Levels5 - 8

HomeworkFrequently Asked Question’s

Q - How often will it be set?A - Once a week

Q - How will it be assessed/graded?A – You will receive an effort grade A, B, C, D, E or U and an attainment grade 1, 2, 3, 4 or 5. Along with this you will be told what level you are working at, depending on which exam questions you performed well in.

Q – What if it’s not done on time?A – In the first instance a detention then the maths department strike system will be followed.

Q – What do I do if I get stuck?A – Either see your maths teacher for help or go to homework club.

Basic 4 Rules of Number (5 – 8)

Level 5 question (a) A football club is planning a trip. The club hires 234 coaches. Each coach holds 52 passengers. How many passengers is that altogether? Show your working.

2 marks (b) The club wants to put one first aid kit into each of the 234 coaches. These first aid kits are sold in boxes of 18. How many boxes does the club need? 1 markLevel 6 question - Here are six number cards. Arrange these six cards to make the calculations below.The first one is done for you.

a) b) b)

c) Now arrange the six cards to make a difference of 115 3 marks

Level 7 question a) The ship ‘Queen Mary' used to sail across the Atlantic Ocean. The ship's usual speed was 33 miles per hour. On average, the ship used fuel at the rate of 1 gallon for every 13 feet sailed. Calculate how many gallons of fuel the ship used in one hour of travelling at the usual speed. (There are 5280 feet in one mile.) Show your working and write down the full calculator display.

2 marks

b) Now write your answer correct to 2 significant figures. 1 markLevel 8 question – The table below shows information about some countries.

a) Which country has the largest population?1 mark

b) Which country has the smallest area?1 mark

c) On average, how many more people per km2 are

there in the UK than in the USA? Show your working. 3 marks

Decimals (5 – 8)

1. Solve the following (show all working):a) 492 + 39 b) 16.91 + 708.7c) 6230 – 781 d) 93.1 – 3.65e) 187 x 816 f) 8.14 x 682.9g) 45975 ÷ 5 h)

2. (a) I pay £16.20 to travel to work each week. I work for 45 weeks each year. How much do I pay to travel to work each year? Show your working. (b) I could buy one season ticket that would let me travel for all 45 weeks. It would cost £630. How much is that per week?

1 2 3 4 5 6

4 52 13 6939 = +

Country Population

Area (km2)Canada 3.1 × 10

71.0 × 10

7

France 6.0 × 107

5.5 × 105

Gambia 1.4 × 106

1.1 × 104

India 1.0 × 109

3.3 × 106

UK 6.0 × 107

2.4 × 105

USA 2.8 × 108

9.3 × 106

1. Answer the following (Draw a decimal number line to help)a) How many 1 digit decimals are there between

i) 2.3 and 2.9 ii) 8.5 and 9.8 iii) 0.5 and 6.2 iv) 3 and 4b) How many 2 digit decimals are there between

i) 3.42 and 3.49 ii) 8.02 and 8.17 iii) 3.9 and 4.0 iv) 3.2 and 3.5

Level 5 question The number 6 is halfway between 4.5 and 7.5

Fill in the missing numbers below

(a) The number 6 is halfway between 2.8 and ..................... 1 mark

(b) The number 6 is halfway between –1.5 and ..................... 1 markLevel 6 question – Fill in the missing decimal number.

(a) 15 ÷ ……….. = 15 x 0.1 1 mark

(b) 15 ÷ 1000 = 15 x ……….. 1 mark

(b) 15 x 0.01 = 15 ÷ ………….. 1 markLevel 7 question Each of these calculations has the same answer, 60. Fill in each gap with a number.

2 marksLevel 8 question – A housing report gave this information.

In the year 2001, the population of England was 49.87 million people. Most of these people lived in households. The total number of households was 20.97 million. The average (mean) household size was 2.34 people.

In the year 2001, what percentage of people in England did not live in households?

Give your answer to 1 decimal place.3 marks

Negative Numbers (5 – 8)

2. Round the following to one decimal place. a) 4.79 b) 7.43 c) 12.42 d) 13.64 e) 19.99 f) 16.47 3. Round the following to two decimal places. a) 0.473 b) 3.721 c) 8.648 d) 15.192 e) 81.196 f) 0.08524. Round the following to the nearest whole number. a) 2.53 b) 7.43 c) 13.64 d) 23.493 e) 13.642 f) 29.962

4.5 7.5

6

= 60

2.4 x 25

0.24 x ……

60 ÷ 1

6 ÷ ……

1. Put these numbers into ascending order (smallest to biggest). a) 5, -9, 2, -3, 1 b) -11, 4, 8, -3, -7 c) 49, -34, 6, -8, 112. What number is half way between a) 5 and -1 b) -6 and -14 c) 7 and -19 d) -7 and -21 e) 2 and -34

3. Work out the following a) 4 – 7 b) 7 – 13 c) 8 – (-4) d) 0 – 5 e) -11 – (-9) f) -34 + 19 g) -20 – 13 h) 11 + (-11) i) -8 – (-17) j) 15 – 7 k) -16 – 22 l) 62 – (-41)4. A deep sea diver needs to return to the surface. He is at a depth of -75 metres below and rises 40 metres. At what depth is he now?5. Billy is overdrawn at the bank by £180. His brother Mark is better off than him by £70. How much money does Mark have?6. What temperature is 12°C warmer than -4°C?7. Work out the following a) 4 x 5 b) -3 x 7 c) -14 x -2 d) 7 x -8 e) -9 x -1 f) -19 x 0 g) 82 ÷ 2 h) -36 ÷ -6 i) -54 ÷ 9 j) 350 ÷ -25 k) -81 ÷ 3 l) -56 ÷

Level 5 question – Write a number in each box to make the calculations correct.

a) b)

2 marksLevel 6 question – Write the missing numbers in the table. The first row is done for you.

Level 7 question - Write the missing numbers in these multiplication grids.

a) b)

3 marksLevel 8 question – Write a number in each box to make the inequalities true.

a) ÷ < -11 mark

b) –1 < ÷ < 0 1 mark

Primes, Factors and Multiples (5 – 8)

Level 5 question – (a) I am thinking of a number. My number is a multiple of 4.

First numbe

rSecondnumber

Sum of first and second

numbers

Product of first

and second numbers

3 6 9 185 –3 1

mark–8 –5 1

× 0.23 1.2

6

× 89 72–6 30

1. Find the Highest Common Factor (HCF) of the following sets of numbers a) 56 an 42 b) 36 and 54 c) 105 and 75 d) 64 and 80 e) 27, 18 and 992. Find the Lowest Common Multiple (LCM) of the following sets of numbers a) 6 and 9 b) 20 and 8 c) 16 and 12 d) 20 and 24 e) 15, 20 and 24 3. Write down all the prime numbers between 0 and 100.4. Find all the prime factors of these numbers. Write your answers in index notation (e.g. 2 x 2 x 2 x 5 = 23 x 5) a) 8 b) 20 c) 36 d) 42 e) 80 f) 99 g) 108 h) 168 i) 2165. Find all the prime factors of the following numbers. Use the prime factors to find the HCF and the LCM of each set.

a) 70 and 98 b) 90 and 165 c) 126 and 72d) 6 and 15 e) 48 and 88 f) 124 and 160

My numbermust be even

My numbermust be odd

My numbercould be odd or

even

My numbermust be

evenMy numbermust be odd

My numbercould be odd or

even

43

37

31

25

19

13

7

1

44

38

32

26

20

14

8

2

45

39

33

27

21

15

9

3

46

40

34

28

22

16

10

4

47

41

35

29

23

17

11

5

48

42

36

30

24

18

12

6

colum n X colu m n Y

Tick ( ) the true statement below.

Explain how you know. 1 mark

b) I am thinking of a different number. My number is a factor of 20 Tick ( ) the true statement below.

Explain how you know 1 markLevel 5+ Question -The diagram shows part of a number grid. The grid has 6 columns. All the prime numbers in the grid are circled.

(a) 35 is not circled. Explain why 35 is not a prime number.

1 mark(b) There are no prime numbers circled in column Y. Explain how you know there will never be a prime

number in column Y.

1 mark(c) There is one prime number circled in column X. Explain how you know there will never be another

prime number in column X. 1 mark

Fractions, Decimals & Percentages (5 – 8)

Level 5 question (a) Look at this diagram: What fraction is shaded?

