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Whole numbers & Decimals Page 2

Percentages Page 3

Integers Page 4

Speed, Distance, Time Page 5

Calculations in Social Context Page 6

Scientific Notation Page 7

Algebra Page 8

Pythagoras Page 9

Statistics Pages 10 & 11

Ratio & Proportion Page 12

Straightline Page 13

Trigonometry Page 14

Angles Page 15

Probability Page 16

Circles Page 17

Volume Page 18

Patterns Page 19

National 4 Mathematics

Homework

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Homework 1: Whole Numbers & Decimals

Q1. Round to the nearest 10 :

(a) 268 (b) 25 093 (c) 2 981 [3 marks] Q2. Round to the nearest 100 :

(a) 34371 (b) 12 086 (c) 489 795 [3 marks] Q3. Round to 1 decimal place :

(a) 6·284 (b) 139·936 (c) 0·4839 [3 marks] Q4. Round to 2 decimal places :

(a) 3·6853 (b) 0·43535 (c) 2·7984 [3 marks] Q5. Partick Thistle played a testimonial match which attracted a crowd of 6694.

(a) The crowd was quoted in the local press to the nearest 100. What was this figure ? [1 mark] (b) The manager gave the crowd to the nearest 1000. How many did he say attended the game ? [1 mark]

Q6. Write down the answers to these:

(a) 10 x 6.32 (b) 0.073 x 100 (c) 43.17 x 1000 (d) 5.2 ÷ 10 (e) 571 ÷ 100 (f) 64120 ÷ 1000 (g) 14.21 ÷ 100 (h) 134.05 ÷ 1000

[8 marks] Q7. (a) 14.76 + 3.49 (b) 26.48 – 7.51 (c) 34.79 x 7 (d) 17.34 ÷ 3 (e) 19 – 5.75 (f) 231 x 53 [6 marks]

[Total 28 marks]

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Homework 2: Percentages

Q1. Write each percentage as a decimal (a) 25% (b) 45% (c) 75% (d) 15.8% [4 marks] Q2. Convert each of the following to fractions in their SIMPLEST form (a) 10% (b) 15% (c) 25% (d) 30% (e) 85% (f) 2% [6 marks] Q3. Which is greater in each pair? (a) 55% or 0.45 (b) 0.02 or 5% (c) 0.8 or 78% (d) 0.1 or 99% [4 marks] Q4. Write these as common fractions in their simplest form (a) 0.04 (b) 0.8 (c) 0.06 (d) 0.94 (e) 0.65 (f) 0.2 [6 marks] Q5. Express each fraction in decimal form

(a)

1

10 (b)

7

10 (c)

9

10 (d)

2

5 (e)

5

8 (f)

6

15 [6 marks] Q6. Calculate

(a) 10% of 230 (b) 30% of 450 (c) 25% of 488 (d) 171

2 % of 40 [8 marks] Q7. Tom scored 16 out of 35 in her French exam. He scored 22 out of 40 in his maths exam.

(a) Turn both scores into percentages. [3 marks] (b) In which exam did he do better? [1 mark]

Q8. The Smith family put £240 aside each fortnight for groceries. They spend 75% of this at

the supermarket.

(a) How much did they spend at the supermarket? [2 marks]

(b) For every £10 spent, the supermarket gives a gift voucher. How many vouchers do the Smith family receive? [2 marks]

[Total 42 marks]

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Homework 3: Integers

Q1. I had £11.60 in my bank account and wrote a cheque for £32.45.What will my new balance show? [1 mark] Q2. Find the following: (a) 8 + (-2) (b) 7 + (-5) (c) 10 + (-4) (d) 5 + (-5)

(e) (-3) - 5 (f) (-1) - 5 (g) (-4) - 4 (h) (-6) - 9

(i) (-5) + (-4) (j) (-3) + (-7) (k) (-7) + (-8) (l) (-8) + (-8) [12 marks]

Q3. A deep sea diver rose from a depth of -27 metres to a new depth of -9 metres. By how many metres has he risen? [1 mark]

Q4. (a) (-32) 4 (b) (-14) 7 (c) (-24) (-4) (d) (-35) (-7)

(e) 6 x (-4) (f) 9 x (-3) (g) (-2) x 4 (h) (-1) x 6

(i) (-2) x (-4) (j) (-3) x (-7) (k) (-4) x (-8) x (-2) [11 marks]

Q5. (a) Draw a 5 x 5 coordinate diagram, and plot the following points: A(2,3), B(3,-1),C(-3,-5) and D(-4,-1) [3 marks]

(b) What shape is ABCD? [1 mark] Q6. The table shows the points scored in rounds A,B and C of a game.

