Gradients and Straight Lines (1) - Dunblane High School · S2/3 Revision Pack 2 Gradients and Straight Lines (2) 1. A straight line has as its equation y 2x. (a) Copy and complete

S2/3 Revision Pack 2

Gradients and Straight Lines (1)

1. Calculate the gradient of each ladder below :

2. Calculate the gradient of each line below, leaving your answer as a fraction in its simplest

form where necessary.

2 m

4 m

8 m

2 m

3 m

10 m

12 m

2 m

6 m

8 m

1 m

8 m

(a) (b) (c)

(d) (e) (f)

(a)

(b)

(c)

(d)

(e) (f)

(g) (h)

(i)

(j)



1. A straight line has as its equation xy 2 .

(a) Copy and complete the table for this line.

(b) Plot the points from the table on a coordinate diagram and draw the line through them.

2. A straight line has as its equation xy 3 .



3. A straight line has as its equation xy2

1 .



4. A straight line has as its equation xy3

1 .



5. A straight line has as its equation xy .



x 0 1 2 3 4 5

y 2 10

x 0 1 2 3 4 5

y 3

x 0 2 4 6 8 10

y 1 4

x 0 3 6 9 12

y 0 3

x 1 2 3 4 5 6

y 1 5



1. A straight line has as its equation 2 xy .






3. A straight line has as its equation 42

1 xy .



4. A straight line has as its equation 54

1 xy .






x 0 1 2 3 4 5

y 2 5

x 0 1 2 3 4 5

y 3 9

x 0 2 4 6 8 10

y 4 8

x 0 4 8 12

y 6

x 1 2 3 4 5

y 1 10


Worksheet Name : ___________________________

Class : _____________

x

y

0 1 2 3 4 5 6 7 8 9 10 11 12

1

2

3

4

5

6

7

8

9

10

11

12

13

x

y

0 1 2 3 4 5 6 7 8 9 10 11 12

1

2

3

4

5

6

7

8

9

10

11

12

13

x

y

0 1 2 3 4 5 6 7 8 9 10 11 12

1

2

3

4

5

6

7

8

9

10

11

12

13

x

y

0 1 2 3 4 5 6 7 8 9 10 11 12

1

2

3

4

5

6

7

8

9

10

11

12

13

This worksheet can be used along with the gradient, straight line and scatter diagrams worksheets


Trigonometry (1)

You need a scientific calculator for this worksheet.

1. Calculate the angle marked x in each triangle below :

(a) (b) (c)

(d) (e) (f)

2. Calculate the angle marked x in each triangle below :

(a) (b) (c)

(d) (e) (f)

(g) (h) (i)

19 21

x

12

14

x

4 9

x

3 11

x

5

8

x

10

17

x

15

14

3

4

9 16

7

12

5

5 27

34

4 5.6

7.3

8.9

3.2 12.8

x x x

x x

x

x

x x

Remember

SOH CAH TOA


Trigonometry (2)


1. Calculate the length of the side marked x in each triangle below :

(a) (b) (c)

(d) (e) (f)

2. Calculate the side marked x in each triangle below :

(a) (b) (c)

(d) (e) (f)

x

x

x

x x

x

32o

45o

50o 48o

78o

24o

16

7

12

14

11

20

7

80o

x 35o

20

x

20o

26

x

25o

15 x

3

42o

x

9

32o

x

Remember

SOH CAH TOA


Trigonometry (3) - Angles & Sides


Calculate the value of x in each triangle below :

5 8

xo

3

11

xo

x

19 9 x

x

8

11

16

4.5

2.7

27 x

12

37

x

17

4.7

3.5

xo

20o

58o xo

xo

xo

xo

75o

26o 28o

(a) (b)

(c)

(d)

(e)

(f)

(g)

(h)

(i)

(j)

(k)

(l)

12

8

xo 27

x

72o

(m) (n)

11

7


Trigonometry (4)


1. To test the stability of a bus a tilting platform is used.

It is known that a bus will topple if the angle between the platform and the ground is greater that 20o.

Which of the buses below would topple?

Each answer must be accompanied with the appropriate working.

(a) (b) (c) (d)

(e) (f) (g) (h)

2. To comply with building regulations a roof must have

an angle of between 22o and 28o to the

horizontal (see diagram opposite).

Which of the roofs below comply, and which do not comply,

with building regulations?

(a) (b)

(c) (d)

(e) (f)

(g) (h)

8 m

2 m

10 m

4 m

14 m

4.8 m

6.2 m

2 m

7.45 m

2.7 m

9.8 m

3.6 m

8.43 m

3 m

6.8 m

2.6 m

x

x must lie between 22o and 28o

4 m

1.8 m

3.6 m

1.4 m

6.2 m

1.5 m

6.8 m

1.9 m

6 m

2.1 m

8 m

4.5 m

7.4 m

2.2 m

12.3 m

2.4 m


Fractions, Decimals and Percentages (1)

** You need a calculator for this worksheet.

1. Calculate :

kgofotonnesofnofm

oflmmofkofj

ofikgofhofg

gramsoffofecmofd

ofckgofbofa

525)(480)(2540£)(

08.1£)(984)(10.5£)(

92.10£)(45)(96.15£)(

558)(136£)(48)(

40.36£)(65)(96£)(

17

5

16

9

20

11

12

9

8

3

6

5

7

3

10

9

3

2

9

7

8

5

4

3

7

1

5

1

3

1

2. Calculate :

tonnesofoofnofm

oflofkgofj

ofiofhofg

cmoffofekgofd

ofcgofbofa

1200%7)(12£%4)(1500£%78)(

360£%94)(250£%80)(4500%8)(

880£%65)(340£%5)(64£%19)(

85%21)(10£%17)(60%42)(

45£%13)(300%54)(90£%26)(

3. Calculate each of the following rounding your answers to the nearest penny.

pofoofnofm

poflofkofj

ofiofhofg

poffofepofd

ofcofbofa

97%57)(08.12£%3)(53.1£%71)(

88%34)(57.2£%9)(45.3£%81)(

65.834£%5)(20.341£%4)(30.18£%12)(

51%41)(43.10£%57)(89%47)(

35.6£%18)(71.12£%24)(20.13£%36)(

4. Change each of the following fractions to percentages.

Round your answer to the nearest percent when necessary.

29

6

95

48

365

38

31

6

7

3

15

2

13

8

32

4

12

5

23

18

11

3

9

5

20

19

100

17

10

7

25

7

4

3

5

4

)()()()()()(

)()()()()()(

)()()()()()(

rqponm

lkjihg

fedcba

5. John's schedule marks are shown in the table below :

(a) Copy and complete the table by calculating John's "percentage mark" for each subject.

Round each answer to the nearest percent where necessary.

(b) Which was John's best subject ?

(c) Which was his worst ?

Subject Maths English Tech Science Art History French

Mark 45 out of 60 64 out of 72 40 out of 65 38 out of 55 75 out of 90 27 out of 40 63 out of 95

%




1. Increase each of the following by 15%.

(a) £250 (b) 160kg (c) 25cm (d) £36

(e) 2100g (f) 210oC (g) £8 (h) £3500

2. Decrease each of the amounts in Q1 by 20%.

3. The nine workers in a small factory are given different percentage wage rises dependant upon

their length of service. The table below represents their weekly wages.

Copy and complete the table .......