1 mark

What percentage is shaded?

(b) Shade 52 of the diagram: 1 mark

What percentage of the diagram have you shaded?

1 mark

1. For each question, find the equivalent percentage: a) 0.45 b) c) d) 0.07 e) f) 0.483 g) h) 2. For each question, find the equivalent decimal: a) 57% b) c) d) 39% e) 5.4% f) g) 0.61% h)

3. For each question, find the equivalent fraction: a) 42% b) 0.36 c) 0.78 d) 97% e) 1.38 f) 137% g) 7% h) 0.08

70 × 0 .9 70 × 1.9 70 × 0.09 70 × 1.09

0 1 2

Level 6 question – Some of the statements below are correct. Circle the correct ones.

2 marksLevel 7 question - A teacher said to a pupil:

The pupil said:

Show that the pupil is wrong. 1 markLevel 8 question a) One calculation below gives the answer to the question What is 70 increased by 9%?Tick () the correct one.

1 markb) Choose one of the other calculations. Write a question about percentages that this calculation represents.

calculation chosen: ...........................question it represents: .............................. 1 mark

c) Now do the same for one of the remaining two calculations.calculation chosen: ...........................question it represents: ............................... 1 mark

Fractions (5 – 8)

Level 5 question – Fill in the missing numbers.a)

21 of 20 =

41 of ....................... b)

43 of 100 =

21

of .......................

c) 31 of 60 =

32

of ....................... 3 marks

Level 6 Question –

(a) Add 106 and

56 Now use an arrow ( ) to show the result on the number line

2 marks(b) How many sixths are there in 3

31 ? 1 mark

21 = 0.5

103

309

43750 .

21 is equivalent to 10%

51 is equivalent to

5%

To the nearest per cent is 17%

So, to the nearest per cent, must be 34%

61

62

1. Evaluate the following (Write each fraction in its simplest form)a) b) c) d) e) f)

g) h) i) j) k) l)

2. Solve each question. a) of 28 b) of 56 c) of 452 d) of 48 e) of 108 f) of 1475

g) of 36 h) of 84 i) of 111 j) of 48 k) of 143 l) of 72

A ll un it fractio ns m ust have

a n um era tor tha t is 1

a d en om ina tor tha t isan in te ge r grea ter than 1

13

(c) Work out Show your working 2 marks

Level 7 Question –

31 ,

81 ,

51 are all examples of unit fractions.

The ancient Egyptians used only unit fractions.For

43 , they wrote the sum

21 +

41

(a) For what fraction did they write the sum 21 +

51 ? Show your working. 1

mark(b) They wrote

209 as the sum of two unit fractions. One of them was

41

What was the other? Show your working 1 mark(c) What is the biggest fraction you can make by adding two different unit fractions? Show your working. 1 markLevel 8 Question –

I fill a glass with orange juice and lemonade in the ratio 1 : 4. I drink 41

of the contents of the

glass, then I fill the glass using orange juice. Now what is the fraction of orange juice in the glass? Show your working, and write the fraction in its simplest form.

3 marks

Percentages (5 – 8)

Level 5 question – Work out the following answersa) 10% of 84 = ___ 5% of 84 = ___ 2.5% of 84 = ___ 2 marksb) The cost of a CD player is £84 plus 17½% tax. What is the total cost of the CD player? You can use part (a) to help you. 2 marks

Level 6 Question – Kate asked people if they read a daily newspaper. Then she wrote this table to show her results.

The values in the table cannot all be correct.The error could be in the number of people.Complete each table to show what the correct numbers could be.

2 marks

1. Evaluate the following (Do Not use a calculator)a) 10% of 30 b) 25% of 460 c) 1% of 40 d) 15% of 70 e) 75% of 28 f) 30% of 61 g) 17.5% of 520 h) 99% of 57 i) 4% of 91 j) 42% of 310 2. Find the missing number (Do Not use a calculator)a) ___% of 100 = 45 b) 25% of ___ = 17 c) ___% of 75 = 15 d) 90% of ___ = 3. Evaluate the following (you may use a calculator) a) 4% of 28 b) 17% of 56 c) 71% of 452 d) 65% of 48 e) 9% of 108 f) 61% of 1475 g) 76% of 36 h) 97% of 84 i) 47% of 111 j) 88% of 484. Find the missing number (you may use a calculator)a) 42% of ___ = 189 b) ___% of 208 = 52 c) ___% of 34 = 19 d) 76% of ___ = 79

No 80 people = 40%Yes 126 people =

60%

No 80 people = 40%

Yes ......... people =

No .......... people = 40%

Yes 126 people =

Level 7 Question – In a quiz game two people each answer 100 questions. They score one point for each correct answer. The quiz game has not yet finished. Each person has answered 90 questions. The table shows the results so far.

Can person B win the quiz? Tick the correct answer, then Explain your answer.

2 marks

Level 8 Question – Here is part of a newspaper report about wildlife in a country in Africa.

About how many gorillas were there in this country ten years earlier? 2 marksRatio (5 – 8)

Level 5 question – Work out the number of boys and girls in each class below.a) In class 8K, there are 28 pupils. The ratio of boys to girls is 3 : 1 1 markb) In class 8T, there are 9 boys. The ratio of boys to girls is 1 : 2 1 mark

Level 6 Question – The screens of widescreen and standard televisions look different.

They have different proportions.

Keri starts to draw scale drawings of the televisions. For each, the height is 4.5 cm.What should the width of each scale drawing be?

Widescreen:Width = ____cm

Standard:Width = ___cm 2 marks

Level 7 Question – The diagram shows a shaded rectangle.It is divided into four smaller rectangles,

Person A Person B60% of the first 90questions correct

50% of the first 90

questions correctB can win.B cannot win but can draw.B cannot win or draw.

The number of gorillas has fallen by 70% in the last ten years. Only about 5000 gorillas are left.

1. Cancel down fully the following ratios.a) 6 : 4 b) 7 : 28 c) 8 : 20 d) 14 : 8 e) 15 : 35 f) 640 : 720 g) 96 : 24h) 2 : 4 : 10 i) 7 : 28 : 77 j) 18 : 30 : 54 k) 36 : 63 : 81 l) 28 : 35 : 562. Change the following into the same units, then cancel down the ratio.3. In a sandwich bar 120 ham, 30 egg and 10 chicken sandwiches are sold. Find the ratio of ham to egg to chicken sandwiches sold. Write it in its simplest form.4. Divide the following amounts by in the given ratios.a) £40 in the ratio 3 : 2 b) £49 in the ratio 5 : 2 c) £1540 in the ratio 9 : 5d) £65 in the ratio 7 : 3 e) £200 in the ratio 3 : 7 f) £240 in the ratio 5 : 3 : 2 g) £52.50 is split between Alec, Beth and Chloe in the ratio 3 : 5 : 7. How much does each one receive?

Widescreen Television

Standard Television

Ratio of height to width is 9 : 16

Ratio of height to width is 3 : 4

5 cm

3 cm

10 cm5 cm

A B

C DNot d rawnaccura tely

Number of boys

Number of girls

..................... .....................Number of boys

Number of girls

..................... .....................

4.5 cm Widescreentelevis ion

4.5 cm Standardte levision

labelled A, B, C and D.

The ratio of area C to area B is 1 : 2Calculate area A.

2 marksLevel 8 Question – Films at the cinema and films on television are shown at different speeds.

At the cinema a film lasts 175 minutes. How many minutes does the same film last on television? 2 marks

Number Review 1 (5 – 8)Level 5 questions1. a)Write the missing numbers. 50% of 80 = ......... 5% of 80 = ........ 1% of 80 = .......... 2 marks b) Work out 56% of 80 You can use part (a) to help you. 1 mark2. Look at this diagram it may help you work out some of these fraction calculations.

a) 1 mark

b) 1 mark

c) 1 mark

Level 6 Questions1. a) Give an example to show the statement below is not correct.

1 mark b) Now give an example to show the statement below is not correct.

1 mark c) Is the statement below correct for all numbers?

Explain how you know. 1 mark2. I think of a number. I multiply this number by 8, then subtract 66. The result is twice the number that I was thinking of. What is the number I was thinking of?

