wyvern college...wyvern college 2 year 8 homeworks homework 1 q always write questions, workings and...

Wyvern College │1

Year 8 Homeworks

Wyvern College

Year 8 Maths Homeworks Welcome to your year 8 maths downloadable homeworks! Save this file somewhere safe like your laptop, PC or iPad where you are going to regularly open it from to do your homeworks.

These homeworks have been specially designed to follow topics that you have been taught in class. From homework 4 onwards, each homework that you do will jump between lots of different topics. This is deliberate as it helps you keep things you learned a day, a week and a month ago in class still in your mind. It helps you remember things long term.

You should have notes in your notebook about every topic that appears in the homeworks so if you are stuck make sure you look in your notebook for help.

A lot of work went into creating these homeworks so that it improves your learning and hopefully you’ll enjoy them too! Do your best on them.

Click these links below to go to your homeworks:

Contents Homework 1 ............................................................................................................................................ 2

Homework 2 ............................................................................................................................................ 3

Homework 3 ............................................................................................................................................ 4

Homework 4 ............................................................................................................................................ 5

Homework 5 ............................................................................................................................................ 8

Homework 6 .......................................................................................................................................... 11

Homework 7 .......................................................................................................................................... 14

Homework 8 .......................................................................................................................................... 17

Homework 9 .......................................................................................................................................... 20

Homework 10 ........................................................................................................................................ 22

Homework 11 ........................................................................................................................................ 24

Homework 12 ........................................................................................................................................ 28

Homework 13 ........................................................................................................................................ 31

Homework 14 ........................................................................................................................................ 33

Homework 15 ........................................................................................................................................ 36

Wyvern College │2

Year 8 Homeworks

Homework 1

Q Always write questions, workings and answers L C

1 3 + 8 3 N

2 7 + 12 3 N

3 8 – 5 3 N

4 19 – 16 3 N

5 23 + 41 3 N

6 38 + 29 3 N

7 27 + 94 3 N

8 65 – 42 3 N

9 78 – 69 3 N

10 30 – 17 3 N

11 192 + 75 4 N

12 32 + 99 4 N

13 83 + 109 4 N

14 783 – 81 4 N

15 912 – 93 4 N

16 89 + 943 4 N

17 948 + 903 + 72 4 N

18 2389 – 902 4 N

19 908 – 287 4 N

20 5001 – 839 4 N

21 3.5 + 93.1 5 N

22 73.3 – 9.9 5 N

23 9.84 + 18.4 5 N

24 93.2 – 3.49 5 N

25 785.193 – 9.83 5 N

26 650.1 – 39.33 5 N

27 83.001 – 45.1 5 N

28 932.3 + 940.23 5 N

29 902 – 39.221 + 7.99 5 N

30 9007.33 – 7832.1 + 943.992 5 N

Wyvern College │3

Year 8 Homeworks

Homework 2


1 7 X 0 3 N

2 3 X 4 3 N

3 5 X 9 3 N

4 10 X 4 3 N

5 12 X 6 3 N

6 3 X 15 3 N

7 32 X 5 3 N

8 83 X 6 3 N

9 9 X 68 3 N

10 7 X 80 3 N

11 14 X 35 4 N

12 93 X 71 4 N

13 50 X 79 4 N

14 8 X 190 4 N

15 552 X 7 4 N

16 49 X 942 4 N

17 228 X 32 4 N

18 976 X 543 4 N

19 9302 X 756 4 N

20 9876 X 5432 4 N

21 3 X 1.7 5 N

22 2.9 X 6 5 N

23 12.1 X 3.5 5 N

24 6.21 X 9.7 5 N

25 5 X 39.81 5 N

26 16.72 X 83 5 N

27 0.3 X 0.4 5 N

28 99.9 X 2.35 5 N

29 44.92 X 930.7 5 N

30 642.34 X 5 X 0.0001 5 N

Wyvern College │4

Year 8 Homeworks

Homework 3


1 8 ÷ 2 3 N

2 18 ÷ 6 3 N

3 40 ÷ 5 3 N

4 64 ÷ 8 3 N

5 100 ÷ 10 3 N

6 8 ÷ 1 3 N

7 0 ÷ 4 3 N

8 110 ÷ 11 3 N

9 72 ÷ 12 3 N

10 81 ÷ 9 3 N

11 86 ÷ 2 4 N

12 69 ÷ 3 4 N

13 184 ÷ 4 4 N

14 306 ÷ 9 4 N

15 125 ÷ 5 4 N

16 256 ÷ 8 4 N

17 155 ÷ 5 4 N

18 2248 ÷ 4 4 N

19 3912 ÷ 6 4 N

20 784 ÷ 14 4 N

21 57 ÷ 5 5 N

22 126 ÷ 8 5 N

23 2 ÷ 3 5 N

24 6.3 ÷ 3 5 N

25 18.4 ÷ 8 5 N

26 50.8 ÷ 8 5 N

27 214.02 ÷ 6 5 N

28 10 ÷ 0.2 5 N

29 8 ÷ 0.4 5 N

30 35 ÷ 0.25 5 N

Wyvern College │5

Year 8 Homeworks

Homework 4


1 15 + 47 3 N

2 64 + 88 3 N

3 65 – 48 3 N

4 82 – 45 3 N

5 4 X 8 3 N

6 6 X 45 3 N

7 24 ÷ 6 3 N

8 56 ÷ 7 3 N

9 12 + 93 + 5 3 N

10 2 X 8 X 3 3 N

11 389 + 236 4 N

12 704 – 67 4 N

13 34 X 65 4 N

14 124 ÷ 4 4 N

15 Solve x + 5 = 7 4 N

16 Solve 15 – x = 12 4 N

17 Solve 2x = 8 4 N

18 Solve 4 N

19 What is the area of this shape if it is drawn on centimetre squared paper?

4 N

20 What is the perimeter of this shape if it is drawn on centimetre squared paper?

4 N

21 3.47 X 8 5 N

22 6.8 ÷ 4 5 N

23 If you choose one card at random from a deck of cards are all the possible outcomes equally likely?

5 N

24 What is the probability of rolling a factor of 6 on a fair die? 5 N

25 If a = 4, what is the value of 5a? 5 N

26 Expand 3(x + 2) 5 N

27 Solve 6a = 42 5 N

28 Solve 5 N

29 Calculate the area of this rectangle

5 N

30 Calculate the perimeter of this rectangle

5 N

31 List all the possible outcomes of rolling a die and tossing a coin. The first one is (1, Head) 6 N

32 Complete this sample space diagram to show all the outcomes of rolling two dice and subtracting the smallest number from the largest one

6 N

8m

4m

8.5 cm

7 cm

Wyvern College │6

Year 8 Homeworks

1 2 3 4 5 6

1 0 1

2

3

4

5

6

33 The probability of Tom winning a game of Fifa against his friend David is 0.4. What is the probability that David will win the game?

