s3 General Homeworks

8/8/2019 s3 General Homeworks

1/12

S3 GENERAL HOMEWORK 1

1) Round: -

(a) 2137 to the nearest 10 (b) 15379 to the nearest 100

(c) 237641 to the nearest 1000 (d) 3099265 to the nearest million

2) Find: -

(a) 23.7 10 (b) 1875 100 (c) 0.135 x 100(d) 2.1 1000 (e) 1.7 x 1000 (f) 0.93 10

3) Read the number on these scales: -

(a) (b)

60 80 100 120 1200 1300

(c) (d)

300 400 500 3000 3100 3200

4) How many: - (a) 100s are there in 2000?

(b) 50s are there in 750?

(c) 25s are there in 225?

5) By rounding appropriately estimate the following (do not find the actualanswer and do not use a calculator): -

(a) 312 x 198 (b) 3897 5796 (c) (39)

(d) 598 19 (e) 19 x 29 x 39 (f) 185 x 4119

6) Round to 2 decimal places: -

(a) 2.179

(b) 0.8321

(c) 16.0856

(d) 0.0397

(e) 10.006


2/12


1) Round to 1 decimal place: -

(a) 3.83 (b) 9.76 (c) 0.67 (d) 1.032 (e) 0.093

2) Round to 2 decimal places: -

(a) 3.248 (b) 19.173 (c) 0.828 (d) 0.0641 (e) 10.0384

3) Do the following, rounding your final answer to 1 decimal place (do not use acalculator): -

(a) 6.27 + 1.42 (b) 38.26 17.98 (c) 14.31 x 9 (d) 6.5 4

4) A car is sitting on a garage ramp.

Find the length of the ramp.6m

8m

5) How long do these overnight journeys take?

(a) 2215hrs to 0355hrs (b) 8.55pm to 6.10am

6) Find: -

(a) 1 of 75cm (b) 1 of 48kg (c) 1 of 73 4 10

(d) 2 of 60 (e) 3 of 40m (f) 4 of 35 litres3 8 5

7)

?

8.4m9.2m

The 9.2 metre drawbridge of a castle issupported by a chain that is attached to abolt 8.4 metres up the castle wall.Calculate the length of the chain, roundyour answer to 1 decimal place.


3/12


1) In each of the following one of the answers is a reasonable estimate. Saywhich: -

Question Possible Answers(a) 194 x 314 = (600, 6000, 60000, 600000)(b) 815 x 29 = (240, 2400, 24000, 240000)(c) 59 x 31 = (180, 1800, 18000, 180000)(d) 7864 389 = (20, 200, 2000, 20000)

2) How long does each of these bus journeys take?

(a) (b) (c)Depart 0730 1350 1825Arrive 0915 1720 2305

3) In a sports competition the following distances were recorded in the triple jump.

Triple Jump Competitor Best Distance

AsifDougalDarrenImranArthurPatrick

7.98m7.77m8.02m8.20m8.00m8.33m

4) Try the following, without using a calculator: -

(a) 10 2 x 3 (b) (4 + 7) (3 x 5) (c) 4 x (7 - 3) x 5

(d) 8 + 4 2 (e) 6+8 (f) 3 x 22+5

5) Karen is flying two kites.

22m

20m

(a) Write the triple jump distances inmetres and centimetres.

(b) Write the names of the competitors inorder, staring with the competitor who

jumped the furthest.

(c) Find the difference between the longest

and shortest jumps.

(d) Find the average distance jumped inmetres and centimetres.

She lets 1 kite out for 20 metres, theother for 22 metres. Both kites are nowhovering directly above a hot air spring8 metres from where Karen is standing.

Calculate: -

(a) The height of each kite above

the spring.

(b) The distance between two kites.


4/12


1) Some percentages and their fraction equivalents should be memorised. Writethe following percentages as fractions: -(a) 50% (b) 25% (c) 10% (d) 20% (e) 75% (f) 33 %

2) Without a calculator, do the following (mentally): -

(a) 50% of 240 (b) 10% of 3500 (c) 25% of 28(d) 20% of 150 (e) 33% of 1200 (f) 75% of 16

3) Use a calculator to find: -

(a) 15% of 360 (b) 28% of 4210 (c) 7% of 140(d) 12.5% of 380 (e) 6.2% of 1500 (f) 1.1% of 4000

4) J ohn has two pieces of electric cable. One is 4 metres long and the other is

7 metres.(a) What length ob cable does John have altogether?(b) John cut 6 metres from the longer piece, how much is left of that

piece?

5) The pass mark in an exam is 55%. Does a boy who gained 27 marks out of36 pass or fail?

6) There are 5.4 million people living in Scotland.(a) Write this number out in full.(b) Write this number in standard form (scientific notation).

7) The smallest coin issued was the Jawa, used in Nepal. The weight of theJawa was 0.014g. Write this number in standard form.