2 marksLevel 7 Questions 1. A three-digit number is multiplied by a two-digit number. How many digits could the answer have? Write the minimum number and the maximum number of digits that the answer could have. You must show your working. 2 marks2. Look at these number cards.

Cinema24 pictures per

second

Television25 pictures per

second

16

13 1

4

112

112

112

When you multiply a number by 2, the answer is always greater than 2When you subtract a number from 2, the answer is always less than 2

The square of a number is greater than the number itself.

0.2 2 10 0.1 0.05 1

a) Choose the two cards which give the lowest possible answer when they are multiplied.

____ x ____ = 2 marksb) Choose the two cards that give the answer 100 when divided.

____ ÷ ____ = 1 markLevel 8 Questions 1. a) Is 3100 even or odd? Explain your answer. 1 mark b) Tick ( ) the number below that is the same as 3100 × 3100 3200 6100 9200 310 000 910 000 1 mark2. People were asked if they were considering changing what they eat.

29% of the people asked said yes. Of these, 23% said they were considering becoming vegetarian. What percentage of the people asked said they were considering becoming vegetarian? 1 mark

Number Review 2 (5 – 8)Level 5 questions1 a) Show that 9 × 28 is 252 1 mark b) What is 27 × 28? You can use part (a) to help you 2 marks2. a) Nigel pours 1 carton of apple juice and 3 cartons of orange juice into a big jug. What is the ratio of apple juice to orange juice in Nigel's jug? apple juice : orange juice = ..................... : ..................... 1 mark b) Lesley pours 1 carton of apple juice and 1 ½ cartons of orange juice into another big jug. What is the ratio of apple juice to orange juice in Lesley's jug? apple juice: orange juice = ..................... : ..................... 1 mark c) Tandi pours 1 carton of apple juice and 1 carton of orange juice into another big jug. She wants only half as much apple juice as orange juice in her jug. What should Tandi pour into her jug now? 1 markLevel 6 Questions1. Write the missing numbers in the table. The first row is done for you.

2. Find the values of t and r.

a) b) 2 marks

Level 7 Questions1. a) Circle the best estimate of the answer to 72.34 ÷ 8.91

6 7 8 9 10 11 1 mark b) Circle the best estimate of the answer to 32.7 x 0.48

1.2 1.6 12 16 120 160 1 mark

c) Estimate the answer to5.23

22.18.62 . Give your answer to 1 sig. figure 1 mark

First number

Secondnumber

Sum of first and second numbers

Product of first and second numbers

3 6 9 185 –3 1 mark–8 –5 1 mark

Birth rate per 1000 population1961 1994

England 17.6Wales 17.0 12.2

d) Estimate the answer to 4.025.6724.428.6

1 mark

2. A newspaper printed this information about the world’s population.

On average, how many times as wealthy as one of the other 94 people would one of  these 6 people be? 2 marksLevel 8 Question 1. a) Each side of a square is increased by 10% By what percentage is the area increased? 2 marks

Number Review 3 (5 – 8)Level 5 questions1. Fill in the missing numbers of 20 = of ___ of 100 = of ___ of 60 = of ___ 3 marks2. Complete the sentences. a) ............................... out of 10 is the same as 70% 1 mark b) 10 out of 20 is the same as ..............................% 1 mark c) ..................... out of ..................... is the same as 5% 1 mark Level 6 Questions1. a) How many eighths are there in one quarter? 1 mark b) Now work out 2 marks2. a) Look at these numbers 16 25 34 43 52 61

Which is the largest? _____ Which is equal to 64? ____ 2 marks b) Which two of the numbers below are not square numbers?

24 25 26 27 28 ____ and ____ 1 mark

Level 7 Questions1. Look at the table

a) In England, from 1961 to 1994, the birth rate fell by 26.1%. What was the birth rate in England in 1994? Show your working. 2 marksb) In Wales, the birth rate also fell. Calculate the percentage fall from 1961 to 1994. Show your working. 2 marks2. A square of area 64cm2 is cut to make two rectangles, A and B.

The ratio of area A to area B is 3 : 1Work out the dimensions of rectangles A and B.Rectangle A: ......... cm by ............ cmRectangle B: ......... cm by ............ cm

2 marksLevel 8 Questions1. Look at the table:

If the world was a village of 100 people,6 people would have 59% of the

total wealth.The other 94 people would have the rest.

Area = 64cm2

Earth MercuryMass (Kg) 5.98x1024 3.59x1023

Atmospheric pressure (N/m2)

2x10-8

91

91

No 80 people = 40%

Yes 126 people = No 80 people =

40%Yes ....... people =

a) The atmospheric pressure on Earth is 5.05 × 1012 times as great as the atmospheric pressure on Mercury. Calculate the atmospheric pressure on Earth. 1 mark b) What is the ratio of the mass of Earth to the mass of Mercury? Write your answer in the form x : 1 1 mark c) The approximate volume, V, of a planet with radius r is given by 3

34V rπ

Assume the radius of Mercury is 2400 km. Calculate the volume of Mercury. Give your answer, to 1 significant figure, in standard form. 2 marks

Number Review 4 (5 – 8)Level 5 questions1. I am thinking of a number. What is my number? 2 marks 2.

a) 240 people paid the entrance fee on Monday. How much money is that altogether? Show your working.2 marks b) The museum took £600 in entrance fees on Friday. How

many people paid to visit the museum on Friday? Show your working.

2 marks3. Here is a list of numbers:

–7 –5 –3 –1 0 2 4 6 a) What is the total of all eight of the numbers on the list? 1 mark b) Choose the three numbers from the list which have the lowest possible total. Write the three numbers and their total. ...... + ...... + ...... = ...... You must not use the same number more than once. 2 marksLevel 6 Questions 1. Calculate 57.3 × 2.1 Show your working. 2 marks2. a) Some of the fractions below are smaller than Tick ( ) them.

101

94

21

1001

81

1 mark b) To the nearest per cent, what is as a percentage? Tick ( ) the correct percentage.

0.9% 9% 10% 11% 19% 1 mark c) Complete the sentence by writing a fraction. is half of ............. 1 mark

Level 7 Questions1. People who live to be 100 years old are called centenarians. In 1998 there were 135 000 centenarians. The ratio of male to female was 1 : 4. How many female centenarians were there in 1998? Show your working. 2 marks2. Kate asked people if they read a daily newspaper.

Then she wrote this table to show her results.The values in the table cannot all be correct.

a) The error could be in the number of people.

My number multiplied by 15 is 315My number multiplied by 17 is

Complete each table to show what the correct numbers could be.

1 markb) The error could be in the percentages.

Complete the table with the correct percentages.

2 marksLevel 8 Questions1. I start with any two consecutive integers. I square each of them, then I add the two squares together. Prove that the total must be an odd number. 3 marks2. A shop had a sale. All prices were reduced by 15%. A pair of shoes cost £38.25 in the sale. What price were the shoes before the sale? Show your working. 2 marks

Sequences and Nth Term (5 – 8)

Level 5 question (a) Here is a number chain:

2 4 8 16 32 64What could the rule be? 1 mark (b) Some number chains start like this:

1 5Show three different ways to continue this number chain. For each chain write down the next three numbers. Then write down the rule you are using.

Level 6 question - Uri makes a sequence of shapes using square tiles as in the diagram. The number of square tiles in shape number n is 2n + 1.Uri makes a different sequence of shapes. This time the number of tiles in shape number n is 3n + 1. Draw what the first 3 shapes might look like.

Level 7 question Look at this part of a number line. Copy and fill in the 2 missing numbers

-7 9........ 1 5 ........ 17

Finish the sentence:The numbers on this number line go up in steps of .............................. 2 marks

No 80 people = ......... %

Yes 126 people = ......... %

Find the next 5 terms of the following sequences and describe the rule:b) 3, 6, 9, 12, 15, ………….c) 4, 7, 10, 13, 16, …………d) 23, 21, 19, 17, 15, …………e) 1, 2, 4, 8, 16, …………f) 8000, 4000, 2000, 1000, …………

Find the nth term and the 20th term for each of these sequences:a) 5, 7, 9, 11, 13, …… b) 7, 11, 15, 19, 23, ……c) -1, 1, 3, 5, 7, …… d) 9, 12, 15, 18, 21, ……e) 5, 8, 13, 20, 29, …… f) -2, 1, 6, 13, 22, ……

shapenum ber

1

shapenum ber

2

shapenum ber

3

Level 8 question - Each pattern below shows a square grid that is 2 squares high. Only one square at each end of the top row is shaded. All squares in the bottom row are shaded.