6 N

34 Factorise fully 2a + 10 6 N

35 Factorise fully 4x – 8 6 N

36 Solve 3x + 8 = 20 6 N

37 Solve 5x – 4 = -14 6 N

38 Calculate the area of this shape

6 N


6 N

40 This rectangle has an area of 56 m2. Calculate the missing length x

6 N

41 The table below shows the results of spinning a spinner 100 times. What is the relative frequency of getting a red? Give you answer as a decimal.

Colour Green Red Blue

Frequency 35 40 25

7 N

42 What happens to the relative frequencies in a probability experiment as the number of trials is increased?

7 N

43 The probability that Karen gets to school on time is 0.95. In 200 days of school, approximately how many times would we expect Karen to be late?

7 N

44 3a X 4ab 7 N

45 Expand (x + 4)(x + 3) 7 N

46 Solve 3x + 5 = 2x + 9 7 N


7 N

3.2 cm

6 cm

4.2 cm

2.6 cm

7 m

x

9 m 6 m

8 m

13 m

2 cm

Wyvern College │7

Year 8 Homeworks


7 N

49 A rectangular room measures 5m by 6m. Sophie is going to tile the floor of the room using square tiles that are 0.25m by 0.25m. Each tile costs £1.20. What is the total cost of all the tiles Sophie needs to buy?

7 C

50 In Q49, if Sophie had bought 32m2 of tiles. How many tiles would she have had left over at the end of the job?

7 C

12 cm

20 cm

8 cm

Wyvern College │8

Year 8 Homeworks

Homework 5


1 22 + 39 3 N

2 59 + 69 3 N

3 71 – 4 3 N

4 80 – 27 3 N

5 3 X 7 3 N

6 7 X 38 3 N

7 72 ÷ 9 3 N

8 120 ÷ 10 3 N

9 28 + 33 – 15 3 N

10 7 X 5 X 2 3 N

11 56 + 979 4 N

12 540 – 44 4 N

13 387 X 320 4 N

14 3055 ÷ 5 4 N

15 Solve x – 8 = 2 4 N

16 Solve 8 + x = 19 4 N

17 Solve 5x = 30 4 N

18 Solve 4 N

19 What is the area of this shape if it is drawn on centimetre squared paper?

4 N

20 What is the perimeter of this shape if it is drawn on centimetre squared paper?

4 N

21 0.91 X 7.12 5 N

22 10 ÷ 0.1 5 N

23 Fred picks a card at random from a deck of cards (no jokers). What is the probability he picks an ace card?

5 N

24 You are asked to test whether a die is fair. What could you do to find out? 5 N

25 If x = 5, what is the value of 3x – 4? 5 N

26 Expand 6(x – 4) 5 N

27 Solve 8a = 56 5 N

28 Solve 5 N

29 A rectangular room measures 3.5m by 6m. Susie wants to lay a new carpet in the room that costs £14 per m2. What will be the total cost of the carpet (ignoring offcuts)?

5 N

30 Susie then needs to buy some skirting board to go around the bottom of all the walls in the room. Ignoring the gap for the door, what length of skirting board does Susie need to buy?

5 N

31 A football match between Wyvern and Wildern ends in a 2 – 1 win for Wyvern. List all the possible half-time scores in the match

6 N

32 Complete this sample space diagram to show all the possible outcomes of tossing a coin and rolling a 6 sided die

6 N

Wyvern College │9

Year 8 Homeworks

1 2 3 4 5 6

Head (H, 1)

Tail

33 The probability of Jamie scoring a penalty is 0.65. What is the probability he will miss a penalty?

6 N

34 Factorise fully 6c + 18 6 N

35 Factorise fully 2xy – 10y 6 N

36 Solve 6 N

37 Solve 6 N


6 N

39 This parallelogram has an area of 24 cm2. What is the missing length?

6 N

40 These shapes have the same perimeter. What is the missing length?

6 N

41 The table below shows the results of traffic outside a school. If 1000 vehicles pass the school, approximately how many would we expect to be cars?

Vehicle Car Lorry Van

Frequency 30 15 5

7 N

42 If we rolled a fair die 36 times approximately how many sixes would we expect to get? 7 N

43 Draw a sample space diagram for the outcomes of rolling two fair 6 sided dice and use it to calculate the probability of rolling a double (two numbers the same)

7 N

44 10ab2 ÷ 5b 7 N

45 Expand (3x + 2)(x – 5) 7 N

46 Solve 2(x + 5) = 3(x – 2) + 11 7 N

47 Write an expression for the area of this shape

7 N


7 N

5 cm 3 cm

6 cm

7 m ? m

2x + 7

x + 4

5 cm

12 cm

4 cm

3.5 m

Wyvern College │10

Year 8 Homeworks

49 Fred wants to wallpaper a rectangular wall that measures 2.5m high by 4m wide. Wallpaper comes in rolls that are 0.8m wide by 3m long and cost £12.49 each. Fred doesn’t want any horizontal overlaps. How much will the total cost of the wallpaper be?

