Www.mathsrevision.com Level 3/4 Mathematics All the basics you need to know for the Level 3/4...

transcript

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Level 3/4 Mathematics

All the basics you need to All the basics you need to know for the Level 3/4 know for the Level 3/4

course.......course.......

I can ....I can ....11 22 33 44 55 66 77 88 99 1010 1111 1212 1313 1414

1515 1616 1717 1818 1919 2020 2121 2222 2323 2424 2525 2626 2727 2828

2929 3030 3131 3232 3333 3434 3535 3636 3737 3838 3939 4040 4141 4242

4343 4444 4545 4646 4747 4848 4949 5050 5151 5252 5353 5454 5555 5656

5757 5858 5959 6060 6161 6262 6363 6464 6565 6666 6767 6868 6969 7070

7171 7272 7373 7474 7575 7676 7777 7878 7979 8080 8181 8282 8383 8484

8585 8686 8787 8888 8989 9090 9191 9292 9393 9494 9595 9696 9797

Created by Mr. Lafferty

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Question 1Question 1

multiply small decimal multiply small decimal numbers together ?numbers together ?

0.04 x 0.7answer

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Answer to Question 1Answer to Question 1

multiply numbers together

then count number of decimal places.

0.0280.028

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Question 2Question 2

divide small decimal divide small decimal numbersnumbers

15.3 ÷ 0.0315.3 ÷ 0.03

answer

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Do not divide by a decimal scale it up to a whole number

Scale the number to be divided by the same amount

1530 ÷ 3 = 510

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Question 3

tell you the meaning of the words

(a) Profit(b) Loss(c) Salary(d) Overtime

answer

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Answer to Question 3

Profit:Profit: When you sell something for When you sell something for MOREMORE than than you bought it.you bought it.

Loss : Loss : When you sell something for When you sell something for LESS than you than you bought bought it.it.

Salary : Salary : How much a person is paid to do a job.How much a person is paid to do a job.

Can be measured weekly, monthly or Can be measured weekly, monthly or annually.annually.

Overtime : Extra work outside normal work time.Usually at night or weekends.

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answer

Question 4

tell you the meaning of the words

(a)Hire Purchase(b)Foreign Exchange

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Hire Purchase : Hire Purchase : When you pay for goods byWhen you pay for goods by

putting down a deposit and then putting down a deposit and then

paying the rest up in small fixed paying the rest up in small fixed

payments over a period of time.payments over a period of time.

Foreign Exchange :Foreign Exchange : Converting one currency to another.Converting one currency to another.

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answer

Question 5

explain the meaning of

Significant Figures

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A measure of both:A measure of both:

(i)(i) QuantityQuantity

(ii)(ii)AccuracyAccuracy

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Question 6

explain the term double negative.

(-4) – (-6)

answer

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Double negative changes to a positive

(-4) – (-6) = (-4) + 6 = 2

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Question 7

tell you the instrument that helps us to add and subtract integers.

answer

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thermometerthermometer

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answer

Question 8

explain the rules of multiplication and

division of integers.

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Different signs = negative answer

Same signs = positive answer

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Question 9

explain BODMAS

3 – ( 2 x (-4))2

answer

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B - BracketsO – OtherM - MultiplicationA - AdditionS- Subtraction

3 – ( 2 x (-4))2

3 – (-8)2

3 – 64

– 61

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Question 10

explain what an integer is.

answer

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A positive or negative number including zero.

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Question 11

explain the term scientific notation / standard form

and convert to it.

(a)5680000

(b)0.00623answer

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a x 10n

a between 1 and 10

n is an integer

(a) 5.68 x 106

(b) 6.23 x 10-3

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Question 12

answer

write numbers in normal form

(a) 5.93 x 104

(b) 7.43 x 10-5

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Normal Form

(a) 59300

(b) 0.0000743

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Question 13

write these numbers to 3 significant figures

(a)92418400(b)0.04057090100

answer

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3 significant figures

(a)92400000(b)0.0406

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Question 14

round decimals to any significant figures

answer

(a) 93.0108 ( to 2 s.f.)(b) 0.0706194 ( to 4 s.f.)