Name Old Wage % Increase Increase New Wage

John Hughes £230 4% £9.20 £239.20

Steven Higgins £168 6%

Susan Marshal £210 4%

Stewart Aitken £145 2%

Pamela Grant £360 3.5%

Neil McShane £225 6%

James Mackie £235 8%

Lorna Graham £210 4.5%

Pat Lavery £468 5%

4. For each diagram below, write down i) the fraction shaded; ii) the percentage shaded .

(a) (b) (c) (d)

(e) (f) (g)

5. Calculate the percentage of vowels in each word below.

(a) (b) (c)

6. (a) In a class of thirty pupils, 6 were absent. Calculate the percentage absent.

(b) A machine produces 300 heating elements in a morning. Six are found to be defective.

What percentage of the elements are defective ?

(c) A small farm has 160 sheep. During a severe storm the farmer loses 8 sheep.

What percentage of the sheep got lost ?




1. VAT is charged at %172

1 . Calculate the VAT on each item below.

(a) A stereo costing £230 (b) A fridge costing £148

(c) A cooker costing £456 (d) A watch costing £68

(e) A computer costing £650 (f) A gold ring costing £134

2. Find the total cost of each item in Q1 after the VAT has been added.

3. A man places £2300 in a savings account which has an annual interest rate of 4%.

(a) How much interest will he earn in the first year ?

(b) Assuming he does not touch his money, how much does he now have in the bank

at the beginning of year two ?

(c) Hence calculate the interest he will get at the end of year two.

4. A woman places £22100 in a Post Office savings account which has an annual interest rate of 5%.

(a) How much interest will she earn in the first year ?

(b) Assuming she does not touch her money, how much does she now have in the bank

at the beginning of year two ?

(c) Hence calculate the interest she will get at the end of year two.

5. Steven places £800 in a Building Society at an annual interest rate of 3%.

How much will he have in his account after two years ?

6. Susan invests £800 in a Building Society at an annual interest rate of 6%.

How much will she have in her account after two years ?

7. Mr Banks places £1300 in a savings account which has an annual interest rate of 2%.

How much will he have in his account after three years ?

8. Miss Anderson places £5600 in a Building Society at an annual interest rate of 7%.

How much will she have in her account after three years ?


Solving Equations (1)

1. Solve each of the following equations :

37710)(3829)(2158)(

2623)(2062)(2516)(

3137)(1756)(2243)(

1314)(1132)(1885)(

ylxkaj

xiphhg

dfaeyd

mctbxa


3610)(3369)(16412)(

2758)(1839)(2426)(

3527)(306)(2037)(

1624)(1536)(1235)(

yylxxkaaj

xxipphhhg

ddfaaeyyd

mmcttbxxa


11486)(40749)(5198)(

405411)(364127)(238716)(

513315)(192111)(432312)(

356710)(32629)(2658)(

1628)(244610)(30446)(

16217)(29256)(12547)(

21318)(15336)(8325)(

xxuxxtmms

aarddqyyp

xxohhnppm

yylxxkaaj

xxipphhhg

ddfaaeyyd

mmcttbxxa




27312)(4316)(2378)(

2447)(2912)(3246)(

1927)(3118)(576)(

1554)(932)(1644)(

ylxkyj

uiphhg

dfaeyd

mctbxa


5512)(3057)(16210)(

14455)(11158)(12426)(

14470)(536)(12528)(

9204)(9186)(7125)(

yylxxkaaj

xxirrhhhg

xxfyyeyyd

mmcttbxxa


?4486)(38345)(33128)(

406410)(38427)(238714)(

33395)(21267)(432)(

173)(347211)(3427)(

263112)(2489)(21476)(

19216)(35358)(15517)(

20518)(17337)(8325)(

xxuxxtaas

aarkkqyyp

xxohhnppm

yylxxkxxj

xxiyyhhhg

ddfkkemmd

mmcttbxxa




80)2(10)24)2(6)45)1(9)

48)5(8)25)1(5)21)2(3)

12)3(6)16)2(4)10)1(5)

30)6(2)35)1(7)24)3(6)

40)6(5)12)4(2)20)2(4)

rownem

zlkkyj

xiphag

hfwegd

fcebca


80)210(4)24)62(3)20)31(2)

28)77(2)22)35(2)21)21(3)

12)32(4)28)13(2)27)15(3)

35)14(7)52)35(4)20)42(2)

60)24(6)12)42(2)28)13(4)

rownem

ulzkkj

yiphhg

wfgetd

fcebca


)15(2)32(4))1(4)2(7))4(6)1(8)

213)1(7)33)2(6)73)1(5)

)28(4)2(8))5(4)2(7))8(2)1(4)

342)1(6)293)3(8)153)1(7)

242)3(5)302)3(4)12)2(3)

xxoxxnwwm

uulxxkddj

aaixxhaag

yyfhheddd

mmcxxbaaa


Equations (Extension Examples)

1. Solve each of the following equations (a warm up) :

3235)(611312)(517)(

1219)(6159)(5248)(

1627)(15337)(2645)(

vvimmhxxg

yyfddevvd

mmcttbxa


35278)(15315)(19453)(

12246)(5279)(1331)(

52462)(226414)(2126)(

24558)(5213)(32112)(

4406)(2202)(425)(

221)(3245)(123)(

xxrvvqxxp

xxoxxnccm

ddlaakxxj

rripphyyg

xxfaaettd

yycmmbxxa


21831222445137

42936220523122

6230861855113

6166421042688

11573123275

cc)o(kk)n(xx)m(

aa)l(yy)k(xx)j(

ee)i(mm)h(xx)g(

aa)f(hh)e(vv)d(

y)c(x)b(x)a(


Statistics - Stem-and-Leaf Diagrams

1. A sample of tomato plants are measured for height. Their heights are recorded

to the nearest centimetre.

The stem-and-leaf diagram shows the results.

(a) How many plants were in the sample?

(b) What height is the tallest plant?

(c) Write out level 5 in full.

(d) What fraction of the plants were more

than 50cm tall?

2. Susan decided to visit various shops in her surrounding area in order to

compare the price of an identical CD player.

Her results, shown below, are given to the nearest pound.

£68 £75 £73 £80 £75 £79 £81 £66 £71 £92 £83 £75 £78

(a) Construct a stem-and-leaf diagram to represent this data.

(b) What was the median price?

3. A factory has a small workforce of eleven people. The owner decides to compare absence

rates (in days) over the last two years.

The results are shown in the back-to-back stem-and-leaf diagram below.

(a) What is the largest number of absences recorded?

(b) State the median of the absences for "last year" and "this year".

(c) Compare the absences and comment.

4. Two makes of matches are being compared,"Brighto" and "Sparky", they both cost the same per box.

14 boxes of each type are sampled to find the number of matches in a box. Here are the results.

Brighto Sparky

(a) Construct a back-to-back stem-and-leaf diagram to represent this information.

(b) Which make of match, if any, is a better buy? Give a reason for your answer.

Height of Plant (cm)

2 1 3

3 0 2 2 7

4 4 5 6 8 9 9

5 6 7 9

6 3

n = 16 2 1 represents 21cm

Absences (days)

last year this year

7 6 0 3 9 9

5 1 1 1 7

8 5 1 2 4 6

7 2 0 3 3

4 2 4 1 5

n = 11 0 3 represents 3 days n = 11

48 45 47 39 52 36 58

41 38 39 46 50 61 37

38 42 49 39 62 56 52

40 58 49 29 51 64 57


Frequency Tables (Mean,Median & Mode)


1. Fifty arrows were fired at a target. The outside ring scored 1 point and the centre ring

was worth 10 points. The results are shown below.