7 N

50 How many 0.2m by 0.2m square tiles would fit in a rectangular room 3m by 4.6m? 7 N


Year 8 Homeworks

Homework 6


1 56 + 78 3 N

2 70 – 54 3 N

3 5 X 9 3 N

4 42 X 7 3 N

5 60 ÷ 5 3 N

6 I buy a Marz Bar for 55p. I pay with a £1 coin. How much change will I get? 3 N

7 I buy 2 Snickerz bars for 48p each. How much do they cost altogether? 3 N

8 I have 18 humbug sweets. I want to share them equally between me and my friend George. How many sweets do we get each?

3 N

9 I buy 4 packs of cola. Each pack has 6 cans. How many cans are there in total? 3 N

10 How many minutes are there between quarter past eight and quarter to nine? 3 N

11 638 + 83 4 N

12 602 – 239 4 N

13 I have £2. I want to buy as many pens as possible. Each pen costs 32p. How many pens can I buy?

4 N

14 In Q13 how much change would I get after buying as many pens as possible? 4 N

15 43 X 837 4 N

16 171 ÷ 3 4 N

17 Solve 3x = 15 4 N

18 Solve 12 – x = 3 4 N

19 Calculate the perimeter of this shape if it was drawn on centimetre squared paper

4 N

20 Name a sensible metric unit for measuring the capacity of a washing up bowl 4 N

21 Name this part of a circle:

5 N

22 Name this part of a circle:

5 N

23 Calculate the mean of this data: 5, 7, 2, 5, 23, 6

5 N

24 Calculate the mode of this data: 4, 6, 2, 6, 7, 4, 9, 10, 6

5 N

25 Calculate the median of this data: 5, 12, 6, 3, 1, 2, 10

5 N

26 Calculate the range of this data: 64, 3, 56, 44, 60, 33, 41

5 N


Year 8 Homeworks

27 Which would you expect to have a larger range, 100 m sprint race times in seconds or 400 m sprint race times in seconds?

5 N

28 Solve 5 N

29 6.3 ÷ 3 5 N

30 Simplify 3a + 7b + 2a – 4b 5 N

31 Calculate the area of a circle with a radius of 5 m 6 Y

32 Calculate the circumference of a circle with a diameter of 8 cm 6 Y

33 Calculate the volume of this cuboid

6 N

34 Calculate the surface area of this cuboid

6 N

35 Calculate the surface area of this cylinder

6 Y

36 Give one advantage of using the median average rather than the mean or the mode 6 N

37 3 US dollars = £1.90 Use this information to plot a straight line conversion graph and use it to convert £1 into US dollars

6 N

38 Draw x and y axes that go from -10 to 10 and plot the line y = 5 6 N

39 On the axes in Q38 plot the line y = 2x + 2 6 N

40 Is the point (2, 10) on the line y = 3x + 4? 6 N

41 A circle has an area of 30 cm2. What is the radius? 7 Y

42 What is the diameter of a circle that has a circumference of 50m? 7 Y

43 Calculate the volume of this cylinder

7 Y

44 Explain what a prism is 7 N

45 A prism has a cross-sectional area of 18 cm2. If the volume of the prism is 216 cm3, what is the length of the prism?

7 N

46 Calculate the mean, median and mode number of TVs

TVs Frequency

0 1

1 15

2 8

3 5

7 N

6 cm

3 cm

4 cm

6 cm

3 cm

4 cm

5 cm

6 cm

5 cm

6 cm


Year 8 Homeworks

47 Find the equation of this line

7 N


7 N

49 Is the line y = 3x + 7 parallel to the line y = −3x + 7? Explain the reasons for your answer 7 N

50 Is the line y = 2x + 5 parallel to the line 2y − 4x = 8? Explain the reasons for your answer 7 N


Year 8 Homeworks

Homework 7


1 24 + 38 3 N

2 67 – 32 3 N

3 8 X 7 3 N

4 25 X 8 3 N

5 72 ÷ 12 3 N

6 David bought a packet of sweets for 75p. He paid with a £1 coin. How much change did he get?

3 N

7 How many candles that cost 15p each can James buy if he has £1? 3 N

8 In Q7, if James bought as many candles as he could, how much change would he have left over?

3 N

9 In block C at a football stadium there are 20 seats in a row and there are 8 rows of seats. How many seats are there in block C?

3 N

10 Hollie looks at a clock and it says ten minutes past nine. She looks at the clock again half an hour later. What time did she look at the clock the second time?

3 N

11 705 – 95 4 N

12 42 X 823 4 N

13 222 ÷ 6 4 N

14 If the probability of something happening is 0, what word can we use to describe this? 4 N

15 Solve 6x = 66 4 N

16 Solve 8 – x = 0 4 N

17 Which of these shapes has a bigger area?

4 N

18 Which of these shapes has a bigger perimeter?

4 N

19 If the length of a ruler is x, write an expression for the length of a ruler that is 5cm longer

4 N

20 If there are y marbles in a packet, write an expression for how many marbles there would be in 5 packets

4 N

21 What is the name of the line that just touches the circle?

5 N

22 If a = –8, what is the value of 5 – 3a? 5 N

23 Calculate the mean, mode, median and range of this data: 13, 52, 45, 33, 20, 13, 19, 11, 20, 7

5 N

24 3 + (–8) 5 N

Shape A Shape B

Shape A Shape B


Year 8 Homeworks

25 (–9) X (–5) 5 N

26 19 – 34 5 N

27 (–6)2 5 N

28 Expand and simplify 5(a + 4) – 8 5 N

29 Solve 5 N

30 Which has a larger perimeter, a rectangle that measures 40cm by 65cm or an equilateral triangle with sides of length 69cm?

5 N

31 Calculate the area of a circle with a radius of 21 cm 6 Y

32 Calculate the circumference of a circle with a radius of 5 cm 6 Y


6 N

34 A can of paint covers an area of 50m2. How many cans of paint would be needed to paint all of this cuboid?

6 N


6 Y

36 Solve 4x + 13 = 5 6 N

37 Solve 6 N

38 Factorise fully 3a + 6 6 N

39 The vase below is filled with water flowing at a constant rate. Copy the graph then continue the line to show how the height of water in the vase would change with time:

6 N

40 Calculate the gradient of this line:

6 N

41 A bicycle wheel can travel 2.2m in one revolution (whole turn). What is the distance from the centre of the wheel to the edge?

7 Y

10 cm

2 cm

3 cm

6 m

4 m

5 m

4 cm

4 cm

Water

height

Time


Year 8 Homeworks

42 Expand and simplify (x + 5)(3x – 3) 7 N

43 Calculate the capacity of this cylinder container in litres to the nearest whole litre? Remember 1 litre = 1000 cm3

7 Y

44 Simplify 4a2bc3 X 3ab 7 N

45 Solve 8(x + 1) = 2(x + 16) 7 N

46 Calculate the mean, median and mode number of goals scored in matches in a hockey tournament

Goals Frequency

0 3

1 8

2 4

3 3

4 2

7 Y


7 N


7 N

49 The area of this trapezium is 12.75 m2. Calculate the missing length

7 Y

50 Phoebe picked a card at random from a normal deck of cards (no jokers), wrote down the name of the card she had chosen and then put it back into the pack. If she did this 300 times, approximately how many times would she choose a red king card?