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(a) 93 ( to 2 s.f.)(b) 0.07062 ( to 4

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Question 15

write numbers to any decimal place

(a) 29.0864 ( to 2 dp)(b) 0.0109964 ( to 4 dp)

answer

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Higher Mathematics: ©HappySmile Higher Mathematics: ©HappySmile ProductionsProductions

(a) 29.09 ( to 2 dp)(b) 0.0110 ( to 4 dp)

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answer

Question 16

explain how to get triangular numbers

and write down the first 6 triangular

numbers.

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1, 3, 6, 10, 15, 21

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answer

Question 17

explain how to get square numbers

and write down the first 10

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1, 4, 9, 16, 25, 3649, 64, 81, 100

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answer

Question 18

decompose a number into product of primes

e.g. 18

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= 3 x 6

= 3 x 3 x 2All Prime !

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answer

Question 19

explain what the LCM is between a set of

numbers

e.g. LCM for 3, 4 and 5

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the lowest number that 3, 4, 5 all divide into

without leaving a remainder is 60

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answer

Question 20

explain what the HCF is between a set of

numbers

e.g. HCF for 25, 50 and 100

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the highest number that divides into 25, 50, 100

without leaving a remainder is 25

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answer

Question 21

know the basic angle properties at Level E

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120o 95

Angles round a pointAdd up to 360

Two angles making astraight line add to 180

angles opposite each otherat a cross are equal.

34o 34

3 angles in a triangle ALWAYSadd up to 180

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answer

Question 22

explain the term alternate angles

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two angles that form a Z - shape

= equal angles

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answer

Question 23

explain the term corresponding angles

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two angles that form a F - shape

= equal angles

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answer

Question 24

explain the term interior angle of a shape

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Pentagon

Hexagon

Octagon

Interior AnglesInterior Angle

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Higher Mathematics: ©HappySmile Higher Mathematics: ©HappySmile ProductionsProductions

answer

Question 25

explain the term exterior angle of a shape

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Pentagon

This is called the“Exterior angle”

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answer

Question 26

find the exterior angle of a shape

Pentagon Find Exterior angle

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Exterior angle = 180o – interior angle

Pentagon

This is called the“Exterior angle”

Exterior angle = 180o – 108o = 72o

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answer

Question 27

find the interior angle of a shape

Octagon

Find the interior angles

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Octagon

Interior angle = (180o – 45o) = 135o

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answer

Question 28

use angle properties to calculate missing angles

Find all missing angles ao , bo and co

d = 115o

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ao = co = 115o

bo = 65o

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answer

Question 29

remove a single bracket

(a) -2 ( 8y – 3)(b) 4b ( – 5b + a)

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(a) -16y + 6

(b) -20b2 + 4ab

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remove a single bracketand simplify

(a) 2 (x + 5) - 7(b) 3(a + 4) + 2(a – 1)

Question 30

answer

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(a) 2x + 10 -7 =2x + 3

(b) 3a + 12 + 2a – 2 =5a + 10

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answer

Question 31

evaluate algebraic expressions

22 3 30a b c

a = 3 ; b = 4 and c = -1

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22 3 30a b c

(2 3 3) (3 4) (30 ( 1)) (2 ) (3 ) (30 )a a b c

18 12 30 0

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answer

Question 32

factorise algebraic expressions

(a) 4y + 80(b) 9x – 6x2

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(a) 4y + 80 = 4(y + 20)

(b) 9x – 6x2 = 3x(3 – 2x)

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answer

Question 33

simplify algebraic expressions

(a) -6x + 7y – 16x + 11y(b) 2b – 3b2 – 5b + 5b2

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(a) -22x + 18y

(b) -3b + 2b2

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answer

Question 34

find a percentage of quantity (with a calculator)

What is 17.5 % of £450

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450100

= £76.50

17.5 % of £450

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answer

Question 35

explain the term appreciation with reference to percentages

The average house prices in Glasgow have appreciated by 50% over the past 10 years. If you bought the house for £80 000 ten years ago.

How much would the house be worth now?

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when an item has increased in value by a certain percentage.

Appreciation = 50% x £ 80 000= 0.50 x £80 000

= £ 40 000

New value = Old Value + Appreciation

= £ 80 000 + £40 000= £ 120 000

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answer

Question 36

explain the term depreciation with reference to percentages

A Mini Cooper cost £15 000 in 2005.At the end 2006, it will have depreciated by 20%What will the mini cooper worth at end

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when an item has decreased in value by a certain percentage.