4 4 5 4 1 4 7 7 9 5 2 2

1 1 8 1 9 1 2 5 8 1 8 10

9 5 6 7 8 4 2 3 5 6 6 4

1 5 4 4 2 9 4 4 4 10 4 8

4 8

(a) Copy and complete the frequency table below

(b) Calculate the mean score.

(c) Determine the median score and state the modal score.

2. For each of the frequency tables below ......

(i) Copy the table and add an extra column for F x .

(ii) Calculate the mean value from the table.

(iii) Determine the median and state the mode.

(a) (b) (c)

Score (x) Tally Frequency (F) F x

1

2

3

4

5

6

7

8

9

10

Totals

x F

5 3

6 5

7 4

8 7

9 8

10 2

11 1

x F

12 1

13 2

14 2

15 12

16 4

17 6

18 9

19 3

20 1

x F

20 12

21 13

22 13

23 8

24 15

25 9


Scatter Diagrams

1. Plot each of the following sets of points on a separate coordinate diagram and comment

on the correlation (if any).

SET 1 SET 2 SET 3

SET 4 SET 5 SET 6

2. Where possible, insert a line of best fit on the appropriate diagram.

3 3

4 3

1 1

7 9

9 7

3 5

2 2

7 2

6 6

5 5

9 8

8 7

3 2

7 6

3 7

4 6

10 4

11 5

7 5

12 3

13 3

2 6

9 5

5 5

8 4

11 4

10 3

6 7

11 3

1 8

3 1

14 2

1 6

2 1

3 4

4 5

5 6

6 4

6 3

8 4

9 3

11 6

11 1

12 1

13 1

13 2

x y

x y x y

1 9

1 4

3 2

3 5

3 6

3 4

5 5

7 6

8 5

9 6

10 7

11 1

11 6

11 8

12 6

13 8

13 7

13 5

x y

2 2

7 3

5 8

10 2

9 5

9 7

1 9

3 6

4 4

6 11

6 5

7 8

x y

1 8

2 2

3 3

4 3

5 5

6 5

6 6

7 2

7 7

8 7

8 8

9 9

x y

x o

. . .

. . . .

. .

. .

. .

.

. .

. .

y


Best Buy


Which item is the best buy in each group below ?

(a) (b)

(c) (d)

(e) (f)

(g) (h)

(i) (j)

3 litres

£1.68 2 litres

£1.20

1 litre

£0.62

3 litres

£1.74 1 5 litres

84p

550 g

£8.20

0 8 litres

48p

350 g

£5.60

200 g

£3.60 1 kg

£1.80

750 g

£1.20 500 g

£1.00

200 g

44p

4 litres

£2.56

2 litres

£1.39 150ml

£1.20

0 7 litres

40p 250ml

£1.75 500ml

£2.50

kg80

£4.20

kg50

£2.80

kg30

£1.59

600 g

£2.50

320 g

£1.40 200 g

£1.05

6 kg

£10.50

0

kg52

£4.80

kg51

£3.06

Twin pack

( kg532 )

£11.90

250ml

80p

650ml

£1.99

550ml

£1.60 950ml

£2.95


Direct Proportion


1. Fred walked at a steady rate of 5km/h for 7 hours. The table below represents his distance,

from the start, at the end of each hour.

(a) Copy and complete the table. (b) Draw a graph of distance (D) against time (t).

(c) Explain why the relationship between D and t is directly proportional.

2. 300g of flour is used to make 6 cakes. How much flour is needed to make:

(a) 12 such cakes? (b) 3 cakes? (c) 9 cakes?

3. Eight bars of chocolate cost £3.36. Calculate the cost of:

(a) 1 bar of chocolate (b) 3 bars (c) 11 bars.

4. A stack of six identical books weighs 381 kg. How much would a stack of 10 books weigh?

5. (a) 4 cakes cost £3.12. Find the cost of 9 cakes.

(b) The height of 12 stacked CD cases is 8136 mm. Calculate the height of 7 such cases.

(c) A row of 24 staples measures 414 mm. How long would a row of 38 staples be?

(d) The weight of 3 baskets of fruit is 45 kg. Calculate the weight of 5 baskets.

6. 4 CD's cost £35.92 and 3 cassettes cost £15.78. Find the total cost of .......

(a) 7 CD's and 2 cassettes. (b) 3 CD's and 5 cassettes.

7. Carpet is priced relative to its area.

A rectangular carpet measuring 5m by 4m costs £264.

(a) Calculate the cost for 1 square metre of this carpet. (the cost per sq.m)

(b) How much would a carpet measuring 8m by 6m cost?

8. A bedroom carpet measuring 4m by 7m costs £180.60.

How much would the same type of carpet measuring 5m by 8m cost?

9. A car uses 15 litres of petrol to travel 210 miles. How much petrol would the car use for a

journey of 378 miles at the same rate of consumption?

10. Fifteen books cost £123. How many books could you buy for £73.80?

Time (t) hours 0 1 2 3 4 5 6 7

Distance (D) km 5 20

S2/3 Revision Pack 2 11. For £250 you receive 2750 francs. How much would 1364 francs cost you in pounds sterling?

Inverse Proportion


1. If 20 men can load a ship in 4 days, how long would it take 10 men ?




5. If 4 men can build a house in 40 days, how long would it take 10 men to build the same house ?




9. A fort has enough food to feed 60 men for 15 days. How long would the food last if there were

100 men in the fort ?

10. A fort has enough food to feed 80 men for 24 days. How long would the food last if there were

60 men in the fort ?

11. A town under seige has enough food to feed 500 people for 30 days. How long would the food last if

there were 300 people in the town?

12. A fort has enough food to feed 80 men for 12 days. How long would the food last if an extra 16

men arrived at the fort ?

13. A fort has enough food to feed 160 men for 6 days. How long would the food last if an extra 80

men arrived at the fort ?

14. A fort has enough food to feed 50 men for 10 days. How long would the food last if 30 men

left the fort ?


Proportion (Direct & Inverse) Mixed Exercise


1. In 5 hours an electric fire uses 20 units of electricity. How many umits will it use in :

(a) 1 hour (b) 8 hours (c) 20 hours ?

2. A car can travel 26km on 2 litres of petrol. How far can it travel on :

(a) 1 litre (b) 6 litres (c) 2

112 litres of petrol ?

3. 12 dinner plates cost £29.40. How much would you pay for 16 plates ?

4. 20 metres of copper piping costs £28.40. How much would 17 metres cost ?

5. If 8 men take 12 days to dig a ditch how long would it take 6 men to dig the same ditch ?

6. A builder employed 14 men to landscape a garden. It took them 6 days. How long would it have

taken 12 men to landscape the same garden ?

7. At a constant speed a train can travel 497 km in 7 hours. How far could it travel in 10 hours ?

8. Two dozen oranges cost £3.12. How much would you pay for 8 oranges ?

9. A woman worked for 9 hours and was paid £61.20. How much would she be paid if she worked

for 16 hours ?

10. A farmer has enough feed to last his 20 cows 16 days. How long would the feed last if he had

64 cows ?

11. A car can complete a journey in 6 hours at an average speed of 65 km/h. How long would it

take to complete the same journey at an average speed of 78 km/h ?

12. Six bottles of wine is the exact amount you need to give 21 people one glass each.

(a) How many bottles would you need to give 56 people one glass each ?

(b) How many people could you give a glass of wine if you had 32 bottles ?

13. A town, with a population of 144, is under seige. It has enough food to last the people 24 days.

If they take in an extra 48 people how long will the food supply now last ?

14. A gang of 36 dockers can unload a ship in 8 hours. If 4 of the dockers are ill, and don't show

S2/3 Revision Pack 2 for work, how long will it now take to unload the ship ?