7 N

18 cm

28 cm

? m

3 m

2 m


Year 8 Homeworks

Homework 8


1 33 + 87 3 N

2 71 – 28 3 N

3 3 X 9 3 N

4 14 X 6 3 N

5 42 ÷ 6 3 N

6 Apples cost 45p each. How much would two apples cost? 3 N

7 I have 80p. Pencils costs 15p each. Do I have enough money to buy 5 pencils? 3 N

8 If I have £30 and I would like to share it equally between 6 people, how much would each person get?

3 N

9 There are 6 cans of beans in a pack. How many cans of beans would there be in 15 packs?

3 N

10 What time is three-quarters of an hour after 8:30am? 3 N

11 There are 23 043 people in St Mary’s Stadium at the start of a match. 257 people leave at half time. How many people are in the stadium at the start of the second half?

4 N

12 If I can walk 4300 m in one hour. How many metres can I walk in 3 hours? 4 N

13 What is the answer to Q12 in km? 4 N

14 Put a cross (X) on the number line to show that the probability of something is likely.

4 N

15 Solve 2x = 34 4 N

16 Solve 4 N

17 What is the area of this triangle?

4 N

18 What is the area of this shape?

4 N

19 If the length of a brick is x, write an expression for the length of two bricks 4 N

20 There are 50 buttons in a jar. I take x buttons out of the jar. Write an expression for the number of buttons left in the jar

4 N

21 What do we call the distance around the edge of a circle? 5 N

22 If a = 12, what is the value of 5a – 60? 5 N

23 Calculate the mean, mode, median and range of this data: 6.3, 1.0, 3.9, 3.8, 2.5

5 Y

24 How could we find out what the probability is of a drawing pin landing with the point facing upwards when dropped?

5 N

25 (–8) X 4 5 N

26 Expand and simplify 3(b + 7) + 8 5 N

27 Expand and simplify 4(c + 10) + 2(d – 5) 5 N

0.5 1 0


Year 8 Homeworks

28 Solve 72 5 N

29 Solve 5 N

30 What is the area and perimeter of this rectangle?

5 N

31 Calculate the area of a circle with a diameter of 10 cm 6 Y

32 Calculate the circumference of a circle with a diameter of 8 cm 6 Y

33 Calculate the area and perimeter of this parallelogram

6 N

34 Calculate the surface area of this cuboid

6 N


6 Y

36 Solve 4(x + 3) = 40 6 N

37 Solve 6 N

38 Factorise fully 9c + 12 6 N

39 Thomas went on a walk. His journey is shown on this distance vs time graph. How far did Thomas walk?

6 N

40 In Q39, what speed did Thomas walk for the first hour? 6 N

41 The circumference of a circle is π cm. What is the radius of the circle? 7 Y

42 Expand and simplify (x – 4)(2x – 8) 7 N

43 Water is poured into the cylindrical container shown below so that it is 8cm deep. A metal cube with sides of length 5 cm is then put into the water. Does the water flow over the sides at the top of the cylinder?

7 Y

8m

6m

9 cm

4 cm 3 cm

10 m

6 m

3 m

7 cm

10 cm

Time (hrs) 0

3

0 1 2 3

Distance

(miles)


Year 8 Homeworks

44 Simplify 3a2bc3 X 6ab3 7 N

45 I drop a drawing pin 300 times. It either lands on its side or it’s back. It lands on its back 125 times. What is the probability it lands on its side?

7 N

46 Using your answer in Q45, if I drop the drawing pin 60 times, approximately how many times would it land on its side?

7 Y


7 N


7 N

49 Explain how you can look at two equations of straight lines that are in the form y = mx + c and identify if they are parallel

7 N

50 Is the line y = 2x + 1 parallel to the line 2y = 4x + 6? Explain how you know 7 N

10 cm

10 cm


Year 8 Homeworks

Homework 9


1 43 + 12 3 N

2 38 – 12 3 N

3 4 X 8 3 N

4 23 X 5 3 N

5 60 ÷ 12 3 N

6 12 ÷ 1 3 N

7 49 + 17 – 21 3 N

8 If I buy 2 sweets costing 30p each, how much change will I get if I pay with a £1 coin? 3 N

9 David earns £60 a month from a part-time job. He has to pay £15 per month to get to work and back on the bus. How much money has he got left over each month?

3 N

10 A coach carries 54 people. How many people do 2 coaches carry? 3 N

11 Round 142 to the nearest 10 4 N

12 Round 38.6 to the nearest whole number 4 N



15 What is 50% as a fraction? 4 N

16 What is 0.25 as a percentage? 4 N

17 What is 0.1 as a percentage? 4 N

18 Calculate 50% of 20 4 N



21 Round 5.642 to 1 decimal place 5 N

22 Round 325.388 to 2 decimal places 5 N



25 What is 3 as a percentage of 10? 5 N

26 What is the ratio of black dots to white dots?

5 N

27 Write the ratio 4 : 8 in its simplest form 5 N

28 Beth has some red and green apples in the ratio 1 : 3. If she has 2 red apples, how many green apples does she have?

5 N


30 12 out of 32 Smarties in a packet are yellow. What percentage of the Smarties are yellow?

5 N

31 Write 0.32 as a percentage 6 Y

32 What is 7% as a decimal number? 6 Y

33 Convert into a decimal number 6 N

34 What is 0.351 as a fraction? 6 N

35 Put these numbers in order from the smallest to the largest:

67% 0.66

6 Y

36 Share £60 in the ratio 2 : 3 6 N

37 Share £35 in the ratio 1 : 2 : 4 6 N

38 Rule: start at 2 and add 7 each time. Write the first 5 terms in this sequence 6 N

39 The nth term rule for a sequence is 2n + 3. Write the first four terms in this sequence. 6 N

40 Find the nth term rule of this sequence: 6 N


Year 8 Homeworks

5, 8, 11, 14, 17…

41 Round 325 to 1 significant figure 7 N

42 Round 35.63 to 2 significant figures 7 N

43 Round 0.00452 to 1 significant figure 7 Y

44 Write down a calculation that you would use to estimate the answer to: 4.676 X 49.223 Now do your calculation to estimate the answer.