8)

9)

55m

Aberdeen to London

Aberdeen d 18 55Dundee d 20 45Edinburgh d 22 50Berwick d 23 51Newcastle d 01 05York d 02 45Doncaster d 03 30

London a 06 42

d: depart a: arrive

Miss Smith wants to travel by trainfrom Edinburgh to London.

How long should her journey take?

The local football field is60 metres wide and thedistance from the centrespot to the corner flag is55 metres. How long isthe football field (L m)?

60m

L


5/12


1) The temperature in a large freezer was -22C. The freezer broke down andthe temperature rose by 3C every hour.

What was the temperature after: -(a) 1 hour (b) 6 hours (c) 10 hours

2) Morven is a painter and decorator. She works a basic 37-hour week and ispaid 4.16 per hour. Overtime is paid at time and a half. In one week sheworks 45 hours. Find her: -

(a) basic pay (b) overtime pay (c) gross pay

3) Write these numbers out in full: -

(a) 10 4 (b) 3.7 x 10 5 (c) 1.48 x 10 -2

4) Express in standard form (scientific notation): -

(a) 23 (b) 0.000 006 1 (c) 3572

5) Mrs Kelly is a pensioner. She used to receive fuel bills with no VAT, but thischanged and her bills now have VAT added (at 17.5%).Calculate: -

(a) Her total fuel bill (for gas and electricity)(b) The extra she must now pay (as VAT)

6) Claire has 188 in the Capital Building Society. Mhairi has 192 in thePremier Bank.

Mrs Kelly May 2001

Gas 48.36

Electricity 61.24

Who will have moremoney in their accountafter 1 year?(Dont forget to showyour working)

CAPITAL BUILDING

SOCIETY

PREMIER BANK

Interest: 3.2% p.a


6/12


1) Nadia is playing and adventure game. Her scores for each round are asfollows: -

-12, -6, 1, -4, 3, -2, 0, 4(a) Calculate her total score(b) Calculate her average score(c) Paul plays eight rounds of the game. In each round he scores 4.

What is his total score?

2) John Packhard is a computer salesman. Here is his monthly salary slip: -

Employee No.086

NameJ Packhard

Tax Code621L

Month03

Basic Pay

1000

Overtime

-

Commission

-

Bonus

?

Gross Pay

?Income Tax250

Pension?

Nat Ins120

Other Deductions-

Total Deductions400

Net Pay1500

Use the information provided in the payslip to calculate Johns: -

(a) Gross pay (use his net pay and total deductions)(b) Pension contribution(c) Bonus

3) Grace borrows 2400 at 7% per annum to buy a car. Calculate the simple

interest she will pay if she borrows the money over: -(a) 1 year (b) 2 years (c) 4 months

4)

5) If 2 hours = 2.5 hours when written in decimal form, write the following timesin the same way: -

(a) 8 hours (b) 1 hours (c) 4 hours (d) 20 minutes

6)

For this dining table and chairs find:(a) The deposit(b) The total hire purchase (HP) price(c) The difference between the HP price

and the cash price

Cash Price 1600

HP termsDeposit 15%Twent -four instalments

A train leaves Hollywell Central at1420 and arrives at BakerfieldStation at 1620.If the train travelled at an averagespeed of 95km/hr, how far away isBakerfield Street from Hollywell?


7/12


1)(a) Solve algebraically the equation 4 x -5 = x + 22

(b) Factorise 8a 12b(c) Multiply out the brackets and simplify 3 (x - 2) - x

2)

3)

4)

5) The shape below is made up of a rectangle and an isosceles triangle.Calculate its PERIMETER.

6.5 m

2.8 m

4.8 m

4 m

An town

2.5cm

Othertown

A motor launch leaves the jetty at 9.15am. Ithas to tour the islands, a journey of 27kilometres and be back at the jetty by 10.45am.What average speed will it need to maintain inorder to do this?

The scale on a map is 1: 100000.If two towns are 2.5cm apart onthe map, how far apart is the realdistance. Give your answer inkilometres. Scale 1: 100000

Calculate the area of this

garage wall.

5 m

3 m


8/12


1) Multiply out the brackets and simplify: 5(m + 2) + 2(m 4)

2) The price of buying juice was increased by 1p per litre. This meant that thenew cost of 3 litres was 99p.Solve 3(j + 1) = 99 to find the cost (j pence) of one litre of juice.

3) David, Malcolm and Kate all collect badges. David has twice as manybadges as Kate. Malcolm has 12 badges less than Kate. Kate has x badges.

(a) Write down in terms of x (i) How many badges David has(ii) How many badges Malcolm has

(b) If David, Malcolm and Kate have 80 badges altogether, write down an

equation and solve it to find x.

4) A cyclist travels 85.5km at an average speed of 30km/hr. Find the time takenfor the journey in hours and minutes.

5) Calculate (i) the area and (ii) the perimeter of each shape.

(a) Parallelogram (b) Rhombus

6) Calculate the perimeter and area of the field.

30m

12cm

10cm

5cm4cm

12cm

16cm

100m


9/12


1)

2)

3) The diesel tank in a tractor is in the shape of a cuboid with dimensions 80 cmby 40 cm by 30cm.