Imagine one of these patterns that has n squares in the bottom row. Write an expression for the fraction of the pattern that is shaded. 2 marks

Simplifying (5 – 8)

Level 5 question

Simplify these expressions.5k + 7 + 3k ........................... 1 markk + 1 + k + 4 ......................... 1 markLevel 6 question

Write the correct operations (+ or – or × or ÷) in these statements.a .............. a 0a .............. a 1a .............. a 2a

a .............. a a2

2 marks

Level 7 question

Write these expressions as simply as possible.9 – 3k + 5k ............................ 1 mark

k2

+ 2k + 4k ............................ 1 mark3k × 2k ............................ 1 mark

kk

39 2

............................ 1 mark

Level 8 question

(a) Show that baba

–– 22

simplifies to a + b 1 mark

(b) Simplify the expression 22

23

baba

1 mark

1) 3r + 2r – 2r 2) 6p + p – 3p3) 8u + 5u – 2u + u 4) 6h – 2h – h – h 5) 8j – 2j + j + 3j – 4j 6) 3x – 2y – 4x + 8y

a) b) c)

d) e) f)

g) h) n)

(c) Simplify the expression 22

3223

bababa –

Show your working. 2 marks

Manipulation (5 – 8)

Level 5 question 1. Brackets

Jenny wants to multiply out the brackets in the expression 3(2a + 1)She writes:

3(2a + 1) = 6a + 1Show why Jenny is wrong. 1 mark

Level 6 question2. Bracket multiplication

Multiply out the brackets in these expressions.y (y – 6) .......................................................... 1 mark

(k + 2)(k + 3) .................................................. 1 mark

Level 7 question3. Factors again

(a) Ring the expression below that is the same as y2 + 8y + 12

(y + 3) (y + 4) (y + 7) (y + 1) (y + 2) (y + 6)(y + 1) (y + 12) (y + 3) (y + 5) 1 mark

(b) Multiply out the expression (y + 9) (y + 2)

Write your answer as simply as possible. 2 marks

Level 8 question4. Factorising

(a) Complete these factorisations.

x2 + 7x + 12 (x + 3)(........... + ...........) 1 mark

x2 – 7x – 30 (x + 3)(........... – ...........) 1 mark

(b) Factorise these expressions.

x2 + 7x – 18 2 marks

x2 – 49 1 mark

Factorisea) 4x + 24 b) 3a2 + 9a c) 8b – 12 d) 4p2 + 3p

Expand these bracketsa) 3(4+a) b) 6(2-3a) c) a(a+3) d) a(2a+3b)e) 3a(5a-2b) f) (x+2)(x+5) g) (x-3)(x+4) h) (2x+1)(3x+5)i) (5x-2)(5x+2) j) (3a+2)2 k) (p+3q)(2p-5q)

Solving Equations (5 – 8)

Level 5 question 1. Solving

Solve these equations.32x + 53 = 501 1 mark375 = 37 + 26y 1 mark

Level 6 question2. Finding y

Solve this equation.3y + 14 5y + 1 2 marks

Level 7 question3. x and y

Solve these simultaneous equations using an algebraic method.3x + 7y 18x + 2y 5

You must show your working.

x = ......................... y = ......................... 3 marks

Level 8 question4. Equation solving

Solve this equation.Show your working.

33

3)–5(2y

y2 marks

Substitution (5 – 8)

Solve these equations1) 4x + 3 = 2x + 11 2) 5x + 7 = 3x + 11 3) 2x – 4 = 5x – 194) 6x – 2 = 3x + 10 5) 7x + 4 = 10x – 20 6) 9x + 7 = 15x + 17) 8x + 3 = 2x + 21 8) 3x – 6 = 10 – x

Solve these equations1) x – 5 = 15 2) e – 7 = 10 3) u – 5 = 5 4) 8 + t = 235) 16 – y = 8 6) 34 – r = 18 7) 4x = 16 8) 5r = 259) 2w = 18 10) 6y = 36 11) 5m = 30 12) 2a = 1613) 2x + 3 = 15 14) 3x + 1 = 13 15) 2x + 6 =12 16) 6x – 8 = 1017) 25 = 5x + 15 18) 10 = 8x – 14 19) 6x – 3 = 10 20) 7 + 4r = 3

Let a = 4, b = 1, c = 5 and d = 101) a + b + c 2) abc 3) 3(d + c) 4) a(c – b)5) (a + b)(d – c) 6) 2a + 3c 7) 5d – 3c 8) abc – bd

9) 10) 11) 12)

Level 5 question 1. Values

Look at the three expressions below.8 + k 3k k

2

When k 10, what is the value of each expression?

8 + k ........................... 3k ...........................k2 ........................... 2 marks

Level 6 question2. Heron of AlexandriaAbout 2000 years ago, a Greek mathematician worked out this formula to find the area of any triangle.

For a triangle with sides a, b and c

Area csbsass

where 2

cbas

A triangle has sides, in cm, of 3, 5 and 6Use a 3, b 5 and c 6 to work out the area of this triangle. 2 marks

Level 7 question3. Algebra(a) Find the values of a and b when p 10

23 3pa 1 mark

pppb

732 2 –

1 mark

Level 8 question4. Equation

Look at this equation.

1060

–xy

(a) Find y when x 19There are two answers. Write them both.

y = ......................... or y = ......................... 1 mark

Coordinates (5 – 8)

Let a = 2, b = -1 and c = -31) 5c 2) 4b 3) 3c – a 4) 10a + c5) a + c 6) a – c 7) b + c 8) bc

Question 1 – Draw a grid with axis from -5 to 5 and plot these points.

Question 2 – Write the coordinates of the points labelled A to K.

Level 5 question 1. Midpoint

P is the midpoint of line AB.

What are the coordinates of point P?

P is (................ , ................)

1 mark

Level 6 question2. (b) Q is the midpoint of line MN.

The coordinates of Q are ( 30, 50 )

What are the coordinates of points M and N?M is (................ , ................) 1 mark

N is (................ , ................) 1 mark

Level 7 question3.Points and rules(a)The grid shows six points labelled A, B, C, D, E and F.Complete the table to show which points have coordinates that match the rules below.The first one is done for you.

Forming Equations (5 – 8)

Rule A B C D E Fx 3

y –3x y

120

0

P

B

A

y

x120

0

y

x

M

Q

N

(30, 50)

4

3

2

1

0

–1

–2

–3

–4

210–1–2–3–4 43

AB

C

D E

F

x

y

Level 5 question

1. A ruler costs k pence. A pen costs m pence.Match each statement with the correct expression for the amount in pence.The first one is done for you.

3 marks

Level 6 question2. Look at the information.

x = 4 y = 13

Complete the rules below to show different ways to get y using x.The first one is done for you.To get y, multiply x by .........2......... and add ..........5.........This can be written as y =......... 2x + 5.........