7 N

45 What decimal number would you multiply 56 by to increase it by 12%? 7 N

46 Use your answer to Q45 to calculate the result of increasing 56 by 12% 7 N

47 A tablet computer is reduced in a sale from £300 to £270. What percentage decrease was given on the laptop in the sale?

7 Y

48 Last year a loaf of bread cost £1.20. This year it costs £1.44. By what percentage has the cost of a loaf of bread risen?

7 Y

49 Launching space rockets is a dangerous business. NASA launched their Space Shuttles 135 times between 1981 and 2011 and lost 2 of them in disasters. What was the relative frequency that NASA would lose a Space Shuttle on each launch? Give your answer as a decimal number to 3 decimal places.

7 Y

50 I expect to arrive at work on time 99% of the time. I work 170 days each year. How many days in a whole year would I expect to be late to the nearest whole number of days?

7 Y


Year 8 Homeworks

Homework 10


1 19 + 44 3 N

2 49 – 29 3 N

3 3 X 7 3 N

4 34 X 2 3 N

5 48 ÷ 8 3 N

6 5 ÷ 5 3 N

7 2 X 3 X 24 3 N

8 The recommended daily amount of fibre you should eat is 18 g. How many grams of fibre should you eat in a week?

3 N

9 Over a week you should not eat more than 42 g of salt. Turn this information into a recommended daily maximum amount

3 N

10 1 portion of fruit and vegetables is 80g. You should eat 5 portions of fruit and vegetables every day. How many grams of fruit and vegetables should you eat every day?

3 N




14 Round 9.5023 to the nearest whole number 4 N


16 Solve 4 N

17 408 + 939 4 N

18 7003 − 5364 4 N

19 34 X 88 4 N

20 318 ÷ 6 4 N

21 Simplify this ratio by cancelling down: 18 : 22 : 20

5 N

22 On a chess board, what is the ratio of pawns to bishops? Write the ratio in its simplest form

5 N

23 What is 2 as a percentage of 20? 5 N


25 What is written as a percentage? 5 N

26 Convert to a decimal number and give the answer correct to 3 decimal places 5 N

27 Here are the 100m men’s sprint final results (in seconds) for the Beijing Olympics in 2008: 9.69, 9.89, 9.91, 9.93, 9.95, 9.97, 10.01, 10.03 Usain Bolt was the winner. Calculate the mean, median, mode and range times for the athletes in the event

5 Y

28 A volleyball court is a rectangle measuring 18 m by 9 m. What is the area and perimeter of a volleyball court?

5 N

29 During a game of volleyball there are 12 players on court. Using your answer to Q28, what area must each person on the court defend if they all defended the same amount?

5 Y

30 Solve 5 N

31 Write down the first 4 terms in this sequence: Start at 3 and multiply by 2 each time

6 N

32 The nth term rule of a sequence is n2 + 1. Write down the first 5 terms in the sequence 6 N

33 Find the nth term rule of this sequence: 6 N


Year 8 Homeworks

2, 6, 10, 14, 18…

34 Write down an nth term rule for how many stars there would be in pattern n. Use your rule to calculate how many stars there would be in pattern 25

6 N

35 Share £55 in the ratio 5 : 6 6 N

36 Express as a decimal number 6 N

37 Convert 60% to a fraction and write it in its lowest terms 6 N

38 Plot the graph of y = 2x + 1. Make your sure your x axis goes from 4 to 4 6 N

39 What is the gradient of the line plotted in Q38? 6 N

40 Use this mileage chart to write down how many miles it is from Bristol to Plymouth:

6 N

41 My monthly gas bill rose from £40 to £48 in the last year. By what percentage has it increased?

7 Y

42 To calculate the result of decreasing 90 by 15% you can multiply 90 by a decimal number. What is that number?

7 N

43 Use your answer to Q42 to decrease 90 by 15% 7 Y

44 Estimate the answer to 7 N

45 Now calculate the exact answer to Q44 and write it to 3 decimal places. Compare it with your estimate. Was it close?

7 Y

46 Round 1.0045 to 2 significant figures 7 N

47 Calculate the mean, median and mode number of pairs of shoes people have from this frequency table:

Pairs of shoes Frequency

1 5

2 10

3 12

7 Y

48 Calculate the volume of a cylinder that has a base radius of 8 cm and height of 10 cm. Give your answer accurate to 3 significant figures

7 Y

49 The circumference of the London Eye is 424 m. What is the diameter to 2 significant figures?

7 Y

50 Solve 3(a + 2) = 4(a – 1) 7 N

Pattern 1 Pattern 2 Pattern 3


Year 8 Homeworks

Homework 11


1 32 + 92 3 N

2 35 – 19 3 N

3 6 X 6 3 N

4 3 X 29 3 N

5 72 ÷ 8 3 N

6 45 + 23 + 18 3 N

7 2 X 2 X 2 3 N

8 Storing 1 song on an iPod takes up 3 Mb of memory. How much memory does storing 25 songs on an iPod take up?

3 N

9 A man is 6 feet tall. If a giraffe is 3 times as tall as the man, how talk is the giraffe in feet?

3 N

10 Bradley raised £18 in a sponsored 10 km race. He wants to share this money between 2 charities. How much will he give to each charity?

3 N

11 What is the difference between the side lengths of isosceles and equilateral triangles? 4 N

12 Draw an isosceles triangle. How many lines of symmetry does it have? 4 N

13 Draw an equilateral triangle. What is the order of rotational symmetry for the triangle? 4 N

14 Draw as many nets of a cube as you can. How many can you find? 4 N

15 What common 3D shape is this the net of?

4 N

16 What is the name for an angle that is less that 90:? 4 N

17 What is the name for an angle that is larger than 180:? 4 N

18 43 X 98 4 N

19 288 ÷ 8 4 N

20 Solve 23 – x = 18 4 N

21 Calculate the size of angle a

5 N

22 Give reasons for your answer to Q21 5 N

23 What is special about the interior angles in an equilateral triangle? 5 N

24 Calculate the size of angle b

5 N

37:

b

161: 107:

a


Year 8 Homeworks

25 Give a reason for your answer to Q24 5 N

26 Finish this sentence. Angles on a straight line…. 5 N

27 What is special about the two angles shown below?

5 N

28 Give a reason for your answer to Q27 5 N

29 What do the angles in a quadrilateral add up to? 5 N

30 If b = 4, what is the value of 2b + 5? 5 N

31 I am a quadrilateral that has two pairs of parallel lines, no lines of symmetry, rotational symmetry of order 2 and two pairs of opposite interior angles the same size. What am I?