A B C Total Tom -4 2 -1 -3 Sam -1 7 3 Liam -5 0 2

(a) Write down the total scored by Sam. [1 mark]

(b) Write down the total scored by Liam. [1 mark]

(c) Mary scored a total of 6. By how many points did Mary beat Tom? [1 mark]

[Total 32 marks]

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Homework 4: Speed, Distance and Time Q1. Change these 12 hour clock times to 24 hour clock times:

(a) 5.20 am (b) 8.45 pm (c) 12pm (d) 10.25 am (e) 12 am [5 marks] Q2. Change these 24 hour clock times to 12 hour clock times:

(a) 15 40 (b) 02 12 (c) 12 20 (d) 00 45 (e) 23 27 [5 marks] Q3. The Christmas show started at 7.10 pm and lasted 1 hour 45 minutes.

(a) When did it end? [1 mark] (b) Sarah and her family arrived home at 9.35 pm.

How long did it take them to travel home? [1 mark] Q4. A train has an average speed of 50mph for 300 miles. How long does the train take to arrive at its destination? [2 marks] Q5. Susan travels 540km in 6 hours. What is her average speed? (km/hr) [2 marks] Q6. A is the point (1,3) and B is the point (7,5). Draw the line on a coordinate diagram and use Pythagoras to find the length of the line AB. [3 marks] Q7. The graph above shows Tom’s car journey to visit a friend. He stopped to pick up some shopping on his way.

(a) How far did Tom travel before stopping at the shops? [1 mark] (b) How long did he stop for? [1 mark] (c) Calculate Tom’s average speed on his journey home. [2 marks] Q8. Use your calculator to change these times to decimal form:

(a) 15 minutes (b) 48 minutes (c) 20 minutes (d) 1 hour 30 minutes [4 marks]

[Total 27 marks]

Distance from home (km)

30 60 90 120 150

20

0

40

Time (minutes)

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Homework 5: Calculations in Social Context Q1. Howard borrows £15, 000 to improve his shop. He takes the loan out for 18 months. His monthly repayment is £60 for each £1000 borrowed. Calculate:

(a) the monthly repayment [2 marks] (b) the total repayment [2 marks] (c) the cost of the loan [1 mark]

Q2. Brian Hughes works for £5.10 an hour. He works 36 hours at the basic rate. On Saturday he does 9 hours at time and a half. On Sunday he works four hours at double time. (a) How much does he earn at: (i) the basic rate (ii) time and a half (iii) double time [3 marks] (b) How much does he earn in a week? [3 marks] Q3. Sam is paid £36 a day for working a 6 hour shift in a factory. One day last week Sam was asked to work 9 hours. (a) How much is Sam paid an hour? [2 marks] (b) How much is he paid for working the 9-hour shift? [2 marks] Q4. Five light bulbs cost £5.35. (a) Find the cost of one. (b) Find the cost of nine. [2 marks]

Q5. Calculate the annual Building insurance premium due by Mrs Jones, who owns a flat which is worth £48000, and she stays in the centre of Glasgow. [3 marks]

Q6. Calculate the annual Contents premium paid by the White family who live in Ayr. Their contents are worth £9 500. [3 marks] Q7. In order to buy a television using hire purchase a deposit of £100 is required along with 12 instalments of £25.50. Calculate the hire purchase price. [3 marks]

Q8.

The Peter family are going on holiday to France. They want to exchange £840 into euros. How many euros will they get? [3 marks]

[Total 29 marks]

Exchange Rates £1 buys:

USA 1.81 dollars France 1.32 euros

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Homework 6: Scientific Notation Q1. Find each of the following:

(a) 23 (b) 52 (c) 64 (d) 30 (e)26 [5 marks] Q2. Express each of the following in scientific notation:

(a) 450 000 (b) 27 300 (c) 4300 (d) 210 (e) 12 500 000 (f) 6 000 000 (g) 100 million (h) 5.61 million (i) ½ million [9 marks]

Q3. Write each of the following out fully: (a) 2·6 x 103 (b) 4·21 x 104 (c) 8·1 x 105

(d) 3·14 x 107 (e) 5·123 x 106 [5 marks] Q4. Express each of the following in scientific notation:

(a) 0.000 432 (b) 0.0005 (c) 0.014 (d) 0.000 500 3 [4 marks]

Q5. Write each of the following out fully:

(a) 2·684 x 10-3 (b) 3·2 x 10-4 (c) 5·14 x 10-5

(d) 3·09 x 10-7 (e) 5 x 10-6 [5 marks] Q6. Calculate (Write your answer in scientific notation): (a) 1.42 x 10 9 x 15 (b) 1.0453 x 10 11 x 18 [4 marks]

[Total 32 marks]

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Homework 7: Algebra

Q1. Simplify: (a) 4y + 3y (b) 12a – a (c) 8t – 5t + t (d) 2x + 4y – x + 3y (e) 8 x p (f) y x y (g) 2a x 3b (h) 8t x 5q [8 marks]