End 2006 Depreciation = 20% x £15 000

= 0.2 x £15 000= £3 000

New value = Old value - Depreciation= £15 000 - £3000

= £12 000

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answer

Question 37

express a value as a percentage of another value.

Frances scored 13 out of 20 in a Maths test.What was her percentage score?

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13= 100

20=65%

scored 13 out of 20

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answer

Question 38

work backwards to find initial value.

After a 10% increase the price of a house is £88 000. What was the price before the increase.

Tricky

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Price before is 100% :

£800 x 100 = £80 000

£88 000 110 = £8001 % :

110 % = £88 000We have :

100 % + 10 % = £88 000

Deduce from question :

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answer

Question 39

work backwards to find initial value.

Tricky

The value of a car depreciated by 15%. It is now valued at £2550. What was it’s original price.

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Price before is 100% :

£30 x 100 = £3 000

£2 550 85 = £301 % :

85 % = £2 550We have :

100 % - 15 % = £2 550

Deduce from question :

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answer

Question 40

find a percentage of quantity (with out a calculator)

What is 17.5 % of £600

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10% 600 ÷ 10 = £ 60 5% half of 10% = £ 30

2.5% half of 5% = £ 15

17.5% £105

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answer

Question 41

identify the main parts of a circle.Name the main parts of the circle

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radius

Circumference Diameter

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answer

Question 42

explain the connections between the radius, diameter and the

circumference of a circle.

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radius

Circumference Diameter2D r

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answer

Question 43

explain the difference between the circumference and the area

of a circle.

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Circumference is the name given to the perimeter of the circle

(the length round the outside of the circle)

The area is the inside of the circle

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answer

Question 44

calculate the perimeter and area for a circle.

Find the area and perimeter of the circle ?

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24A250.26A cm

225.13C cm

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answer

Question 45

explain how to calculate the area of a

composite shape.

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Area = rectangle + semicircle21

A l b r

2120 5 10

100 157 A 2257 cmA

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answer

Question 46

calculate the area of any triangle.

Find the area below.

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Area b h

Altitude h outside triangle this time.

220Area cm

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answer

Question 47

calculate the area of a rhombus.

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1Rhombus Area ( )

1Area = (5 2)

2Area = 5cm5cm

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answer

Question 48

calculate the area of a kite and inverted kite.

4cm 7cm4cm

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4cm 7cm4cm

1Kite Area ( )

1Area = (9 4)

2Area = 18cm

1Kite Area ( )

1Area = (7 4)

2Area = 14cm

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answer

Question 49

calculate the area of a parallelogram.

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Parallelogram Area b h

Area = 9 32Area = 27cm

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answer

Question 50

calculate the area of a trapezium.

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Trapezium Area = (5 6) 42

1Trapezium Area = ( )

2Trapezium Area = 22cm

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answer

Question 51

calculate the area of composite shapes.

Find the area shaded grey below.

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1Trapezium Area = ( )

2a b h

Trapezium Area - Triangle Area

1Triangle Area =

21= (10 8) 11 99

21 = 4 11 22

2Shaded Area = 99 - 22 77cm

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answer

Question 52

write down the area formula for(a) Any triangle(b) Rhombus(c) Parallelogram(d) Kite(e) Trapezium

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The area formula for(a) Any triangle(b) Rhombus(c) Parallelogram(d) Kite(e) Trapezium

1Area = ( )

2a b h

Area b h

1Area ( )

Area b h

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answer

Question 53

write down in words Pythagoras Theorem

for right-angled triangles.

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b c2 2 2a b c

Two shorter sides squared and added together

equal to the longest side

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answer

Question 54

calculate the longest side given the two shorter sides.

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c2 2 2c =a +b2 2 2c =12 +8

2c =208

c = 208 =14.42km

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answer

Question 55

calculate a shorter sidegiven the longest side

and the other shorter side.

20cm 12cm

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2 2 2c =a +b

2 2 2a =20 -122a =256

a= 256 =16cm

2 2 2a =c - b

Check answer ! Always smaller

than hypotenuse

20cm 12cm

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answer

Question 56

write down the three different versions of Pythagoras

Theorem

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om Finding hypotenuse c

2 2 2c =a +b

2 2 2a =c - b

2 2 2b =c - a

Finding shorter side a

Findingshorter side b

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answer

Question 57

write down the rule for a linear pattern.

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b = 3s + 8

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answer

Question 58

write down the steps for finding the rule for a

linear pattern.