(a) Calculate its capacity in litres.(b) How far can the tractor travel if it uses up 1 litre of diesel every 3

kilometres?

4) Calculate the volume of wood used to make this draught excluder.

5) The operation means square the first number and multiply by the second.

(a) Evaluate 6 4

(b) If a 5 = 245, find a

20 cm

10 cm

4 cm

3m

3m

1m

This bathroom carpet consists of asquare with half a circle removed.

Calculate the area of: -(a) The square before the circle is cut out(b) The half circle with a diameter of 1m(c) Carpet left when the semi-circle isremoved.

This box is a cube that is open at the top.Calculate its total outside surface area.

2 cm

A kitchen roll is shown. The outsidediameter is 10cm. The diameter ofthe hole is 2cm. The length of the rollis 20cm. Calculate: -

(a) The area of the hole(b) The area of the large circle hadthere been no hole(c) The area left when the hole ismade(d) The volume of paper making upthe kitchen roll


10/12


1) Simplify: -

(a) 3 - 1 (b) 4 + 2

2) Solve the equation 3 (x 4) = x + 14

3) Factorise 81 9 n

4) A special birthday cake, in the shape of a garage, is shown. Its height fromground to its highest point is 12cm. The front part, rectangular in shape,measures 8cm by 15cm. When oven ready, the cake stretches back for20cm. Calculate: -

5) John changed 630 into bath to take with him to Thailand. While in Thailandhe spent 34000 baht. Before he returned home he went to a bank to changehis money back into pounds and found that the exchange rate was then 61baht to the , instead of 55.9.

If he went ahead and changed his money at this new rate, how much moneywould he (to the nearest 1) would he bring home?

6)

5cm

40cm

50cm

15cm

8cm12cm

20cm

(a) The area of the end of the triangularroof.

(b) The area of the front of the rectangle.

(c) The total area of the front of the cake.

(d) The volume of the garage cake.

A tank with dimensions 80cm by40cm by 50cm is filled with waterup to 5cm from the top of the tank.

Calculate the volume of water inthe tank.

80cm


11/12


1) Calculate: -

(a) 75% of 200 litres (b) 60% of 850

2) Brenda and her brother went to EuroDisney for Easter. They kept a note asto how long they had to queue to get on the rides. Here are their results (inminutes).

10 17 25 22 16 110 10 20 40 30

(a) Calculate the mean time waited(b) Find the median and modal times waited(c) Say which average should be chosen to give a fair representation of

the data. Give two reasons for your choice.

3) It takes 16 men 12 days to complete a job. How many men would be neededto complete the job in 10 days?

4) It is planned to build a warehouse 160m away from a park. The warehouse isto be 20m high. It is to be hidden from the park by planting trees that willgrow to a height of 15m. How far away from the warehouse should the treesbe planted? (Draw a diagram and use similarity).

PARK 15m

160m

5) Wonkas Chocolate Company claim that there are 20 mini -wonka bars in theireconomy packs. Some economy packs were purchased and the results ofthe contents were as follows:

No. Bars Frequency Number x Frequency

18

19

20

21

22

23

2

9

8

5

5

5

Total = Total =

Warehouse

20m

(a) Copy and complete thetable

(b) What was the range inthe number of bars?

(c) Calculate: -(i) The mean (ii) The median (iii) The mode

(d) Which average did thecompany use to backtheir claim?


12/12


1) Simplify: -

(i) 2 + 1 (ii) 7 - 2

2) Solve for y: 5y 8 = 3y + 12

3)

4) Ali walked 4 miles in 2 hours 15 minutes (2 hours). If she walked at asteady pace throughout, how far did she walk in the first 30 minutes?

5)

6) Here is a table of exam marks (out of 50) from a science department.

PupilName Tom Jen Fred Don Tim Jess Pete Dave Sid Trev

ChemistryMark 5 10 10 20 15 30 30 40 40 45

Physics Mark 5 5 10 15 20 25 30 35 35 45

20

15

10

5

2015105

3cm

4.1cm

7.5 cm

x

The two triangles hereare similar. Calculatex, showing working.

Calculate the area ofthe smaller triangle.

St. Mirren had a mean score of 3 goals per game intheir first eight games!

(a) How many goals had they scoredaltogether?

(b) In their next game they scored two, butfailed to score in their next four matches.What was their mean score over the 13

matches?

(a) Draw a diagram similar to the oneshown, using the same scale for eachaxis.

(b) Plot the information from the table tomake a SCATTER DIAGRAM.

(c) Describe some of the connectionsbetween the Chemistry marks and thePhysics marks.

(d) Draw a line of best fit through points.(e) Use the graph to estimate what the

Physics mark would be if Chemistrywas 35.(f) One person seems to go against the

trend, who is it and what makes youthink that?

P h y s

i c s

M a r k s

Chemistry Marks

COPY

Date post:	10-Apr-2018
Category:	Documents
Upload:	knoxmaths
View:	222 times
Download:	0 times

s3 General Homeworks

Documents