6 Y

32 Draw plan, front and side elevations of this shape:

6 Y

33 Here are the plan, front and side elevations of a shape:

Which shape below is the same shape as above?

6 N

34 Here are the plan, front and side elevations of a shape:

Which shape below is the same shape as above?

6 N

35 Calculate the size of angle x

6 Y

35: 85:

x


Year 8 Homeworks


37 Calculate the size of angle x

6 N


39 What is the size of an exterior angle in an equilateral triangle? 6 N

40 Calculate the size of the interior angles in a regular pentagon 6 Y

41 During a heavy rainfall, the flow rate of water in the River Itchen increased from 36 m3 per second to 52 m3 per second. By what percentage had the flow rate in the river increased? Give your answer to 1 decimal place

7 Y

42 The Spinnaker Tower in Portsmouth is 170m tall. If it was 81.2% taller it would be as tall as The Shard skyscraper in London. How tall is The Shard to the nearest metre?

7 Y

43 There are 95 floors in The Shard. The average floor area per floor is 1160 m2. Estimate the total floor area of all the floors in the building.

7 Y

44 The total cost of building The Shard was £435 million. Round this number to 2 significant figures

7 N

45 The ground floor of The Shard is a 45 m by 45 m square in plan view. The building is

pyramid shaped. The volume of space inside The Shard is of what it would be if it were

cuboid shaped. Use the information in this question and your answer to Q42 to calculate the volume of space inside The Shard. Give your answer to 2 significant figures

7 Y

46 Simplify 4x2y X 2y2 7 N

47 Simplify 3(x + 5) – 2(x – 5) 7 N

48 Calculate the volume of this triangular prism

7 N

49 What is the equation of this line? 7 N

x

6 m

4 m 8 m

20:


Year 8 Homeworks

50 What is the equation of this line?

7 N


Year 8 Homeworks

Homework 12


1 42 + 82 3 N

2 69 − 42 3 N

3 3 X 9 3 N

4 5 X 56 3 N

5 64 ÷ 8 3 N

6 This pictogram shows how many minutes people spend on the phone on average each day:

Bob

David

Karen

Hollie

Anastasia

Key: represents 10 minutes How many minutes does Hollie spend on the phone each day?

3 N

7 In the pictogram in Q6, how many minutes does Bob spend on the phone each day? 3 N

8 In the pictogram in Q6, how many more minutes does Karen spend on the phone each day than Hollie?

3 N

9 In the pictogram in Q6, how many minutes does Anastasia spend on the phone each day?

3 N

10 How many minutes a day in total do all the people in the pictogram in Q6 spend on the phone?

3 N

11 Copy and complete this data capture sheet:

Pet Tally Frequency

Dog

Cat 19

4 N

12 I am polygon with three sides that are all the same length. What am I? 4 N

13 I am a polygon with three sides that are all different lengths. What am I? 4 N

14 What type of triangle has 1 line of symmetry and no rotational symmetry? 4 N

15 730 − 489 4 N

16 93 X 823 4 N

17 672 ÷ 7 4 N




21 “What is your weight?” Explain why this is a bad question to ask on a questionnaire 5 N

22 “Do you agree that football is a much more interesting game than rugby?” Explain why 5 N


Year 8 Homeworks

this is a bad question to ask on a questionnaire

23 Explain what is wrong with the answer boxes in this question: “On average, how many minutes a day do you spend watching television?” □0 – 60 □60 – 119 □120 or more

5 N

24 Amber wants to find out what people’s favourite type of restaurant is. Design a suitable question that Amber could put in her questionnaire to find out this information

5 N

25 “What do you think of the performance of the England football team in the last World Cup? Write your answer in the space below: ……………………………………………………………………………” Why is this a bad question to ask on a questionnaire?

5 N


5 N


28

5 N

29 Draw a sketch of this pie chart and write in each sector what fraction of the total pie it is:

5 N

30 The pie chart in Q30 shows the results of 300 people. How many people are represented by each sector?

5 N

31 Calculate the size of the interior angles in a regular hexagon 6 Y

32 Calculate the size of the exterior angles in a regular decagon 6 Y

47:a


Year 8 Homeworks


6 N


35 Copy and complete this two-way table:

Year 7 Year 8 Year 9 Total

Boys 104 99

Girls 88 106 305

Total 600

6 Y

36 In Q35, which year group has the most pupils? 6 N

37 In Q35, how many girls are there in year 9? 6 N

38 In Q35, how many more girls are there than boys? 6 N

39 In Q35, if one pupil is chosen at random, what is the chance it will be a year 8 girl? 6 N

40 Construct a pie chart to show this information about people’s hobbies:

Skateboarding Writing Fishing Cricket

10 18 7 1

6 Y

41 Solve 6(a – 2) = 5a − 14 7 N

42 Estimate the answer to 7 N

43 What is the equation of this line?

7 N

44 Construct a scatter diagram of this data and describe the relationship it shows:

Speed (m/s)

12 15 9 10 8 11

Time (s)

6 4 7 7 9 6

7 N

45 Draw a line of best fit on your scatter graph from Q44 and use it to estimate the time taken if the speed was 14 m/s

7 N

46 Explain why it would not be sensible to use the scatter graph to estimate the time taken if the speed was 2 m/s

7 N

47 Simplify b4 X b3 7 N

48 Simplify (a3)2 7 N

49 Find the value of (32)2 7 N

50 Find the value of 210 ÷ 28 7 N

58:

a


Year 8 Homeworks

Homework 13


1 17 + 25 3 N

2 62 − 48 3 N

3 4 X 8 3 N

4 12 X 22 3 N

5 56 ÷ 8 3 N

6 Here is a bar chart showing what pets people have:

How many people have dog as a pet?

