.
4,8m
9,92m
a) How many metres is the length longer than the width?b) What is the distance around Rudo’s bedroom?c) Find the area of Rudo’s bedroom.
10. The following clock faces show the departure and arrival times for a bus which travels from Kwekwe to Harare.
a) What time does the bus leave Kwekwe? Write your time in figures and words.b) How many hours and minutes does the journey take?
11. a) Write an invoice for 2 pairs of socks at $95 each, 1 blazer at $153,99 and a pair of shoesat $85,56.
b) How much change would be given from $500,00?
12. Find the area of this field.250m
108
Answer all questions in this section.
1 a,,) Find the sum of 1 009 and 991.b). Four hundred and three comma zero in figures is ....
2. Calculate the area of a triangle whose height is 9cm and the base is 12cm.
3. Express 7 | as an improper fraction.
4. A school bought a fridge for $350 000. They paid a deposit of $20 000 and paid the balance in12 monthly instalments.9) What was the monthly instalment?b) What was the balance after six months payment?
55. There are 72 people on a bus. — of the people on the bus are adults.
8a) How many adults are on the bus?b) How many children are on the bus?
6. a)' Write factors of 27 and 36.t}) What is the Highest Common Factor (HCF) of 27 and 36?
7. A box has a length of 16cm, width 10cm and a height of 4cm.a) Calculate the volume of the box.
How many boxes measuring 4cm by 2cm by 2cm can fit into the box?
Section A (25 marks)
Section B carries 15 marks
Answer any three from this section.
8. 8 men build a house in 25 days.a) How long would 10 men take to build the same house?b) How many men would be needed to build the house in 10 days?
9. A storekeeper bought 20 blankets for $254,40. He marked them at $15,90 each.a) What profit did he make if he sold them all?b) What percentage profit did he make?
10.
8,5cm
Find a) the total surface area of this shape,b) the volume of the shape.
109
f 11. This is a page from Paida’s Savings Book.
Date Deposit Withdrawal Balance
$ C $ C $ C
Balance brought forward 350 00
16 August 115 00 L I U 1.......1
22 August 272 00 193 00
4September
I I I I 610 00
a) On 16 August she had a balance o f ..........b) How much was her withdrawal such that she had a balance of $193,00?c) How much did she deposit on 4 September?
12. A dealer put some goods in 5 boxes. The full boxes had masses of 485kg, 206kg, 340kg, 517kg and 274kg. The boxes were put on a lorry and the total mass was 2,897 tonnes.a) What was the total mass of the 5 boxes? Answer in tonnes.b) What was the mass of the empty lorry?
110
f '
Section A (25 marks)
Answer all questions in this section.
1. What fs the value of 6 in 254,065?
2: Witte 58mm to the nearest centimetre.
53. a) — of 3 804g = .....kg
6
4: (a) What is the name of this shape?
b) 0,9 -0,38 =
(b) Find the perimeter of this shape below
1,0 0,76m
3,065m
whole journey. °a) What fraction of the journey was she still to go?b) How far was it from Kuda’s house to her uncle’s house?
6. A drum held 50 litres of paraffin. A storekeeper sold 17 drums in a week. How many litres of paraffin did he sell?
7 0,3 of a towerlight 20m high was buried below the ground How many metres of the towerligfit were not buried?
Sc Share 400 apples between Tendai and Chipo in the ration of 3:2. How many does Chipo get?
9. The chart below shows how a father spends his money. The father earns $480.
a) What fraction of the money was saved?b) How much money was used on rent, savings and clothes?q). if the father saved the same amount of money for 1 year, how much was saved after 3
years?
111
Answer any 3 questions in this section.
10. Farai has a mass of 54,5kg. Takudzwa’s mass is 6,5kg less than Farai s# What is Takudzwa’s mass?t4 What is their average mass?
11. 24 litres of water were poured into a rectangular tank 80cm by 60cm wide,a) What was the depth of the tank?b} If the tank was filled up to | , what would be the volume of water in the tank?
12. a) Find the distance around a farm with sides 1,427km, 0*864kr%2$#km and 1,2$6kn|long.
b) How much wire would be needed to put a 4-strand wire fence around the farm?
13. A man using 2 tractors ploughs his lands in 15 daysa) How long would he take to plough his land if he used 5 tractors?b) How many tractors does he need to use if he ploughs his land in 30 # ys?
14. A shirt needs 2^m of material.a) How many shirts can be made from a roll of material 45ri long?b) How much material would be left over?
Section B (15 marks)
112