Q2. Multiply out the brackets : (a) 3(x + 2) (b) 5(x – 3) (c) 8(3m + 4n) (d) 4(5t – 3) (e) 7(6a + 8b) (f) 3(12x – 9)

[6 marks] Q3. Multiply out the brackets then simplify : (a) 2(x + 1) + 3 (b) 20 + 5(b – 3) (c) 5(3t + 2) - 7 (d) 4(t – 3) + 2(t + 6) (e) 7(e + 2) + 2(t – 5) + 4 [10 marks] Q4. Solve for x : (a) x + 3 = 7 (b) x + 6 = 6 (c) x – 9 = 4 (d) 12 = x – 3 (e) 6x = 24 (f) 4x = 18 (g) 5x = 135 (h) 6x = 6

[8 marks] Q5. Solve for x :– (a)2x + 1 = 11 (b) 3x – 2 = 28 (c) 7x – 3 = 60 (d) 18x – 1 = 6x + 11 (e) 5x – 1 = 2x + 20 (f) 10x = 6x + 32

[12 marks] Q6. Solve for x :– (a) 3(x + 2) = 15 (b) 5(x – 2) = 25 (c) 2(3x + 1) = 50 (d) 5(2x – 1) = 65 (e) 4(1 + x ) = 40 (f) 5(x – 3) = 2x

[6 marks] Q7 . Evaluate 5d – 3c when d=4 and c=2 [2 marks]

Q8. The cost of hiring a car is fifteen pounds per day plus 4 pence per mile. How much does it cost to hire a car for 3 days if the number of miles travelled is 310?. [4 marks]

Q9. F = ma is a formula used in science. Evaluate F when m=12 and a=5 [2 marks]

Q10. Factorise (a) 3y + 12 (b) a2 + a (c)3xy -9x2 [6 marks]

Q11. Solve the following inequalities:

(a) y + 5 > 7 (b) 5y < 25 [2marks]

[Total 60 marks]

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Homework 8: Pythagoras

Q1. Calculate x [2 marks each]

Q2. Triangle ABC has been split into 2 right angled triangles. Calculate x and y [3 marks]

[Total 11 marks]

x

x

9 m

14 m

8.7 cm

3.4 cm

20 cm

x

x 8 cm

12 cm

14 mm (a)

(b)

(c)

(d)

24 cm 43 cm

35 cm

x

y

A

B

C

(a)

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Homework 9: Statistics

Q1. A platoon of soldiers were asked to line up “shortest to the right, tallest to the left”. Their heights were : 1·60 m, 1·62 m, 1·62 m, 1·65 m, 1·66 m, 1·68 m, 1·71 m, 1·71 m, 1·71 m, 1·74 m. (a) What is the modal height? (the mode) [1 mark] (b) Write down the median height. [1 mark] (c) Calculate the mean height. [1 mark]

Q2. Complete a stem and leaf diagram using the data below. 50 42 31 39 65 32 41 60 49

[3 marks] Q3.

100 students were asked for their favourite flavour of crisps. How many students prefer salt & vinegar? [2 marks]

3

4

5

6 Salt & Vinegar

Cheese & Onion

Ready Salted

Other

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Q4.

(a) Draw a scattergraph for the marks below [2 marks] Contestant Judge A Judge B Emily 35 38 Chris 50 42 Sam 48 51 Russell 33 29 Claire 47 47 (b) Draw a best-fitting straight line on your graph [1 mark] Q5. Complete the frequency table using the data below: 5 2 3 3 6 3 4 6 5 2 4 3 3 6 4 5 3 2

Score Tally Frequency 2 3 4 5 6 Total:

[4 marks] Q6. The test scores for the French class 1C are:

32 41 28 45 18 25 32 40 32 27 32 11 43 19

Calculate the: (a)mean score [3 marks] (b) modal value [1 mark] (c)median value [1 mark] (d) range [1 mark]

Q7. A dice is rolled. What is the probability that a five is rolled? [1 mark]

[Total 22 marks]

Judge B

20

0

40

10

30

50

20 40 60 80 Judge A

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Homework 10: Ratio & Proportion

Q1. Simplify the following ratios: (a) 12:20 (b) 30:45 (c) 24:32 (d)2100:2400 [4 marks]

Q2. The ratio of blue beads to red beads in a bag was 3:2. There were 40 beads altogether in the bag. How many were blue and how many were black? [3 marks] Q3. 5 identical polo shirts cost £37·50. How much would 8 shirts cost ? [3 marks] Q4. A lorry driver needs 5 trips to transport 45 tonnes of sand to a building site. How much sand could he transport in 7 trips ? [3 marks] Q5. A painter takes 20 minutes to paint 25 m2 of wall. How long would he take to paint 30 m2 of wall at the same pace ? [3 marks] Q6. It takes a woman 4 minutes to walk 480 metres. How long would it take her to walk 720 metres at the same speed ?