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1. Find the difference

2. Write down part of formula

3. Find the correction factor.

4. Write down the full formula

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answer

Question 59

convert hour and minutes to decimal hours.

48 minutes to decimal is

2hr 15 minutes to decimal is

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60= 0.8 hr

60 = 2.25 hr

To change minutes to a decimal divide by 60

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answer

Question 60

convert decimal hours to hours and minutes.

0.7 hrs to minutes is

3.4 hrs to hours and minutes is

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0.7 hrs to minutes is 0.7 60= 42 mins

3.4 hrs to hours and minutes is

3+0.4 60= 3 hrs 24 mins

To change decimal time to minutes ‘multiply by 60’

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answer

Question 61

calculate the speed of an object.

Daniel drove from his house to the Blackpool, a distance of 135 miles.

It took him 2hrs 15mins.

What was his average speed?

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135 miles=

12 hrs

S =60mph

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answer

Question 62

calculate the time taken for an object.

How long did the bus journey take if it travelled a total distance of 60 km at an average speed of 40 km/hr.

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S=1.5 hrs

60 km=

40 km/ hr

T =1 hr 30 mins

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answer

Question 63

calculate the distance travelled for an object.

A racing car travelled at 50 km/hr. What is the distance covered in 6 hours ?

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D =S T =300 km=50 6

D =300 km

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answer

Question 64

write down the three formulae linking distance, speed and time.

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S T DT =

Simple way to remember the 3 formulae !

D = S T

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answer

Question 65

simplify ratios

6 : 812 : 45

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4 : 15

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answer

Question 66

express ratios in unity form

0.1 : 4

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1 : 12

1 : 40

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answer

Question 67

solve questions involving ratio

The ratio of boys to girls is 4:5. If there are 16 boys, how many girls are there.

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The ratio of boys to girls is 4:5. If there are 16 boys, how many girls are there.

boys girls4 516 20

x 4 x 4

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answer

Question 68

work out portions using ratios.

Ryan and Kerry share a raffle win of £400 in the ratio 3:5.

How much does each get ?

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Ryan and Kerry share a raffle win of £400 in the ratio 3:5. How much does each get ?

Step 1 : Since the ratio is 3:5, there are :

3+5 = 8 shares

Step 2 : Each share is worth : 50

Step 3 : Ryan gets 3 x 50 = £150

Kerry gets 5 x 50 = £250Check !

150 + 250 = 400

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answer

Question 69

draw a graph of direct proportionand

state the key points of the graph.

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Two quantities which are in DIRECT PROPORTION

always lie on a straight linepassing through the origin.

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answer

Question 70

solve problems involvingdirect proportion

The cost of 6 cakes is £4.20. Find the cost of 5 cakes.

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19 Apr 202319 Apr 2023

Easier methodCakes Pence6 420

Are we expecting more

or less

(less)

350 £3.50

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answer

Question 71

It takes 10 worker 12 months to build a house.How long should it take 8 men.

solve problems involvingindirect (inverse) proportion

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1 12 x 10 = 120 Easier methodWorkers months

10 12 8

(more)

15 months

Are we expecting more

or less

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answer

Question 72

add two simple fractions

5 36 4

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om 5 3

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answer

Question 73

5 16 5

subtract two simple fractions

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5 16 5

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answer

Question 74

multiply two simple fractions

3 34 5

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3 34 5

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answer

Question 75

divide two simple fractions

5 28 3

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5 28 3

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answer

Question 76

add two mixed fractions

1 22 3

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1 22 3

2 3 4+

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answer

Question 77

7 27 4

subtract two mixed fractions

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7 27 4

8 3 16-

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answer

Question 78

3 14 1

multiply two mixed fractions

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3 14 1

19 64 5

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answer

Question 79

3 23 1

divide two mixed fractions

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3 23 1

15 54 3

3154 5

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answer

Question 80

solve simple equations

2 12x 5 11x

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answer

Question 81

solve simple equations

4 7 17n

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4 17 7n 4 7 17n

6n 24 4n

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answer

Question 82

solve more complex equations

6 1 2 21x x

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6 1 2 21x x

6 2 21 1x x 4 20x

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answer

Question 83

2(2 3) 24x x

solve equations with brackets

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2(2 3) 24x x

4 6 24x x

18 3 6x

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answer

Question 84

5(3 2) 2(4 3) 2 36x x x

solve equations with double brackets

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5(3 2) 2(4 3) 2 36x x x

15 10 8 6 2 36x x x 7 16 2 36x x

20 5 4x

5 16 36x 5 20x

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answer

Question 85

solve equations with fractions

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6 14x 14 6 8x

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answer

Question 86

3 2(2 1) 1

4 3x x

solve equations with brackets & fractions

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3 2(2 1) 1

4 3x x

9(2 1) 8 12x x 18 9 8 12x x

26 21x 21

Multiply EVERY

term by 12

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answer

Question 87

solve simple inequations (inequalities)