Ratio 1 (worked examples)


Try these questions. Once you have completed this sheet try the questions on the next sheet.

1. (a) Divide £50 in the ratio 7:3 . (b) Divide 80kg in the ratio 7:3 .

(c) Divide £35 in the ratio 2:5 . (d) Divide 240 g in the ratio 1:4 .

2. (a) Three boys, Harry, James and Bill divide £120 in the ratio 8:3:1 .

How much does each boy get ?

(b) Three girls, Susan, Beth and Jill divide £56 in the ratio 7:5:2 .

How much does each girl get ?

3. Graeme and Fred invest £3400 in a new company.

(a) If the money each of them put in was in the ratio 3 : 7 , how much

did Fred invest in the new company ?

(b) They decide to split the profits in the same ratio as their investment.

If they made £6200 profit, how much of the profit will Graeme get ?

4. The ratio of boys : girls in a class is 4 : 5. If there are 27 pupils in the class, how many

girls are there.

5. (a) In a piece of jewellery the ratio of gold to silver is 5 : 2.

If the jewellery contains 40 grammes of gold, what weight of silver does it contain ?

(b) An lottery win was shared between three brothers, Dave, Frank and Pat, in the ratio 1 : 3 : 4.

If Pat received £824, how much did each of the other two brothers receive ?

6. Two farmers, Bill and Dan, decided to split a herd of cows in the ratio 5 : 7.

(a) If Dan's share was 42 cows, how many cows did Bill get ?

(b) How many cows were there altogether ?

(c) A third farmer, George, came along and the three farmers decided to split the herd in

the ratio (B : D : G) 3 : 4 : 1.

How many cows will each farmer get

£


Ratio (2)


1. (a) Divide £48 in the ratio 5:3 . (b) Divide £100 in the ratio 3:7 .

(c) Divide £56 in the ratio 6:1 . (d) Divide £50 in the ratio 1:4 .

(e) Divide £120 in the ratio 3:5 . (f) Divide £75 in the ratio 7:8 .

(g) Divide £36 in the ratio 5:4 . (h) Divide £240 in the ratio 7:5 .

2. (a) Three boys divide £88 in the ratio 7:3:1 . How much does each boy get ?

(b) Three girls divide £48 in the ratio 11:3:2 . How much does each girl get ?

(c) Three men divide £60 in the ratio 5:4:3 . How much does each man get ?

(d) Three girls divide £96 in the ratio 5:2:1 . How much does each girl get ?

3. John and David inherit £3400. If they divide the money in the ratio 2 : 3 , how much

does each person receive.

4. The ratio of boys : girls in a class is 3 : 5. If there are 32 pupils in the class, how many

girls are there.

5. The ratio of sand : cement in a certain concrete is 7 : 4. If a cement mixer has been filled with

33 bags, how many of the bags were sand ?

6. (a) The ratio of cats : dogs in an animal hospital is 1 : 5.

If there are 8 cats, how many dogs are there ?

(b) In a school show the ratio of girls : boys is 2 : 1.

If there are 24 girls, how many boys are there ?

(c) In a necklace the ratio of diamonds : emeralds is 3 : 4.

If there are 16 emeralds, how many diamonds are there ?

(d) An estate was shared between three brothers, Tom, John and Dave, in the ratio 2 : 3 : 5.

If Tom received £2400, how much did each of the other two brothers receive ?

7. Three friends, Xena,Gabrielle and Joxar, have found a treasure chest full of gold coins.

They decide to split the coins in the ratio 5 : 3 : 1.

(a) If Gabrielle was to receive 24 coins, how many coins would the others get ?

(b) How many coins are there altogether ?

(c) Before they can share out the coins, Calisto arrives, and persuades

the friends to split the coins in the ratio (X : G : J : C) 9 : 5 : 4 : 6 .

How many coins will each person now receive ?


Similarity and Area

1. For each pair of pictures below i) State the enlargement scale factor for the lengths (kL).

ii) State the scale factor for the areas (kA).

iii) Calculate the area of the larger shape.

(a) (b)

(c) (d)

(e) (f)

2. For each pair of pictures below i) State the reduction scale factor for the lengths (kL).

ii) State the scale factor for the areas (kA).

iii) Calculate the area of the smaller shape.

(a)

(b)

(c)

(d)

16cm2

5cm

10cm

12mm

36mm

12mm 8mm

14cm

33.6cm

6cm 24cm

16cm

28.8cm

96mm2

40mm2

50cm2

22cm2 120cm2

10cm 5cm 70cm2

76mm

19mm

3648mm2

30cm

24cm

150cm2

24mm 18mm

400mm2


.).1(818

6143

pdtomm

dC

The Circle (1)


The Circumference of a Circle

The circumference of a circle is the distance around the outside of the circle

Example 1 .... Calculate the circumference of Example 2 .... Calculate the circumference of

the circle with diameter 18cm. the circle with radius 3mm.

working ........ working ........ If r = 3 then d = 6

1. Calculate the circumference of the circle with .......

(a) diameter 12 cm (b) diameter 14 mm (c) diameter 42 m (d) d = 4 cm

(e) d = 30 cm (f) d = 86 mm (g) d = 80 m (h) d = 17 cm

2. Calculate the circumference of the circle with .......

(a) radius 11 cm (b) radius 23 mm (c) radius 51 m (d) radius 2 cm

(e) r = 14 mm (f) r = 12 cm (g) r = 26 m (h) r = 9 cm

3. Calculate the circumference of each circle below.

4. Calculate the circumference of each circle below.

.).1(256

18143

pdtocm

dC

10cm 36mm 216 cm 42 cm

Remember :

)143( dC

. . . 13mm 7cm

2.7m

(a) (b) (c) (d)

(a) (b) (c)


.).1(9153

7143

2

2

2

pdtocm

rA

.).1(328

3143

2

2

2

pdtomm

rA

The Circle (2)


The Area of a Circle

The Area of a circle is the amount of flat space inside the circle

Example 1 .... Calculate the area of the Example 2 .... Calculate the area of

circle with radius 7cm. the circle with diameter 6mm.

working ........ working ........ If d = 6 then r = 3

1. Calculate the area of the circle with .......

(a) radius 12 cm (b) radius 21 mm (c) radius 51 m (d) radius 6 cm

(e) r = 15 mm (f) r = 12 cm (g) r = 26 m (h) r = 11 cm

2. Calculate the area of the circle with .......

(a) diameter 14 cm (b) diameter 28 mm (c) diameter 41 m (d) d = 6 cm

(e) d = 40 cm (f) d = 47 mm (g) d = 36 m (h) d = 15 cm

3. Calculate the area of each circle below.

4. Calculate the area of each circle below.

Remember :

)143(2 rA

. . . 18cm 26cm

1.5m

12cm 24mm 22cm 9cm

(a) (b) (c)

(a) (b)

(c) (d)


16cm

11cm

20mm

14mm

The Circle (3)

1. A circle has a diameter of 814 cm .

Calculate (a) The circumference of the circle. (b) The area of the circle.

2. A circle has a radius of 15 m .

Calculate (a) The area of the circle. (b) The circumference of the circle.

3. (a) Calculate the area of the rectangular

steel plate shown opposite.

(b) A hole of radius 6cm is drilled through the plate.

Calculate the shaded area

4. Calculate the shaded area in each shape below.

5. Calculate the area of each shape .

24cm

10cm

6cm 8mm

8m

6m

18cm

15cm

8mm

4m

(a) (b)

(a) (b)


Angles and Circles

marks the centre of each circle

1. Calculate the size of each of the

angles marked with letters in the

diagrams below.