To get y, multiply x by .............................. and add ..............................This can be written as y = ............................. 1 mark

To get y, multiply x by .............................. and subtract ..............................This can be written as y = .............................. 1 mark

To get y, divide x by ....................... and add .......................This can be written as y = ........................... 1 markLevel 8 question3. a and b

In this question, a and b are numbers where a b + 2The sum of a and b is equal to the product of a and bShow that a and b are not integers. 3 marks

The change from £5,in pence, when you buy 5 pens

H ow m uch m ore 5 pens costthan 5 ru lers

The total costof 5 rulers and 5 pens

The total costof 5 ru lers

Sta tem ent

5 – 5k m

5 – 5m k

5( )k m +

5 + k m

500 – 5m

5 – 5m

5m

5k

Expression

Linear Graphs (5 – 8)

Level 6 question

1. The graph shows the straight line with equation y 3x – 4

(a) A point on the line y 3x – 4 has an x-coordinate of 50What is the y-coordinate of this point? 1 mark (b)A point on the line y 3x – 4 has a y-coordinate of 50What is the x-coordinate of this point? 1 mark

Level 7 question2. Here are six different equations, labelled A to F

Think about the graphs of these equations. (a) Which graph goes through the point (0, 0)? 1 mark (b) Which graph is parallel to the y-axis? 1 mark (c) Which graph is not a straight line? 1 mark (d) Which two graphs pass through the point ( 3 , 7 )? 2 marks

Level 8 question

3. The graph of the straight line with equation y x + 1 passes through the point (0, 1) (a) Write the equations of two different straight lines that also pass through the point (0, 1)

2 marks

Algebra Review 1 (5 – 8)Level 5 question

Draw the following graphs on the same axis where x goes from -5 to 5. Don’t forget you will need to draw a table first!

a) y = 4x + 5 b) y = 3x + 3c) y = 3x – 3 d) y = 2x + 1e) y = 2x f) x = 3g) y = -2

–4 4

4

–4

0

y

x

A B C

D E F

y x = 3 – 4 y = 4 x = – 5

x + y = 10 y x = 2 + 1 y x = 2

1. Simplify these expressions.5k + 7 + 3k ............................................................................................... 1 mark

k + 1 + k + 4 ............................................................................................. 1 mark

2. Some people use yards to measure length. The diagram shows one way to change yards to metres.

× 36 × 2 .54 100num ber o fya rds

num ber ofm etres

(a) Change 100 yards to metres. 1 markLevel 6 question3. Write the missing numbers.

6x + 2 = 10so 6x + 1 = ............. 1 mark

1 – 2y = 10

so (1 – 2y)2 = ............. 1 mark

4. Multiply out this expression.Write your answer as simply as possible.5(x + 2) + 3(7 + x) 2 marks

Level 7 question5. Look at the triangle.

a ° b °

2b °a °

N ot draw naccurate ly

Work out the value of a 3 marks

6. Multiply out these expressions.Write your answers as simply as possible.5(x + 2) + 3(7 + x) 2 marks

(x + 2)(x + 5) 2 marksLevel 8 question7. I am thinking of a number.

When I subtract 25 from my number, then square the answer,I get the same result aswhen I square my number, then subtract 25 from the answer.

What is my number?You must show an algebraic method. 2 marks

8. For each equation below, when x increases by 3, what happens to y?

Complete the sentences.y = x

When x increases by 3, y increases by................y = 2x

When x increases by 3, y increases by................ 2 marks

Algebra Review 2 (5 – 8)Level 5 question

1. Look at this sequence of patterns made with hexagons.

pattern num ber 1 pattern num ber 2

pattern num ber 3 To find the number of hexagons in pattern number n you can use these rules:

Number of grey hexagons n + 1Number of white hexagons 2n

Altogether, what is the total number of hexagons in pattern number 20? 2 marks

Level 6 question2. Look at this equation.

14y – 51 187 + 4y

Is y 17 the solution to the equation?Yes No

Show how you know. 1 markLevel 7 question3. (a) Draw lines to match each nth term rule to its number sequence.

nth term Number sequence

4n 4, 7, 12, 19 , …

(n + 1 )2 4, 8 , 12, 16, …

n2 + 3 4, 9 , 16, 25, …

n n + ( 3) 4, 10, 18 , 28, …

2 marks (b) Write the first four terms of the number sequence using the nth term rule below.

n 3 + 3

, , , 2 marks

Shapes and Their Properties (5 – 8)

Level 5 question (a) A triangle has three equal sides. Write the sizes of the angles in this triangle.

................°, ................°, ................° (1 mark)(b) A right-angled triangle has two equal sides. Write the sizes of the angles in this triangle. ................°, ................°, ................° (1 mark)Level 6 question - Any quadrilateral can be split into 2 triangles.a) Explain how you know that the angles inside a quadrilateral add up to 360°

(1 mark)(b) What do the angles inside a pentagon add up to? (1 mark)

(c) What do the angles inside a heptagon (7-sided shape) add up to? Show your working. (2 marks)

Level 7 question -The diagram shows a rectangle that just touches an equilateral triangle.

( a) Find the size of the angle marked x(1 mark)

(b) Now the rectangle just touches the equilateral triangle so that ABC is a straight line.

Show that triangle BDE is isosceles.(2 marks)

Level 8 question – A pupil has three tiles. One is a regular octagon, one is a regular hexagon, and one is a square. The side length of each tile is the same. The pupil says the hexagon will fit exactly like this. Show calculations to prove that the pupil is wrong (3 marks)

2. Name the following quadrilaterals.

______ ______ ______ _______ _______ _______3. What is a Re-Entrant Quadrilateral? Draw an example.4. What does the word ‘regular’ mean when used to describe a polygon? (e.g. Regular Pentagon, Regular Octagon, etc)

1. Fill in the blanks with the correct Triangle names:a) A triangle with 3 equal sides and 3 equal angles is a(n) ________ triangle.b) A triangle with no equal sides or angles is a(n) _______ triangle.c) A triangle with a 90º angle is called a(n) __________ triangle.d) A triangle with 2 equal angles and 2 equal sides is a(n) ________ triangle.

Angles and Angle Facts (5 – 8)

Level 5 question - The diagram shows triangle PQR. Work out the sizes of angles a, b and c

a = ………………° b = ………………° c = ………………°

(3 marks)

Level 6 question - Look at the diagram, made from four straight lines. Work out the sizes of the angles marked with letters.

a = .........................° b = .........................°c = .........................° d = .........................°

(3 marks)

Level 7 question - The diagram shows a rhombus.The midpoints of two of its sides are joined with a straight line.

What is the size of angle p?

p = .............................°(2 marks)

Level 8 question – AC is the diameter of a circle and B is a point on the circumference of the circle. What is the size of angle x?

x = .............................° (2 marks)

Isometric Drawing (5 – 8)

1. Use a protractor to accurately measure the following angles.(trace them intoyour book and extend the lines)

2. Find each missing angle.

1) The following solids have been partially completed on isometric paper. On Isometric paper, copy and complete the solid.

Level 5 question 1. a) This cuboid is made from 4 small cubes. On isometric paper draw a cuboid that is twice as high, twice as long and twice as wide.

(2 marks)

b) Graham made this cuboid from 3 small cubes. Mohinder wants to make a cuboid which is twice as high, twice as long and twice as wide as Graham's cuboid. How many small cubes will Mohinder need altogether?

(1 mark)

Level 6 and above questions1) I join six cubes face to face to make each 3-D shape below. I can then join the 3-D shapes to make a cuboid. Draw this cuboid on isometric paper.

2) Four cubes join to make an L-shape.The diagram shows the L-shape after quarter turns in one direction.On isometric paper, draw the L-shape after the next quarter turn in the same direction

Nets and Plan Views (5 – 8)

Level 5 question (a) Alex is making a box to display a shell. The base of the box is shaded.

He draws the net of the box like this:

1. Below are the plan (top), side and front elevations (views) of a solid. For each one identify (name) the solid and sketch a net of the solid.

Alex wants to put a lid on the box. He must add one more square to his net. On each diagram below, show a different place to add the new square. Remember, the base of the box is shaded.

(3 marks)

(b) Alex makes a different box with a lid hinged at the top. The base of his box is shaded. Complete the net below.

(3 marks)Level 6 and above question - The diagram shows a model made with nine cubes. Five of the cubes are grey. The other four cubes are white. (a) The drawings below show the four side-views of the model.Which side-view does each drawing show?

(1 mark)

(b) Complete the top-view (c) Imagine you turn the model upside of the model by shading down. What will the new top-view the squares which are of the model look like? Complete grey. the new top-view of the model by

shading the squares which are grey.

(1 mark) (1 mark)Area and Perimeter (5 – 8)

Level 5 question – Here is a rectangle.a) A square has the same area as this rectangle. What is the side length of this square?

(1 mark)b) A different square has the same perimeter as this rectangle. What is the side length of this square? (1 mark)Level 6 question - The diagram shows a shaded parallelogram drawn inside a rectangle.

(not drawn accurately)

What is the area of the shaded parallelogram?

side–vie w Cs ide –view B

s ide –view Aside–vie w D

top - view n ew top - v iew

1. Find the Area and the Perimeter for each shape. Don’t forget your units!

3 cm10 cm

5 cm

3 cm

You must give the correct unit with your answer.

(2 marks)Level 7 question - The diagram shows two circles and a square, ABCD. A and B are the

centres of the circles. The radius of each circle is 5 cm.(not drawn accurately)

Calculate the area of the shaded part of the square.