2 1 7x

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2 1 7x 2 7 1x

2 8x 4x

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answer

Question 88

solve harder inequations (inequalities)

2(2 3) 9x x

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2(2 3) 9x x 4 6 9x x 3 6 9x

3 15x15 3x 5x

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answer

Question 89

explain the meaning of the terms

MeanMedianModeRange

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1. The Mean

Sum of all the data ÷ by the number of data values

2. The Median (put the data in order then find the MIDDLE value)

3. The Mode (the number that appears the most)

4. Range

Highest value - the lowest value

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answer

Question 90

construct a frequency table12 23 41 55 7715 32 40 51 6921 12 16 43 5671 32 75 34 4255 76 21 73 2256 41 19 20 4778 17

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Class Class IntervalsIntervals

TallyTally FrequencFrequencyy

Choose suitable

Class interval

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answer

Question 91

add a third column to a frequency table

and find the mean from it.

No of No of SiblingSiblings (s (SS))

Freq.Freq.

(f)(f)

Totals

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No of No of SiblingSiblings (s (SS))

Freq.Freq.

(f)(f)

Totals

0 x 9 =0

2 x 6 = 12

5 x 1 = 5

3 x 1 = 3

1 x 13 = 13

S x S x ff

Mean 33= =1.1

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answer

Question 92DayDay Freq.Freq.

(f)(f)

Cum. Freq.Cum. Freq.Total so farTotal so far

find the medianfrom a

cumulative frequency graph.

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median=29 2 =14.5

DayDay Freq.Freq.

(f)(f)

Cum. Freq.Cum. Freq.Total so farTotal so far

it occurred on day 5

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answer

Question 93

construct a Pie-chart

Football

Cricket

Ice Hockey

Favourite Sport

Squash 30

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Football

Cricket

Ice Hockey

Favourite Sport

Squash 30

Total 30075

Rugby angle = 360 0300

90Football angle = 360 8

45Cricket angle = 360 4

3005 ox

60Ice Hockey angle = 360 2

3007 ox

30Squash angle = 360 6

3003 ox

RugbyFo

Cricket Ice Hockey

Squash

90o108o

54o72o

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answer

Question 94

construct a stem-leaf diagram

1212 4040 5757 5454 55551313 5555 1515 3232 55553232 1515 4141 2121 40402323 4141 2929 5151 1212

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stem leaves

n = 20 Key : 2 3 means 23

2 20 1 1

1 4 5 5

1212 4040 5757 5454 55551313 5555 1515 3232 55553232 1515 4141 2121 40402323 4141 2929 5151 1212

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answer

Question 95

construct a scattergraphand describe the main features

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Strong positive correlation

Strong negative correlation

Best fit lineBest fit line

When two quantities are strongly connected we say there is a strong correlation between them.

No correlation

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answer

Question 96

explain the term probabilityin words and numbers

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Probability can be thought of as a fraction or decimal.

It always lies between 0 and 1.

0 meaning impossible ( could not happen)

1 meaning certain ( will definitely happen)

The chance of an event happening

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answer

Question 97

evaluate a probability

There are 3 red and 4 green balls in a bag. What is the probability a green ball is picked.

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There are 3 red and 4 green balls in a bag. What is the probability a green ball is picked.

3 4 7P( )green

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Online Revision Exercises

Integers

Angles

Type of numbers

Scientific Notation 1 2

Algebra

Decimals

Statistics

Percentages

Area of Quadrilaterals

Circle

Fractions

Ratio & Proportion

Equations & Inequalities

Linear Patterns 1 2

Pythagoras 1 2

Level F exam type question

Www.mathsrevision.com Level 3/4 Mathematics All the basics you need to know for the Level 3/4...

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