2. Find the angles marked with letters.

LOOK for .................. * Isosceles triangles

* Angles in a triangle add up to 180o

* Angle in a semicircle is a right angle

* Angle between a tangent and a radius is 90o

3. Find the size of each lettered angle in the diagrams below :

Theorem 1 The angle in a semicircle is a right angle.

Theorem 2 A tangent meets a radius at right angles.

.

. . . . 33o

40o

72o

64o

50o a

b

c

d

e

f

g

h

. . . .

35o

25o

60o 24o

40o

30o

a

b

c

d e f

g

. . .

. .

68o

50o

20o

70o

a

b c

d

e

f

g

h i

j

k

l


Statistics - Simple Probability

1. Use the words below to describe the probability of each statement happening. (It's your choice?)

(a) People will holiday in space within the next 10 years.

(b) You can hold your breath for 10 minutes.

(c) You will watch TV tonight.

(d) Your teacher will be boring next week.

(e) You are reading this question.

(f) The next baby born in Scotland is a boy.

2. Five coloured beads are placed in a bag, two are red and three are green.

If a bead is drawn from the bag at random, calculate the probability that it is :

(a) green (b) red (c) red or green (d) blue?

3. In throwing an ordinary die, what is the probability of obtaining :

(a) a one (b) an even number (c) more than a two

(d) a factor of nine (e) less than one?

4. If the spinner is spun, calculate :

(a) P(7) (b) P(1) (c) P(even)

(d) P(odd) (e) P(prime) (f) P(less than 4)

(g) P(6) (h) P(factor of 24) (i) P(less than 10)

5. A letter is chosen at random from the word STATISTICS . Write, as a decimal fraction :

(a) P(A) (b) P(I) (c) P(not a T) (d) P(vowel) (e) P(not a vowel)

6. The probability of a bus arriving on time at a certain bus stop is 4

1 .

(a) What is the probability of it not arriving on time?

(b) Out of 64 buses arriving at that bus stop, how many are likely to be on time?

7. The probability of a cat having a litter of more than eight kittens is 240 .

(a) What is the probability of a cat having a litter of eight or less kittens?

(b) Out of 75 female cats, how many would you expect to have a litter of more than eight kittens?

8. There are seven blue beads and 6 yellow beads in a bag. A blue bead is drawn from the bag and not

impossible likely

certain even chance unlikely

S2/3 Revision Pack 2 replaced. What is the probability that the next bead drawn is also blue?

Surface Area & Volume of a Cuboid

For each of the following solids below, calculate (i) its surface area (A);

(ii) its volume (V).

(a) (b)

(c)

(d)

(e)

(g)

(f)

8cm

5cm

4cm

3cm

1cm

4cm

1cm

7cm 2cm

4cm

CUBE

12mm

7mm

4mm

8mm 16cm CUBE

6cm

10cm


4.6m

Volume of a Prism

Calculate the volume of each prism below.

3.2m

6m

3m

4m

2.8m 3.4m

5m

18cm

28cm

30cm

12cm

10cm

16cm

8cm

5.4cm

3cm

4cm 11cm

1.5m

0.9m

0.6m

0.3m

0.5m 1.2m

(a) (b)

(c) (d)

(e)

(f)

rectangular hole measuring 0.2m by 0.4m


Formulae (1)

1. A formula is given as 22 pE .

Find the value of E when .... i) p = 2 ii) p = 3 iii) p = 6 iv) p = 1 .

2. A formula is given as 62 eT .

Find the value of T when .... i) e = 3 ii) e = 4 iii) e = 8 iv) e = 2.

3. A formula is given as 236 rQ .

Find the value of Q when .... i) r = 3 ii) r = 4 iii) r = 6 iv) r = 1 .

4. A formula is given as 245 hG .

Find the value of G when .... i) h = 4 ii) h = 6 iii) h = 2 iv) h = 7 ?

5. A formula is given as 4)(2 2 sT .

Find the value of T when .... i) s = 3 ii) s = 5 iii) s = 10 iv) s = 1 .

6. A formula is given as )(325 2xW .

Find the value of W when .... i) x = 2 ii) x = 6 iii) x = 8 iv) x = 7 .

7. A formula is given as 62 2 pL .

Find the value of L when .... i) p = 2 ii) p = 3 iii) p = 5 iv) p = 10 .

8. A formula is given as 122 ttH .

Find the value of H when .... i) t = 2 ii) t = 4 iii) t = 3 iv) t = 10 .

9. A formula is given as 632 kkT .

Find the value of T when .... i) k = 3 ii) k = 6 iii) k = 2 iv) k = 1 ?

All working must be shown.


Formulae (2)

1. A formula is given as qpE 3 .

Find the value of E when .... i) p = 4 and q = 2 ii) p = 6 and q = 3

iii) p = 5 and q = 1 iv) p = 3 and q = 6

2. A formula is given as edT 32 .

Find the value of T when .... i) d = 5 and e = 2 ii) d = 6 and e = 3

iii) d = 8 and e = 5 iv) d = 12 and e = 8

3. A formula is given as srF 27 .

Find the value of F when .... i) r = 2 and s = 5 ii) r = 3 and s = 10

iii) r = 4 and s = 4 iv) r = 6 and s = 20

4. A formula is given as tauV .

Find the value of V when .... 42,3) tandaui

73,6) tandauii

108,2) tandauiii

5. A formula is given as tpC 420 .

Find the value of C when .... 34) tandpi

25) tandpii

508) tandpiii

6. A formula is given as cbaW 3 .

Find the value of W when .... 46,4) candbai

32,5) candbaii

84,6) candbaiii

7. A formula is given as hbblhlA 222 .

Find the value of A when .... 23,6) handbli

64,5) handblii

All working must be shown.

S2/3 Revision Pack 2 47,8) handbliii

Pythagoras' Theorem (Practical Questions)


Answers should be rounded to 1-decimal place where necessary.

1. A ladder leans against a wall as shown in the diagram

opposite.

From the information given calculate the length of the ladder.

2. Calculate the perimeter of each shape below.

3. Blackpool light decorations are suspended above the street by wire cables as shown below.

Calculate the total length of cable in each diagram.

4. Three trees are situated as shown with angle PQR = 90o.

Calculate the distance between the trees Q and R.

(careful !)

5. Calculate the total length of each mountain bike ramp shown below.

6m

3m

8cm

12cm

17cm

5m

13m

7m

12m

4m 4.6m

3m 3.8m

6m 4.6m

16m

12m

P

Q

R

4m


Scientific Notation (Basic Practice)

1. Write each of the following numbers in scientific notation.

(a) 2 300 (b) 425 000 (c) 120 (d) 67 000 000

(e) 500 (f) 41 000 (g) 84 (h) 5 000 000 000

(i) 3 450 000 (j) 1 903 (k) 346 000 000 (l) 28 000 000 000 000 000

(m) 463 (n) 7121 (o) 4 007 (p) 6

2. For each of the following numbers i) write it out in figures ;

ii) write it in scientific notation.