(3 marks)

Level 8 question – Two right-angled triangles are joined together to make a larger triangle ACD.

a) Show that the perimeter of triangle ACD is 78 cm.

(2 marks)

b) Show that triangle ACD is also a right-angled triangle.

(2 marks)Volume and Surface Area (5 – 8)

Level 5 question – This shape is made from 4 cubes put together.The table shows information about the shape.

The same four cubes are then used to make this new shape.Copy and Complete the table for the new shape.

(2 marks)Level 6 question - The drawing shows 2 cuboids that have the same volume.

a) What is the volume of cuboid A? (Remember to state your units.)

(2 marks)

5 cm

5 cmA

B

C

D

2. Dog food comes in two types of tins. A square based tin of side 8.5cm and height 15cm and a circular based tin of radius 5cm and height 13cm.a) Calculate the Volume of each tin. Which one holds more and by how much?b) A label will be made for each tin. It will go around the tin covering everythingexcept the top and bottom lids. How much paper will each tin need for its label?

1. Find the volume and surface area of the following objects. (Don’t forget the correct units)

Volume 4 cm3

Surface Area 18 cm2

Volume......... cm3

Surface Area......... cm2

b) Work out the value of the length marked x

(1 mark)Level 7 question a) Look at the triangular prism. Work out the volume of the prism. (Not drawn accurately) (1 mark)

b) One face of another prism is made from 5 squares. Each square has side length 3cm. (not drawn accurately) Work out the volume of the prism. (1 mark)

Level 8 questions

Transformations & Loci (5 – 8)

Level 5 question (a) I have a square piece of card. I cut along the dashed line to make two pieces of card. Do the two pieces of card have the same area? Explain your answer. (1 mark)

(b) The card is shaded grey on the front, and black on the back.I turn piece A over to see its black side. Which of the shapes below shows the black side of piece A?

(1 mark)Level 6 question

The grid shows an arrow. Copy the grid carefully into your book, then draw an enlargement of scale factor 2 of the arrow. Use point C as the centre of enlargement.

(2 marks)

Level 7 question In a wildlife park in Africa, wardens want to know the position of an elephant in a certain area.They place one microphone at each corner of a

10 cm

4 cm

6 cm

10 cm

3 cm

2.5 cm

he igh t

1) Six cubes each have a surface area of 24 cm2. They are joined together to make a cuboid. What could the surface area of this cuboid be? There are two different answers. Write them both.

(2 marks)

2) A cylinder has a radius of 2.5 cm. The volume of the cylinder, in cm3, is 4.5π. What is the height of the cylinder? Show your working.(3 marks)

1. Trace the diagram into your book. By measurement, reflect the Flag A in the mirror line M1. Label this A1. Then, by measurement, reflect the Flag A1 in mirror line M2. Label this A2.

fron t o fpiece A

2. Draw each shape, Reflect each shape along the marked side (●) without the use of a mirror. Then Draw the shape again and Rotate each shape about the marked point (●) 180º clockwise and 90º anticlockwise.

4 km by 4 km square. Each microphone has a range of 3½ km.The elephant is out of range of microphones A and B.Where in the square could the elephant be? (Draw an 8cm by 8cm square and use the scale 2cm = 1km)Show the region accurately on the diagram, and label the region. (2 marks)Level 8 question- A picture has a board behind it.The drawings show the dimensions of the rectangular picture and the rectangular board.(a) Show that the two rectangles are not mathematically similar.

Shape and Space Review 1 (5 – 8)Level 5 questions1. These two congruent triangles make a parallelogram.a) Draw another congruent b) Draw another congruent c) Draw another congruent triangle to make a triangle to make a bigger triangle to make a rectangle. (1 mark) triangle. (1 mark) different bigger triangle.

(1 mark)

2. Three shapes fit together at point B. Will ABC make a straight line? Explain your answer.

(1 mark)

Level 6 questions 3. The diagram shows three straight lines.Work out the sizes of angles a, b and cGive reasons for your answers.a = ................° because ……………………………. (1 mark)b = ................° because ……………………………. (1 mark)c = ................° because ……………………………. (1 mark)

4. Kevin is working out the area of a circle with radius 4 He writes: Area = π × 8. Explain why Kevin’s working is wrong.Level 7 questions5. Look at the triangle. Work out the value of a

(3 marks)

6. The diagram shows a shaded rectangle. It is divided into four smaller rectangles, labelled A, B, C and D. The ratio of area C to area B is 1 : 2 Calculate area A

(2 marks)

Level 8 question7. The diagram shows a square inside a triangle.

93º

61º24ºA

B

C

Not draw naccurately

4

DEF is a straight line. The side length of square ABCE is 12 cm. The length of DE is 15 cm. Show that the length of EF is 20 cm. (3 marks)

Shape and Space Review 2 (5 – 8)Level 5 question1. Some statements in the table are true. Some are false. Beside each statement, write true or false. For true statements you must draw an example. The first one is done for you. (3 marks)

Statement Write true or false. If true, draw an example.

Some triangles have one right angle and two acute angles. true

Some triangles have three right angles.Some triangles have three acute angles.Some triangles have one obtuse angle and two acute angles.Some triangles have two obtuse angles and one acute angle.

Level 6 questions2. The diagrams show nets for dice.Each dice has six faces, numbered 1 to 6Write the missing numbers so that the numbers on opposite faces add to 7

(2 marks)3. This shape has been made from two congruent isosceles triangles. What is the size of angle p? (Not drawn accurately)

(2 marks)

Level 7 question4. The diagram shows two circles and a square, ABCD. (Not drawn accurately) A and B are the centres of the circles. The radius of each circle is 5 cm. Calculate the area of the shaded part of the square. (3 marks)Level 8 question5. Engineers have worked on the leaning tower of Pisa to make it safe. A website gave this information about the tower before the work. Give calculations to show that the information cannot all be true. (2 marks)

5 cm

5 cmA

B

C

D

- The height of the tower is 56 m.- The angle of tilt is 5.5°- The tower leans 5.2 m from the perpendicular.

35°

35 °

p

Shape and Space Review 3 (5 – 8)Level 5 question1. Look at these angles

a) One of the angles measures 120° Write its letter. (1 mark)b) Using a protractor accurately draw an angle measuring 157°. Label the angle 157°.

(2 marks)c) 15 pupils measured two angles. Here are their results. Use the results to decide what each angle is most likely to measure.

Angle A is ..............°

How did you did decide? (1 mark)

Angle B is ……………º

How did you Decide? (1 mark)

Level 6 questions2. Each diagram shows an enlargement of scale factor 2. Where is the centre of enlargement in these diagrams? Mark each one with a cross. (2 marks)

3. The diagram shows a rectangle. (Not drawn accurately) Work out the size of angle a You must show your working

(3 marks) Level 7 questions4. Calculate the area of this triangle. You must show your working. The picture is not drawn to scale. (3 marks)

5. ABC and ACD are both right-angled triangles. (Not drawn accurately)a) Explain why the length of AC is 10 cm.

(1 mark)b) Calculate the length of AD. Show your working. (2 marks)Level 8 question6. A satellite passes over both the north and south poles, and it travels 800 km above the surface of the Earth. The satellite takes 100 minutes to complete one orbit. Assume the Earth is a sphere and that the diameter of the Earth is 12,800 km. Calculate the speed of the satellite, in kilometres per hour. Show your working. (3 marks)

Shape and Space Review 4 (5 – 8)Level 5 question b) Where could you put point E so1. a)Where should you put point D so that shape ABCDE is a trapezium?