3 N

7 In the bar chart in Q6, how many people have a fish? 3 N

8 In the bar chart in Q6, how many more people have a dog than have a cat? 3 N

9 In the bar chart in the Q6, how many people have a pet? 3 N

10 In the bar chart in Q6, how many people were there in the class? 3 N

11 Design a data capture sheet to record the outcomes of rolling a die 100 times 4 N

12 I am a polygon with 3 sides all the same length. What am I? 4 N

13 In Q12, there is something special about the interior angles of this shape. What is it? 4 N


15 34 X 701 4 N


17 Solve 4 N

18 Explain what the word perimeter means 4 N


20 What is the mode of this list of data? Oak, Chestnut, Chestnut, Birch, Oak, Oak, Beech, Birch, Beech, Oak, Chestnut, Oak

4 N

21 Explain why this is a poor question to ask on a questionnaire: Do you agree that cheddar cheese tastes nicer than soft cheese?

5 N

22 Rewrite the question in Q21 so that it is suitable for a questionnaire 5 N

23 What is the ratio of days of the week with an ‘n’ in the name to those without an ‘n’ in the name

5 N

24 There are 60 red squirrels in some woodland and 300 grey squirrels. What is the ratio of red to grey squirrels in its simplest form?

5 N

25 If the ratio of red to grey squirrels in another woodland is the same and in Q24, how many red squirrels would there be if there are 600 squirrels altogether?

5 N

26 In a shop 35% of the people inside are male. If there are 200 people in the shop, how many males are there inside?

5 N

0

2

4

6

8

10

12

14

Dog Cat Fish None

Nu

mb

er

of

pe

op

le

Pet

What pets people have in my class

Frequency


Year 8 Homeworks

27 What percentage of the months in the year have a ‘j’ in their name? 5 N


29 75.6 ÷ 3 5 N

30 12 ÷ 0.2 5 N

31 I pick a card from a normal deck of cards (without jokers) and make a note of the suit (spade, club, heart or diamond) and then I put the card back in the deck. I choose another card and make a note of the suit and put it back. Draw a probability sample space to show all the combinations of outcomes I could get

6 N

32 Use your probability space from Q31 to calculate the probability of getting two cards of the same suit

6 N

33 Use your probability space from Q31 to calculate the probability of getting a spade and a heart

6 N

34 The chance of it raining tomorrow is 0.81. What is the probability of it not raining tomorrow?

6 N

35 Factorise fully 12xy2 – 8x 6 N

36 Solve 5a + 27 = 57 6 N

37 Solve 3b – 10 = 2b − 5 6 N

38 Expand 4(3y + 8) 6 N

39 If a triangle has a base width of 8 cm and an area of 96 cm2, what is the perpendicular height of the triangle?

6 N

40 What is the perimeter of this shape? The rectangle has an area of 72 cm2

6 N

41 Simplify (3x2)3 7 N

42 Calculate the value of if x = 3 7 N

43 What type of correlation would you expect there to be if you plotted a scatter graph of number of miles travelled in your car versus volume of petrol left in the tank? (Assume you didn’t fill up the tank at a petrol station on the journey)

7 N

44 Decrease 73.2 by 19% 7 Y

45 Between 1964 and 2009 the men’s 100 m sprint world record time went down from 10.06 seconds to 9.58 seconds. By what percentage did it decrease by in those 45 years? Give your answer to 2 significant figures?

7 Y

46 What is the equation of the straight line that passes through the points (12, 31) and (0, −5)?

7 N

47 What is the y intercept of the line in Q46? 7 N

48 What is the equation of the straight line that is parallel the one in Q46 but has a y intercept of 7?

7 N

49 Calculate the mean, median and mode from this frequency table:

Number of cards in household

Frequency

0 1

1 5

2 4

7 Y

50 What is the volume of a cylinder that has a base radius of 6 cm and a perpendicular height (length) of 10 cm? Give your answer in cm3 to 5 significant figures

7 Y

6 cm


Year 8 Homeworks

Homework 14


1 75 + 19 3 N

2 87 − 65 3 N

3 4 X 9 3 N

4 25 X 9 3 N

5 90 ÷ 10 3 N

6 The bar chart shows the favourite sports of people in a class:

How many boys’ favourite sport is rugby?

3 N

7 In Q6, how many girls’ favourite sport is rounders? 3 N

8 In Q6, how many people’s favourite sport is karate? 3 N

9 In Q6, how many boys are there in the class? 3 N

10 In Q6, how many more girls like rounders than boys? 3 N

11 Put this list of birds seen in a survey into a frequency table: Duck, Swan, Robin, Swan, Duck, Swan, Bluebird, Robin, Duck, Duck, Robin

4 N

12 Measure the size of all the interior angles in this shape:

4 N

13 In Q12, how many acute, right, obtuse and reflex angles are there? 4 N

14 What do you call a 3 sided polygon whose sides are all different length? 4 N


16 2912 ÷ 8 4 N

17 491 X 929 4 N

0

1

2

3

4

5

6

7

Nu

mb

er

of

pe

op

le

Favourite sport

Favourite sports of people in a class

Boys

Girls


Year 8 Homeworks


19 Solve 4 N

20 7004 − 2394 4 N

21 Mariska is designing a questionnaire and wants to find out how many times a month people eat out at restaurants. Design a suitable question she could put on her questionnaire to find out this information.

5 N


5 N

23 State 2 angle facts that you used to solve Q22 5 N

24 On the back of a bottle of orange squash it says “add 1 part squash for every 6 parts water”. What is the ratio of squash to water if you follow these instructions?

5 N

25 Using the information in Q24, if I make a large jug of orange squash that holds 7 litres. How much water will I need to put in the jug?