(a) 4 thousand (b) 3 million (c) 20 thousand (d) 16 million

(e) 200 million (f) 150 thousand (g) 42 million (h) 218 million

(i) sixteen thousand four hundred (j) one million one hundred and fifty thousand

3. Write each of the following numbers in scientific notation.

(a) 00430 (b) 0000210 (c) 0640 (d) 0000007650

(e) 0005020 (f) 03090 (g) 0000090 (h) 00080

(i) 000050020 (j) 023450 (k) 650 (l) 400000000050

(m) 060670 (n) 00000020 (o) 55080 (p) 0021300000000000

4. Write each of the following numbers out in full.

(a) 31062 (b) 210415 (c) 410457

(d) 510812 (e) 71046 (f) 01026

(g) 110342 (h) 610125 (i) 2100037

(j) 91032 (k) 4100096 (l) 12109

5. Write each of the following as an ordinary number.

(a) 21034 (b) 410573 (c) 11091

(d) 31089 (e) 510047 (f) 2106

3.5m

2.7m

9m

5m 2.6m

1.7m

8m


(g) 7108 (h) 110225 (i) 5100072

(j) 91087 (k) 41014 (l) 610450


Revision Pack Answers

Gradients and Straight Lines (1) - Answers

1. (a) 1

2 (b) 4 (c)

3

10 (d) 6 (e)

3

4 (f)

1

8

2. (a) 5

6 (b)

1

3 (c) 1 (d)

2

5 (e) 2 (f)

3

4

(g) 3

2 (h)

1

3 (i)

4

3 (j)

4

3


1. (a)

x 0 1 2 3 4 5

y 0 2 4 6 8 10

(b)

2. (a)

x 0 1 2 3 4 5

y 0 3 6 9 12 15

(b)

0 1 2 3 4 5 6 7 8 9

1

2

3

4

5

6

7

8

9

10

x

y

0 1 2 3 4 5 6 7 8 9

1

2

3

4

5

6

7

8

9

10

x

y


Gradients and Straight Lines (2) - Answers (continued)

3. (a)

x 0 2 4 6 8 10

y 0 1 2 3 4 5

(b)

4. (a)

x 0 3 6 9 12

y 0 1 2 3 4

(b)

5. (a)

x 0 1 2 3 4 5 6

y 0 1 2 3 4 5 6

(b)

0 1 2 3 4 5 6 7 8 9

1

2

3

4

5

6

7

8

9

10

x

y

0 1 2 3 4 5 6 7 8 9

1

2

3

4

5

6

7

8

9

10

x

y

0 1 2 3 4 5 6 7 8 9

1

2

3

4

5

6

7

8

9

10

x

y



1. (a)

x 0 1 2 3 4 5

y 2 3 4 5 6 7

(b)

2. (a)

x 0 1 2 3 4 5

y 1 3 5 7 9 11

(b)

3. (a)

x 0 2 4 6 8 10

y 4 5 6 7 8 9

(b)

0 1 2 3 4 5 6 7 8 9

1

2

3

4

5

6

7

8

9

10

x

y

0 1 2 3 4 5 6 7 8 9

1

2

3

4

5

6

7

8

9

10

x

y

0 1 2 3 4 5 6 7 8 9

1

2

3

4

5

6

7

8

9

10

x

y


Gradients and Straight Lines (3) - Answers (continued)

4. (a)

x 0 4 8 12

y 5 6 7 8

(b)

5. (a)

x 1 2 3 4 5

y 1 4 7 10 13

(b)

Trigonometry (1) – Answers

1. (a) 158o (b) 513o (c) 305o (d) 648o

(e) 310o (f) 264o

2. (a) 414o (b) 430o (c) 342o (d) 543o

(e) 45o (f) 374o (g) 456o (h) 349o

(i) 145o

0 1 2 3 4 5 6 7 8 9

1

2

3

4

5

6

7

8

9

10

x

y

0 1 2 3 4 5 6 7 8 9

1

2

3

4

5

6

7

8

9

10

x

y

S2/3 Revision Pack 2 Trigonometry (2) - Answers

1. (a) 85 (b) 49 (c) 53 (d) 107

(e) 122 (f) 42

2. (a) 63 (b) 27 (c) 76 (d) 397

(e) 115 (f) 244

Trigonometry (3) - Answers

(a) 387o (b) 153o (c) 101 (d) 87

(e) 72 (f) 466o (g) 229 (h) 310o

(i) 325o (j) 720o (k) 62 (l) 419o

(m) 482o (n) 831

Trigonometry (4) - Answers

1. (a) 140o N (b) 218o Y (c) 189o N (d) 179o N

(e) 199o N (f) 202o Y (g) 196o N (h) 209o Y

2. (a) 242o Y (b) 193o N (c) 213o N (d) 294o N

(e) 258o Y (f) 307o N (g) 292o N (h) 213o N

Fractions, Decimals and Percentages (1) - Answers

1. (a) £32 (b) 13kg (c) £520 (d) 36cm

(e) £85 (f) 455g (g) £1064 (h) 405kg

(i) £468 (j) £425 (k) 369mm (l) £081

(m) £1397 (n) 270 tonnes (o) 75kg

2. (a) £2340 (b) 162g (c) £585 (d) 252kg

(e) £170 (f) 1785cm (g) £1216 (h) £17

(i) £572 (j) 360g (k) £200 (l) £33840

(m) £1170 (n) £0.48 (o) 84 tonnes

3. (a) £475 (b) £305 (c) £114 (d) 42p

(e) £595 (f) 21p (g) £220 (h) £1365

(i) £4173 (j) £279 (k) £023 (l) 30p

(m) £109 (n) £036 (o) 55p

4. (a) 80% (b) 75% (c) 28% (d) 70%

(e) 17% (f) 95% (g) 56% (h) 27%

(i) 78% (j) 42% (k) 13% (l) 62%

(m) 13% (n) 43% (o) 19% (p) 10%

(q) 51% (r) 21%

5. (a)

Maths English Tech Science Art History French

75% 89% 62% 69% 83% 68% 66%

(b) English (c) Tech

S2/3 Revision Pack 2 Fractions, Decimals and Percentages (2) - Answers

1. (a) £28750 (b) 184kg (c) 2875cm (d) £4140

(e) 2415g (f) 2415oC (g) £920 (h) £4025

2. (a) £200 (b) 128kg (c) 20cm (d) £2880

(e) 1680g (f) 168oC (g) £640 (h) £2800

3.

Name Increase New Wage

John Hughes £920 £23920

Steven Higgins £1008 £17808

Susan Marshal £840 £21840

Stewart Aitken £290 £14790

Pamela Grant £1260 £37260

Neil McShane £1350 £23850

James Mackie £1880 £25380

Lorna Graham £945 £21945

Pat Lavery £2340 £49140

4. (a) 3

560% (b)

4

757% (c)

1

250% (d)

1

425%

(e) 11

1669% (f)

2

540% (g)