800 kmN

Angle A Angle BAngle

measured asNumber of

pupilsAngle

measured asNumber of

pupils6° 1 45° 5

37° 2 134° 338° 10 135° 439° 2 136° 3

6 cm

8 cmAB

C

D

6 cm

that shape ABCD is a square? Mark point E on the grid below. Mark point D on the grid. (1 mark) (1 mark)

Now write the coordinates of point E(……….. , ………..) (1

mark)Level 6 question2. The drawing shows an isosceles triangle. (not drawn accurately)

(a) When angle b is 70º, what is the size of angle a? Show your working. (2 marks)

(b) When angle a is 70º, what is the size of angle b? Show your working. (2

marks) Level 7 question3. Some pupils want to plant a tree in the school’s garden. The tree must be at least 12m from the school buildings. It must also be at least 10m from the centre of the round pond.a) Trace the diagram into your book. Show accurately on the plan the region in which the tree can be planted. Shade in this region. (3 marks)

(b) The pupils want to make a gravel path of width 1m around the pond. Calculate the area of the path. Show your working. (2 marks)Level 8 question4. The diagram shows two circles that intersect at P and Q. B is the centre of the larger circle. C is the centre of the smaller circle. ABCD is a straight line. Prove that the line through A and P is a tangent of the smaller circle. (2 marks)

Shape and Space Review 5 (5 – 8)Level 5 questions1. Look at this shape made from six cubes. Four cubes are white Two cubes are grey.Part of the shape is rotated through 90° to make the shape below.

AB C D

P

Q

After another rotation of 90°, the shape is a cuboid.Draw this cuboid on the isometric paper.

(2 marks)

2. The diagram shows a rectangle 18cm long and 14cm wide. It has been split into four smaller rectangles.a) Write the area of each small rectangle on the diagram. One has been done for you. (1 mark)b) What is the area of the whole rectangle? (1 mark)c) What is 18 × 14? (1 mark)Level 6 questions3. The squared paper shows the nets of cuboid A and cuboid B. a) Do the cuboids have the same surface area? Show calculations to explain how you know.

(1 mark) b) Do the cuboids have the same volume? Show calculations to explain how you know. (2 marks)

Level 7 question4. a) The grid shows an arrow. Copy the grid, and draw an enlargement of scale factor 2 of the arrow. Use point C as the centre of enlargement.

(2 marks) b) The sketch below shows two arrows. The bigger arrow is an enlargement of scale 1.5 of the smaller arrow.

Write down the three missing values.(3 marks)

Level 8 question5. The diagram shows five points joined with four straight lines. BC and AD are parallel. BCE and ADE are isosceles triangles. The total length of the four straight lines is 40 cm. What is the length of EA? (3 marks)

............... cm 2

40cm 2

............... cm 2

............... cm 2

10cm 8cm

10cm

4cm

Shape and Space Review 6 (5 – 8)Level 5 question I fold square A in half to make 1. a) I have a square piece of paper. rectangle B The diagram shows information about this square labelled A. Then I fold rectangle B in half to

make square C. Complete the table below to show the area and perimeter of each shape.

(3 marks)

b) I start again with square A. Then I fold it in half to make triangle D. What is the area of triangle D? (1 mark) c) One of the statements below is true for the perimeter of triangle D. Put a ring around the correct one.

The perimeter is less than 24cm The perimeter is 24cm The perimeter is greater than 24cm

Explain your answer (1 mark)Level 6 question2. The drawing shows how shapes A and B fit together to make a right-angled triangle.

Work out the size of each of the angles in shape B.

(3 marks)

Level 7 question3. ABCD is a parallelogram (Not drawn accurately) Work out the sizes of angles h and j Give reasons for your answers.

(2 marks)

Level 8 question4. a) The triangles below are similar. (Not drawn accurately) What is the value of p? Show your working.

(2 marks)b) Triangles ABC and BDC are similar.

What is the length of CD? (1 mark)

A

BC

D

j

h

80°

60°

AB

8 cm

8 cmA B

C

Area PerimeterSquare A cm2 cmRectangle B cm2 cmSquare C cm2 cm

D

x

x

A D

B

C

6 cm

3 cm

Frequency Tables (5 – 8)

Level 6 question1.On World Book Day, each pupil in Year 7 chose one book to read.Some pupils chose a fiction book. Some chose a non-fiction book.

(a) Complete the two-way table. 2 marks(b) What percentage of boys chose a non-fiction book? Show your working. 2 marksLevel 7 question2. Altogether, I have 10 bags of sweets.

The mean number of sweets in the bags is 41The table shows how many sweets there are in 9 of the bags.

Number of sweetsin a bag

Frequency

394041424344

321102

Calculate how many sweets there are in the 10th bag.You must show your working.

2 marks

2. A survey was done to see how many letters were delivered to each house on North Street on one day. The results are shown in the table below.

Number of letters Frequency0 41 62 103 44 35 16 2

a) How many houses had 3 letters delivered?b) What was the highest amount of letters that were delivered to a single

house?c) How many houses were there on the street altogether?d) How many houses has 4 or more letters delivered? How many letters

was this in total?e) Overall how many letters were delivered on North Street on this day?

1. In a taste test, 30 people were asked to select their favourite sausage from four brands. The brands were Porkers (P), Sizzlers (S), Yumbos (Y), and Bangers (B). These are the results:P, B, B, B, B, Y, P, Y, B, Y, P, P, S, B, B, B, S, Y, P, B, P, Y, P, S, P, Y, B, Y, B, PUse a frequency table to organise this data.

F ictio n 77

3 6

6 8 14 2

B oys G irls Tota l

N on-fic tion book

Tota l

Two-w ay table

Averages (5 – 8)

Level 5 question 1.(a) Look at these three numbers.

9 11 10

Show that the mean of the three numbers is 10 1 mark Explain why the median of the three numbers is 10 1 mark (b) Four numbers have a mean of 10 and a median of 10, but none of the numbers is 10

What could the four numbers be?Give an example. 1 mark

Level 6 question2. Statistics

Here are three number cards.The numbers are hidden.

? ? ?

The mode of the three numbers is 5The mean of the three numbers is 8

What are the three numbers? Show your working. 2 marksLevel 8 question3. Here is information about a data set.

There are 100 values in the set.The median is 90The mean is 95

I increase the highest value in the data set by 200

Now what are the median and the mean of the data set? 2 marks

1) Lisa and Lucy have both completed 10 French homeworks. These are their marks out of 10.Lisa 7, 8, 7, 8, 7, 8, 8, 7, 7, 8Lucy 3, 9, 10, 4, 5, 9, 10, 3, 10, 10

a) Calculate the mean, median, mode and range for each person.b) Say who you think is better at French and why?

2) The midday temperatures in two different seaside resorts for a week during July were:Skegness - 22C, 21C, 23C, 24C, 26C, 24C, 24CEastbourne - 28C, 30C, 24C, 20C, 19C, 26C, 30C

a) Find the median midday temperature and the range for Skegness and Eastbourne.

b) Describe the differences between the two resorts.

3) The number of goals scored in eleven Premier League matches one Saturday was:

1, 0, 0, 2, 3, 5, 2, 4, 5, 2, 3Find the modal number of goals scored and the mean, median and range.

Averages from a frequency table (5 – 8)

Level 7 questions1. A pupil investigated how the teachers at his school travel to work.

The table shows the results.Number of teacherswho travel by car

Number of teacherswho do not travel by car

18 7(a) What percentage of these teachers travel by car? 1 mark (b) 18 teachers travel by car. Some of these teachers travel together

Write the missing frequency in the table below.Number of teachersin one car

Number of cars

12 43 2

1 mark (c) What is the mean number of teachers in each car? 2 marks

2. Owls eat small mammals. They regurgitate the bones and fur in balls called pellets. The table shows the contents of 62 pellets from long-eared owls.

Number of mammalsfound in the pellet 1 2 3 4 5 6

Frequency 9 17 24 6 5 1

(a) Show that the total number of mammals found is 170 1 mark (b) Calculate the mean number of mammals found in each pellet. Show your working and give your answer correct to 1 decimal place. 2 marks

(c) There are about 10 000 long-eared owls in Britain. On average, a long-eared owl regurgitates 1.4 pellets per day. Altogether, how many mammals do the 10 000 long-eared owls eat in one day? Show your working and give your answer to the nearest thousand. 2 marksLevel 8 question4. A teacher asked fifty pupils in Year 9 the question ‘How much time did you spend on homework last night?’ The results are shown in the frequency table

Time spent on homework (mins) Frequency0 time 30 630 time 60 1460 time 90 2190 time 120 9

Total 50

Find the mean from the following frequency tables:

Show that an estimate of the mean time spent on homework is 64.8 minutes.

2 marks.

Displaying Data (5 – 8)

Level 5 question 1. Look at this information.

In 1976, a man earned £16 each week.

The pie chart shows how he spent his money.