5 N

26 Calculate 95% of 3000 5 Y

27 What is 8 out of 50 as a percentage? 5 N


29 Calculate the mean, mode and median of this data: 3.2, 4.42, 9.42, 2.34, 4.33

5 Y

30 8.2 ÷ 4 5 N

31 If a circle has a radius of 8 cm, what is the area of the circle in cm2 to 2 decimal places? 6 Y

32 What would the circumference of the circle in Q31 be in cm to 3 decimal places? 6 Y


6 N

34 Calculate the surface area of a cylinder with a base radius of 5 cm and a perpendicular height (length) of 15 cm. Give your answer in cm2 rounded to 3 decimal places

6 Y

35 Calculate the surface area of the cuboid in Q33 6 N

36 Explain why using the mean as the average of these shoe sizes is not sensible if you want to find out what shoe size is the average: 7, 6, 7, 7, 7, 8, 8, 7, 7

6 Y

37 The line y = 5x – 10 is plotted on a graph. What is the missing number in this coordinate? (12, ?)

6 N

38 Is y = 3x2 + 7 the equation of a straight line? Explain how you know 6 N

39 What is the gradient of the straight line that passes coordinates (1, 3) and (4, 9) 6 N

40 Convert into a percentage 6 Y

41 Calculate the volume of a cylinder with a base radius of 5 cm and a perpendicular height (length) of 15 cm. Give your answer in cm3 rounded to 1 decimal place

7 Y

42 Tom wants to create a circular show area of 150 m2 for a village fete. He needs to fence all the way around the show area to keep spectators safe. How many pieces of fencing does Tom need to buy if the fencing comes in 2 m long sections?

7 Y


7 N

48:

58: a

24 cm 6 cm

8 cm


Year 8 Homeworks

44 Find the missing length in this rectangle that has the same area at the trapezium in Q43

7 N

45 How does your answer to Q44 relate to calculation of the area of the trapezium in Q43? 7 N

46 Solve 2(a + 9) = 4a + 5 7 N

47 I am thinking of a number. If I double it and add 5 I get the same value as when I multiply it by 5 and subtract 37. Set up an equation that represents this problem

7 N

48 Solve your equation from Q47 to calculate the number I am thinking of 7 N

49 Expand and simplify (x + 7)(x – 8) 7 N

50 Expand and simplify (2x – 5)(x – 6) 7 N

9 cm

11 cm

6 cm

? cm

6 cm


Year 8 Homeworks

Homework 15


1 56 + 38 3 N

2 81 – 69 3 N

3 78 X 5 3 N

4 7 X 7 3 N

5 81 ÷ 9 3 N

6 If I have £1, how many sweets can I buy if each sweet costs 20p? 3 N

7 I buy 8 packets of paperclips. Each packet costs 12p. How much do have to pay altogether?

3 N

8 If I paid for all the paperclips in Q7 with a £1 coin, how much change would I get? 3 N

9 How many 10p coins would make £1? 3 N

10 My electricity bill was £35 per month last year. This year it is £42 per month. How much has my electricity bill increased by per month in the last year?

3 N

11 What do we call an angle that is less than 90:? 4 N

12 What 3D shape is this a net of?

4 N

13 Draw a sketch of the net in Q12 and then mark on it 3 other dots that would meet up with the black dot shown when the net was folded up to make the 3D shape

4 N


15 1023 X 93 4 N

16 4557 ÷ 7 4 N


18 Solve 4 N


20 Explain what is special about both the side lengths and the interior angles of isosceles triangles

4 N

21 These two pie charts show the proportion of boys and girls in two different classes. Which class has the most number of boys in it?

5 N


Year 8 Homeworks

22 In Q21, if there were 30 pupils in class B, estimate how many boys there are in the class 5 N

23 Calculate the size of angle b

5 N


25 In a class of 28 pupils there are 12 boys. Write the ratio of boys to girls 5 N

26 Simplify the ratio 27 : 18 5 N


28 3 out of every 20 cars that pass outside of a school are red. What percentage of the cars passing the school are red?

5 N

29 Round 79.3299 to 3 decimal places 5 N

30 Which of the averages, mean, median and mode can we calculate for this list data? Pencil, Pen, Pen, Pen, Pencil, Pencil, Pen, Pencil, Pen

5 N

31 Which is larger, five eighths or 63%? Explain how you calculated your answer 6 Y

32 Divide £48 in the ratio 1 : 4 : 3 6 N

33 The nth term rule for a sequence is 2n2 + 4. Write out the first 4 terms in the sequence 6 N

34 What is the nth term rule for this sequence? 28, 33, 38, 43, 48…

6 N

35 What would be the 75th term in the sequence in Q34? 6 Y

36 Would 108 be a term in the sequence in Q34? If so, which term? 6 Y

37 The equation x2 + 10 = 40 has a solution between 5 and 6. Use trial and improvement to find the solution to the equation accurate to 1 decimal place

6 Y

38 I am a quadrilateral that has one line of symmetry, one pair of opposite angles the same size and two pairs of sides that are the same length. I have no interior reflex angles. What am I?

6 N

39 What is the difference between a parallelogram and a rhombus? 6 N

40 Draw the plan, front and side elevations of this 3D shape

6 N

41 I play a game of poker and win 61 out of the 250 hands that I bet on. What is the relative frequency of me winning a hand? Give your answer as a decimal number

7 Y

42 In another game I have the same chance of winning a hand. The game lasts a lot longer this time. It lasts for 605 hands. How many would I expect to win to the nearest whole number?

7 Y

43 If my mean average win in Q42 is 12 chips and my mean average loss is 3 chips, how many chips did I make or lose over the whole game?

7 Y

Class A

Boys

Girls

Class B

Boys

Girls

b 38:


Year 8 Homeworks

44 Simplify 4x2y3z X 2xz2 7 N

45 Write your answer to Q44 in the form where A and B are whole numbers 7 N

46 The Space Shuttle had thermal tiles on its underside to protect it from temperatures of 1650:C during re-entry. A typical HRSI tile was a cuboid that measured 15 cm wide by 15 cm wide in plan. The tiles varied in thickness from 2.5 cm to 13 cm on different parts of the Shuttle. The HRSI tiles covered an area of 479.7 m2 on the bottom of the Shuttle. Estimate how many HRSI tiles there were to 2 significant figures?

7 Y

47 90% of an HRSI tile is empty space. What volume of a tile that is 5 cm thick is empty space? Give your answer in m3 to 1 significant figure

7 Y

48 Convert your answer to Q47 into cm3 7 Y

49 The Space Shuttle’s loading bay was cuboid shaped and measured approximately 4.6m by 4.6m by 18m. What was the capacity of the payload bay in m3?

7 Y

50 If the payload bay had been cylindrical shaped and the same length, what diameter would it have needed to be to have the same payload capacity? Round your answer to the nearest cm

7 Y

Congratulations on an excellent years’ homework!

Now take everything you have learned in years 7 and 8 and go get the best GCSE grade you are

capable of! Hard work always pays off in GCSEs so go and be the best you can be!

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