2

729%

5. (a) 36% (b) 56% (c) 43%

6. (a) 20% (b) 2% (c) 5%

Fractions, Decimals and Percentages (3) - Answers

1. (a) £4025 (b) £2590 (c) £7980 (d) £1190

(e) £11375 (f) £2345

2. (a) £27025 (b) £17390 (c) £53580 (d) £7990

(e) £76375 (f) £15745

3. (a) £92 (b) £2392 (c) £9568

4. (a) £1105 (b) £23205 (c) £116025

5. £84872 6. £89888 7. £137957 8. £686024


Solving Equations (1) - Answers

1. (a) x = 2 (b) t = 4 (c) m = 3 (d) y = 6

(e) a = 2 (f) d = 4 (g) h = 4 (h) p = 7

(i) x = 8 (j) a = 2 (k) x = 4 (l) y = 3

2. (a) x = 6 (b) t = 5 (c) m = 8 (d) y = 5

(e) a = 6 (f) d = 7 (g) h = 6 (h) p = 3

(i) x = 9 (j) a = 2 (k) x = 11 (l) y = 4

3. (a) x = 3 (b) t = 4 (c) m = 4 (d) y = 4

(e) a = 6 (f) d = 3 (g) h = 13 (h) p = 3

(i) x = 2 (j) a = 3 (k) x = 10 (l) y = 7

(m) p = 4 (n) h = 2 (o) x = 4 (p) y = 2

(q) d = 8 (r) a = 6 (s) m = 6 (t) x = 18

(u) x = 3

2


1. (a) x = 5 (b) t = 6 (c) m = 5 (d) y = 2

(e) a = 4 (f) d = 3 (g) h = 6 (h) p = 15

(i) u = 4 (j) y = 2 (k) x = 7 (l) y = 2

2. (a) x = 6 (b) t = 6 (c) m = 4 (d) y = 4

(e) y = 3 (f) x = 7 (g) h = 7 (h) r = 5

(i) x = 5 (j) a = 2 (k) x = 15 (l) y = 5

3. (a) x = 5 (b) t = 5 (c) m = 7 (d) m = 8

(e) k = 8 (f) d = 5 (g) h = 14 (h) y = 2

(i) x = 3 (j) x = 6 (k) x = 9 (l) y = 4

(m) p = 1 (n) h = 3 (o) x = 12 (p) y = 5

(q) k = 12 (r) a = 11 (s) a = 3 (t) x = 21

(u) x = -2


1. (a) c = 3 (b) e = 2 (c) f = 2 (d) g = 1

(e) w = 4 (f) h = 9 (g) a = 3 (h) p = 6

(i) x = 5 (j) y = 5 (k) k = 4 (l) z = 1

(m) e = 4 (n) w = 2 (o) r = 6

2. (a) c = 2 (b) e = 1 (c) f = 2 (d) t = 3

(e) g = 2 (f) w = 1 (g) h = 2 (h) p = 5

(i) y = 3 (j) k = 3 (k) z = 2 (l) u = 1

(m) e = 3 (n) w = 1 (o) r = 5

3. (a) a = 3 (b) x = 9 (c) m = 3 (d) d = 2

(e) h = 1 (f) y = 7 (g) a = 6 (h) x = 2

(i) a = 24 (j) d = 6 (k) x = 5 (l) u = 7

(m) w = 16 (n) x = 6 (o) x = 7

S2/3 Revision Pack 2 Equations (Extension Examples) - Answers

1. (a) x = 6 (b) t = 3 (c) m = 3 (d) v = 8

(e) d = 5 (f) y = 0 (g) x = 1 (h) m = 3

(i) v = 0

2. (a) x = 3 (b) m = 3 (c) y = 7 (d) t = 7

(e) a = 5 (f) x = 4 (g) y = 4 (h) p = 4

(i) r = 5 (j) x = 2 (k) a = 2 (l) d = 2

(m) c = 3 (n) x = 3 (o) x = 1 (p) x = 2

(q) v = 2 (r) x = 3

3. (a) x = 1 (b) x = 3 (c) y = 2 (d) v = 3

(e) h = 3 (f) a = 2 (g) x = 3 (h) m = 3

(i) e = 4 (j) x = 2 (k) y = 2 (l) a = 1

(m) x = 1 (n) k = 2 (o) c = 4

Statistics - Stem and Leaf Diagrams - Answers

1. (a) 16 plants (b) 63cm (c) 56cm, 57cm, 59cm (d) 14

2. (a) (b) £75

3. (a) 45 days (b) last year 28 days; this year 17 days

(c) Absence rate appears to have decreased since last year. or equivalent.

4. (a)

(b) “Both boxes are very poor. Brighto is possibly the better of the two.” or equivalent.

6

7

8

9

6 8

1 3 5 5 5 8 9

0 1 3

2

Cost of CD Player (£)

n = 13 7 4 represents £74

Number of Matches per box

n = 14

2

3

4

5

6

9

8 9

0 2 9 9

1 2 6 7 8

2 4

6 7 8 9 9

1 5 6 7 8

0 2 8

1

n = 14 4 8 represents 48 matches

Brighto Sparky

S2/3 Revision Pack 2 Statistics - Frequency Tables (Mean, Median & Mode) - Answers

1. (a)

Score (x) Frequency (F) F x

1 7 7

2 5 10

3 1 3

4 13 52

5 6 30

6 3 18

7 3 21

8 6 48

9 4 36

10 2 20

Totals 50 245

(b) Mean = 49 or 5 (c) Median = 4; Mode = 4

2. (a) (i)


5 3 15

6 5 30

7 4 28

8 7 56

9 8 72

10 2 20

11 1 11

Totals 30 232

(ii) Mean = 77 or 8 (iii) Median = 8; Mode = 9

(b) (i)


12 1 12

13 2 26

14 2 28

15 12 180

16 4 64

17 6 102

18 9 162

19 3 57

20 1 20

Totals 40 651



Statistics - Frequency Tables (Mean, Median & Mode) - Answers (continued)

2. (c) (i)


20 12 240

21 13 273

22 13 286

23 8 184

24 15 360

25 9 225

Totals 70 1568


Statistics - Scatter Diagrams - Answers

1. SET 1 SET 2

0

2

4

6

8

10

0 5 10

0

2

4

6

8

0 5 10 15

Strong positive correlation Strong negative correlation

SET 3 SET 4

0

2

4

6

8

10

12

0 5 10

0

2

4

6

8

10

0 5 10 15

No correlation Weak positive correlation


Statistics - Scatter Diagrams - Answers (continued)

SET 5 SET 6

0

1

2

3

4

5

6

0 5 10 15

0

2

4

6

8

10

0 5 10

Weak negative correlation Strong positive correlation

2. Pupil’s own line of best fit.

Best Buy - Answers

1. (a) 3 litres (b) 15 litres (c) 550g (d) 750g

(e) 07 litres (f) 500ml (g) 08kg (h) 600g

(i) Twin Pack (j) 550ml

Direct Proportion - Answers

1. (a)

Time (t) hours 0 1 2 3 4 5 6 7

Distance (D) km 0 5 10 15 20 25 30 35

(b) Graph of above

(c) Straight line through origin

2. (a) 600g (b) 150g (c) 450g

3. (a) 42p (b) £126 (c) £462

4. 23kg

5. (a) £702 (b) 798mm (c) 228mm (d) 9kg

6. (a) £7338 (b) £5324

7. (a) £1320 (b) £63360

S2/3 Revision Pack 2 8. £258 9. 27 litres 10. 9 books

11. £124

Inverse Proportion - Answers

1. 8 days 2. 8 days 3. 6 days 4. 2 days



13. 4 days 14. 25 days

Proportion (Direct and Inverse Mixed Exercise) - Answers

1. (a) 4 units (b) 32 units (c) 80 units

2. (a) 13 km (b) 78 km (c) 1625 km

3. £3920 4. £2414 5. 16 days 6. 7 days

7. 710 km 8. £104 9. £10880 10. 5 days

11. 5 hours

12. (a) 16 bottles (b) 112 people

13. 18 days 14. 9 hours

Ratio 1 (worked examples) - Answers

1. (a) £15 : £35 (b) 24kg : 56kg

(c) £25 : £10 (d) 192g : 48g

2. (a) Harry £10; James £30; Bill £80

(b) Susan £8; Beth £20; Jill £28

3. (a) £2380 (b) £1860

4. 15 girls

5. (a) 16g (b) Dave £206; Frank £618

6. (a) 30 cows (b) 72 cows (c) Bill 27; Dan 36; George 9

S2/3 Revision Pack 2 Ratio (2) - Answers

1. (a) £18:£30 (b) £70:£30 (c) £8:£48 (d) £40:£10

(e) £75:£45 (f) £40:£35 (g) £16:£20 (h) £100:£140

2. (a) £8:£24:£56 (b) £6:£9:£33 (c) £15:£20:£25 (d) £12:£24:£60

3. John £1360; David £2040

4. 20 girls

5. 21 bags of sand

6. (a) 40 dogs (b) 12 boys (c) 12 diamonds

(d) John £3600; Dave £6000

7. (a) Xena 40 coins; Joxar 8 coins

(b) 72 coins

(c) Xena 27 coins; Gabrielle 15 coins; Joxar 12 coins; Calisto 18 coins.