Entertainm ent

O ther

C lothes

R ent

Food

(a) How much did the man spend on food each week? 1 mark (b) Now look at this information.

In 2002, a man earned £400 each week.

The table shows how he spent his money.Rent £200Food £100Entertainment £50Other £50

Draw a pie chart to show how the man spent his money.Remember to label each sector of the pie chart. 2 marks

2. a) Draw a stem and leaf diagram to show this information.142, 157, 136, 149, 163, 139, 140, 158, 139, 151, 132, 148, 143

1. Twenty students are given a mark out of 5 for a short test. The results were:

Mark Frequency

012345

219

1383

b) Write down all of the numbers that are represented in the stem and leaf diagram shown.c) Find the median number from the stem and leaf diagram shown.

a) Draw a bar chart to show this information.

b) Draw a pie chart to show this information.

Interpreting Data (5 – 8)

Level 5 question 1. Teachers

The pie charts show how pupils answered three questions about teachers.Question 1 Question 2 Question 3

Shou ld tea chersgive hom ew ork?

Shou ld teache rsm ake jokesin lesson s?

Shou ld tea chers te llp up ils off if they

forge t the ir b oo ks?

Yes No

Key

D on 't know

(a) What was the least common answer to Question 2? 1 mark (b) What was the modal answer to Question 3? 1 mark(c) About what proportion of pupils answered ‘yes’ to Question 1? 1 markLevel 6 question2.I went for a walk.The distance-time graph shows information about my walk.

Tick () the statement below that describes my walk.

Distancetrave lled

Tim e taken

1

1 markLevel 7 question3. Building

A teacher asked 21 pupils to estimate the height of a building in metres.The stem-and-leaf diagram shows all 21 results.6 5 represents 6.5 m 6 5 9

7 0 2 6 8 88 3 3 5 7 7 99 0 5 5 510 4 811 2 7

(a) Show that the range of estimated heights was 5.2 m. 1 mark (b) What was the median estimated height? 1 mark (c) The height of the building was 9.2 m.

What percentage of the pupils over-estimated the height? 1 markLevel 8 question4. Acorns

Two groups of pupils collected a sample of acorns from the same oak tree.The box plots summarise the two sets of results.

G roup A

G roup B

20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35Length (m m )

(a) Explain how the box plots show the median of group B is 3 mm more than the median of group A.

1 mark

(b) Which group has the bigger inter-quartile range?A B

Explain your answer.1 mark

(c) The results from the two groups of pupils are very different.

Give a reason why the results might have been different. 1 mark

I was walking faster and faster.I was walking slower and slower.I was walking north-east.I was walking at a steady speed.I was walking uphill.

Scatter Graphs (5 – 8)

Level 6 question

1. The scatter graph shows information about trees called poplars.

H eigh t o ftree (m )

6

5

4

3

2

1

00 1 2 3 4 5

D iam eter o f tree trunk (cm ) (a) What does the scatter graph show about the relationship between the diameter of the tree trunk and the height of the tree? 1 mark

(b) The height of a different tree is 3 m. The diameter of its trunk is 5 cm.Use the graph to explain why this tree is not likely to be a poplar. 1 mark (c) Another tree is a poplar. The diameter of its trunk is 3.2 cm.Estimate the height of this tree. 1 mark

Maths 9 8 1 4 2 10 6 8Science 8 7 2 5 1 9 7 10a) Plot the points on the scatter graph.b) Comment on the correlation of the graph and what it means.c) Draw a line of best fit on the graph.d) Use the line of best fit to estimate what score someone should get in science if they get 7 in maths.

Calculating Probabilities (5 – 8)

Level 5 question 1. (a) Jo has these 4 coins.

Jo is going to take one of these coins at random.Each coin is equally likely to be the one she takes.

Show that the probability that it will be a 10p coin is 21

1 mark

(b) Colin has 4 coins that total 33p. He is going to take one of his coins at random. What is the probability that it will be a 10p coin? You must show your working. 1 markLevel 6 question2. A computer is going to choose a letter at random from an English book.

The table shows the probabilities of the computer choosing each vowel.Vowel A E I O UProbability 0.08 0.13 0.07 0.08 0.03

What is the probability that it will not choose a vowel? 2 marksLevel 7 question3. A bag contains counters that are red, black, or green.

31

of the counters are red

61

of the counters are black

There are 15 green counters in the bag.How many black counters are in the bag? 2 marks

Level 8 question4. I have three fair dice, each numbered 1 to 6 I am going to throw all three dice.

What is the probability that all three dice will show the same number? 2 marks

Handling Data Review 1 (5 – 8)

Level 5 question

3) A dice is thrown and a coin is flipped, fill in the sample space diagram to find all possible outcomes. Then answer the questions that follow:

1 2 3 4 5 6H H, 2T T, 4

Find the probability of getting:a) a head b) a four c) an even

numberd) a two or a four e) a head and a 5?

1) I have a pack of playing cards. I pick a card at random. What is the probability that the card I select is:

a) A king. b) a diamond c) a black card d) the jack of clubs2) There are four different coloured writing pads. In a pack there are 3 blue, 8 red, 1 white and 4 green. What is the probability when I open a new pack I randomly pick a:

a) blue pad b) red pad c) white pad d) green pade) yellow pad f) red or green pad?

1. I buy 12 packets of cat food in a box.The table shows the different varieties in the box.

(a) I am going to take out a packet at random from the box. What is the probability that it will be cod? 1 mark(b) My cat eats all the packets of cod.

I am going to take out a packet at random from the ones left in the box.What is the probability that it will be salmon? 1 mark

(c) A different type of cat food has 10 packets in a box.The probability that the variety is chicken is 0.7What is the probability that the variety is not chicken? 1 mark

Level 6 question2. In a bag there are only red, blue and green counters.(a) I am going to take a counter out of the bag at random.Complete the table.

2 marks

Level 7 question3. The table shows the number of boys and girls in two different classes.

Class 9A Class 9BBoys 13 12Girls 15 14

A teacher is going to choose a pupil at random from each of these classes.In which class is she more likely to choose a boy?You must show your working. 2 marks

Level 8 question4. 100 students were asked whether they studied French or German.

3 9 2 7 3 0

4

F r e n c h G e r m a n

27 students studied both French and German.(a) What is the probability that a student chosen at random will study only one of the languages? 1 mark (b) What is the probability that a student who is studying German is also studying French? 1 mark (c) Two of the 100 students are chosen at random.Circle the calculation which shows the probability that both the students study French and German?

10027

10027

9926

10027

10026

10027

10027

10027

10026

10027

1 mark

Colour of

counters

Number ofcounters Probability

Red 6

Blue51

Green 6

Variety Number of packetsCod 3

Salmon 3Trout 3Tuna 3

Handling Data Review 2 (5 – 8)

Level 5 question 1. (a) There are four people in Sita’s family.

Their shoe sizes are 4, 5, 7 and 10What is the median shoe size in Sita’s family? 1 mark

(b) There are three people in John’s family.

The range of their shoe sizes is 4Two people in the family wear shoe size 6John’s shoe size is not 6 and it is not 10

What is John’s shoe size? 1 markLevel 6 question2. Hanif asked ten people:

‘What is your favourite sport?’

Here are his results.football cricket football hockey swimminghockey swimming football netball football

(a) Is it possible to work out the mean of these results?

Yes NoExplain how you know. 1 mark

(b) Is it possible to work out the mode of these results?

Yes NoExplain how you know. 1 mark

Level 7 question3. Chris read the first 55 numbers from a book of random numbers. As he read each number he recorded it in the diagram.

0 5 9 9 8 3 4 1

1 6 3 1 0 3

2 8 2

3 1 1 6 9 3

4 6 9 9 4 7 0

5 5 7 7 6

6 0 2 8 4 8 0 3 5

7 6 8 0 1 5 4

8 6 6 9 2 8 5 7

9 6 7 8 0 0

Key

1 3 represents 13

(a) What was the largest number he recorded? 1 mark (b) Explain how Chris could change the diagram to make it easier for him to find the median of his data set. 1 markLevel 8 question4. The mean of a set of numbers is zero. For each statement below, tick ( ) the correct box.

Mustbe true

Couldbe true

Cannotbe true

All the numbers in the set are zero.

The sum of the numbers in the set is zero.

There are as many positive numbers as negative numbers in the set.

2 marks