[3 marks] Q7. A large hotel charges £144 to stay there for 3 days. What should it charge for 5 days ? [3 marks] Q8. The cost, c pounds, of a carpet varies directly as its length, l metres.

A carpet of length 5 metres costs £240. What will a carpet of length 7 metres cost? [3 marks]

Q9. A printer takes 7 minutes to print a document with 63 pages. How many pages can be printed in half an hour? [3 marks]

[Total 25 marks]

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Homework 11: Straight line

Q1. Complete the table of value for y = x – 2

x 0 1 2 3 y

[2 marks] Q2. (a) Complete the table of values for y = 3x +1

x 0 1 2 3 y

[2 marks] (b) Using a suitable grid use your table of values to draw the straightline y = 3x + 1

[2 marks]

Q3. The picture shows a ladder leaning against a wall. Write down the gradient of the ladder as a fraction. [2 marks]

[Total 8 marks]

11 m

2 m

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Homework 12: Trigonometry

Q1. Calculate X. [4 marks each]

Q2. Calculate X [3 marks each]

Q3. ABCD is a trapezium. Calculate the size of angle DAB [4 marks]

[Total 18 marks]

8 km

10°

X 32 metres

X°

12 km

11 cm

5 cm

8 cm D

A B

C

42° X

50 metres

X°

X° 7.1 km

4.3 km

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Homework 13: Angles

Q1. State what KIND of angle is marked with a

[4 marks]

Q2. Use 3 letters to NAME both of these angles and state what KIND each one is:

[4 marks]

Q3. Calculate the value of the angles marked x, y and z [6 marks]

Q4. Calculate the size of angle PRQ [2 marks]

[Total 16 marks]

30°

P

K

A

T

L M

x

y z

150°

P

R 32° Q

62°

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Homework 14: Probability

Q1. A 6-sided spinner is spun and the number it lands at is noted. What is the probability it stops at:

(a) the number 3? [2 marks] (b) an odd number? [2 marks] (c) a number greater than 2? [2 marks]

Q2. A bag of sweets contains 3 red, 4 yellow, 2 green and 6 purple. The corner of the bag is torn and a sweet falls out.

(a) Calculate the probability that this sweet is yellow? [1 mark]

(b) The yellow sweet was put in the bin. What is the probability that the next sweet to fall out is purple? [2 marks]

Q3. A bag contains eleven balls numbered one to eleven. A ball is removed from the bag. What is the probability that this ball has a number more than 6? [2 marks]

Q4. Last month Auto cars sold 11 blue cars, 10 red cars and 15 silver cars. Tony bought one of these cars. What is the probability that the car Joe bought was red? [2 marks]

[Total 13 marks]

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Homework 15: Circles

Q1. Calculate the circumference of the circle with diameter 9 mm. [2 marks]

Q2. Calculate the circumference of the circle with radius 6 cm [2 marks]

Q3. Calculate the area of the circle with radius 4 mm [2 marks]

Q4. A rectangular bar contains four identical circular holes. Find the:

(a) Diameter of each circle [1 mark] (b) Length of the rectangular bar [1 mark] (c) Shaded area [3 marks]

9 mm

8 cm

length

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[Total 11 marks]

Homework 16: Volume

Q1. Find the volume of the cube with height 5 cm [2 marks]

Q2. The volume of this cuboid is 168 cm3. Calculate it’s height. [3 marks]

Q3. Calculate the total volume: [4 marks]

Q4. Calculate the volume of the cylinder [2 marks]

[Total 11 marks]

5 cm

14 cm 3 cm

25 cm

16 cm

11 cm

12 cm

8 cm

19 cm

7 cm

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Homework 17: Patterns

Q1. The cost of buying cans of cola are shown below:

1 can 2 cans 3 cans

cost 50p cost 100p cost 150p

(a) Copy and complete this table: [2 marks]

No. of nuts

(N) 1 2 3 4 5 6

Total Cost (C pence)

50

(b) Write down a formula connecting C and N [1 mark]

(c) Use this formula to find the cost of 12 cans. [2 marks]

Q2. The table shows the cost of hiring a chain saw for several days:

No. of days hired

(D)

1 2 3 4 5 6

Total Cost £’s (C)

15 30 45 60

(a) How much will it cost to hire the saw for (i) 5 days (ii) 6 days (iii) 7 days

[3 marks]

(b) Write down a formula connecting C and D [1 mark]

(d) How much will it cost to hire a saw for 14 days? [2 marks]

[Total 11 marks]