Similarity and Area - Answers

1. (a) kL = 2; kA = 4; A = 64cm2 (b) kL = 3; kA = 9; A = 864mm2

(c) kL = 15; kA = 225; A = 90mm2 (d) kL = 24; kA = 576; A = 288cm2

(e) kL = 4; kA = 16; A = 352cm2 (f) kL = 18; kA = 324; A = 3888cm2

2. (a) kL = 05; kA = 025; A = 175cm2 (b) kL = 025; kA = 00625; A = 288mm2

(c) kL = 08; kA = 064; A = 96cm2 (d) kL = 075; kA = 05625; A = 225mm2

The Circle (1)

1. (a) 377cm (b) 440mm (c) 75m (d) 126cm

(e) 942cm (f) 214mm (g) 2513m (h) 534cm

2. (a) 691cm (b) 1445mm (c) 94m (d) 126cm

(e) 880mm (f) 132cm (g) 390m (h) 565cm

3. (a) 314cm (b) 1131mm (c) 509cm (d) 75cm

4. (a) 817mm (b) 440cm (c) 170m

The Circle (2)

1. (a) 4524cm2 (b) 13854mm2 (c) 71m2 (d) 1131cm2

(e) 7069mm2 (f) 139cm2 (g) 1208m2 (h) 3801cm2

2. (a) 1539cm2 (b) 6158mm2 (c) 15m2 (d) 283cm2

(e) 12566cm2 (f) 430mm2 (g) 10179m2 (h) 1767cm2

3. (a) 10179cm2 (b) 21237cm2 (c) 71m2


4. (a) 1131cm2 (b) 4524mm2 (c) 3801cm2 (d) 636cm2

The Circle (3)

1. (a) 465cm (b) 1720cm2

2. (a) 817m2 (b) 320m

3. (a) 240cm2 (b) 1269cm2

4. (a) 1477cm2 (b) 1795mm2

5. (a) 446m2 (b) 3972cm2

Angles and Circles

1. a = 57o b = 50o c = 18o d = 45o e = 90o f = 26o

g = 40o h = 50o

2. a = 55o b = 65o c = 30o d = 66o e = 57o f = 60o

g = 20o

3. a = 90o b = 22o c = 68o d = 40o e = 40o f = 80o

g = 30o h = 20o i = 70o j = 110o k = 35o l = 55o

Statistics - Simple Probability - Answers

1. Pupils’ own choices.

2. (a) 35

(b) 25

(c) 1 (d) 0

3. (a) 16

(b) 12

(c) 23

(d) 13

(e) 0

4. (a) 18

(b) 14

(c) 38

(d) 58

(e) 12

(f) 12

(g) 0 (h) 34

(i) 1

5. (a) 01 (b) 02 (c) 07 (d) 03

(e) 07

6. (a) 34

(b) 16 buses

7. (a) 076 (b) 18 cats

8. (a) 05

S2/3 Revision Pack 2 Surface Area and Volume of a Cuboid - Answers

(a) A = 184cm2; V = 160cm3 (b) A = 38cm2; V = 12cm3

(c) A = 46cm2; V = 14cm3 (d) A = 96cm2; V = 64cm3

(e) A = 320mm2; V = 336mm3 (f) A = 384mm2; V = 512mm3

(g) A = 632cm2; V = 960cm3

Volume of a Prism

(a) V = 7296m3 (b) V = 62m3 (c) V = 77562cm3

(d) V = 28248cm3 (e) V = 3168cm3 (f) V = 0912m3

Formaulae (1)

1. (i) E = 6 (ii) E = 11 (iii) E = 38 (iv) E = 3

2. (i) T = 15 (ii) T = 22 (iii) T = 70 (iv) T = 10

3. (i) Q = 27 (ii) Q = 20 (iii) Q = 0 (iv) Q = 35

4. (i) G = 29 (ii) G = 9 (iii) G = 41 (iv) G = -4

5. (i) T = 22 (ii) T = 54 (iii) T = 204 (iv) T = 6

6. (i) W = 37 (ii) W = 133 (iii) W = 217 (iv) W = 172

7. (i) L = 2 (ii) L = 12 (iii) L = 44 (iv) L = 194

8. (i) H = 9 (ii) H = 25 (iii) H = 16 (iv) H = 121

9. (i) T = 12 (ii) T = 48 (iii) T = 4 (iv) T = -2

Formulae (2)

1. (i) E = 14 (ii) E = 21 (iii) E = 16 (iv) E = 3

2. (i) T = 4 (ii) T = 3 (iii) T = 1 (iv) T = 0

3. (i) F = 4 (ii) F = 1 (iii) F = 20 (iv) F = 2

4. (i) V = 11 (ii) V = 27 (iii) V = 82

5. (i) C = 68 (ii) C = 60 (iii) C = 36

6. (i) W = 12 (ii) W = 1 (iii) W = 0

7. (i) A = 72 (ii) A = 148 (iii) A = 232

Pythagoras’ Theorem

1. 67m

2. P = 464cm; P = 464m

3. 48m or 49m depending on rounding; 63m or 64m depending on rounding

4. 106m


5. 99m; 84 or 85m depending on rounding.

Scientific Notation

1. (a) 23 103 (b) 425 105 (c) 12 102 (d) 67 107

(e) 5 102 (f) 41 104 (g) 84 101 (h) 5 109

(i) 345 106 (j) 1903 103 (k) 346 108 (l) 28 1016

(m) 634 101 (n) 1217 102 (o) 4007 103 (p) 6 100

2. (a) 4000 = 4 103 (b) 3 000 000 = 3 106

(c) 20 000 = 2 104 (d) 16 000 000 = 16 107

(e) 200 000 000 = 2 108 (f) 150 000 = 15 105

(g) 2 400 000 = 24 106 (h) 8 210 000 = 821 106

(i) 16 400 = 164 104 (j) 1 150 000 = 115 106

3. (a) 43 10-3 (b) 21 10-5 (c) 64 10-2 (d) 765 10-7

(e) 502 10-4 (f) 309 10-2 (g) 9 10-6 (h) 8 10-4

(i) 5002 10-5 (j) 2345 10-2 (k) 65 10-1 (l) 54 10-10

(m) 6067 10-2 (n) 2 10-7 (o) 5508 10-1 (p) 213 10-13

4. (a) 2600 (b) 541 (c) 74 500

(d) 281 000 (e) 64 000 000 (f) 62

(g) 234 (h) 5 120 000 (i) 7003

(j) 2 300 000 000 (k) 60 090 (l) 9 000 000 000 000

5. (a) 0043 (b) 0000357 (c) 019

(d) 00098 (e) 00000704 (f) 006

(g) 00000008 (h) 0522 (i) 000002007

(j) 00000000078 (k) 00014 (l) 000045

Documents

Gradients and Straight Lines (1) - Dunblane High School · S2/3 Revision Pack 2 Gradients and Straight Lines (2) 1. A straight line has as its equation y 2x. (a) Copy and complete