ABC Education · 11+ Practice

Week 58 · Maths Practice Paper

9 questions · 31 marks · Suggested time: 45 minutes.

Question 1

[2 marks]

Work out the number from the following clues: a. It is a whole number b. It is less than 150 c. It is a cube number d. It is 2 more than a square number e. 9 is a factor of this number.

Question 2

[6 marks]

Here are some maths questions with answers. Each answer has at least one mistake. Identify the mistakes and explain them. You do not need to work out the correct answer, but you may if it helps.

(a)

'Work out 3³ + 5². Working shown: 3³ = 9 and 5² = 10, so the answer is 19.'

(b)

'60 people picked Swimming as their favourite sport. The bar for Athletics is half as tall as the bar for Swimming, so there must be about 20 people who picked Athletics, because 60 ÷ 3 = 20.'

(c)

'The temperature in Paris is 4.6°C and in Oslo is −3.2°C. How much warmer is it in Paris? Working: 4.6 − 3.2 = 1.4, so it is 1.4 degrees warmer.'

(d)

'Reflect the point (2,5) in the vertical line x = 6. Answer given: (8,5).'

(e)

'Find the value of 34 + 56. Working: 34 + 56 = 810 = 45.'

Question 3

[4 marks]

Note: an integer is a whole number. Josie and Jim are talking about their favourite numbers. Josie says: 'When I multiply my favourite integer by 8, the answer is a square number!' Jim asks: 'Is your favourite integer 18?' Josie replies: 'No! My favourite integer is between 1 and 10.'

(a)

Is 8 × 18 a square number, like Jim suggested? Show your working.

(b)

What could Josie's favourite integer be? Find all possible answers.

(c)

Are there any numbers between 0 and 1 that can be multiplied by 8 to get a square number? If so, give an example.

Question 4

[3 marks]

Three adults and two children are going to the theatre together. They have a voucher for 40% off a family ticket, but they left it at home! Option 1: go now, pay daytime prices, no discount. Option 2: go home for the voucher, pay evening prices, use the 40%-off family ticket. Prices: Adult — daytime £13.20, evening £16.80. Child — daytime £7.40, evening £9.60. Family ticket (3 adults & 2 children) — daytime £52, evening £64.

Work out which option is cheaper, and by how much.

Question 5

[2 marks]

What is the largest number of 16 cm by 24 cm by 10 cm shoe boxes that can fit in a 1.2 m by 1.6 m by 2.4 m crate? Be careful — you can't chop up the shoe boxes!

Question 6

[4 marks]

Mr Babbage writes the following pattern on the whiteboard: 10 × 10 = 100 9 × 11 = 99 = 100 − 1 8 × 12 = 96 = 100 − 4 7 × 13 = 91 = 100 − 9

(a)

Write down the next line of the pattern.

(b)

Mr Babbage writes a second pattern starting 20 × 20 = 400, 19 × 21 = 399 = 400 − 1, 18 × 22 = 396 = 400 − 4. Complete the following line: 9 × ___ = ___ = 400 − ___

(c)

You are told that 142² = 20,164. Use this fact and the idea above to work out the value of 138 × 146. (Note: do not multiply 138 by 146 directly.)

Question 7

[3 marks]

Dan, Elle and Fay have eighteen beads altogether. Dan says he has 9 beads. Elle says that Fay has two more beads than Dan. Fay says she has the most beads. Exactly one of them is lying. Who is lying? Explain briefly how you know.

Question 8

[1 marks]

A regular hexagon is split by two vertical lines running between its upper and lower slanted edges, dividing it into a central rectangle and two end triangular pieces. The central rectangle is shaded. What fraction of the hexagon is shaded?

Question 9

[6 marks]

Each of the letters A, B, C, D, E, F represents a different whole number between 0 and 12. All of the calculations below are correct: (1) A × A × A = B, (2) A × C = B, (3) D × C = E, (4) D × A = F.

(a)

Work out the value of each letter.

(b)

Using your values, exactly ONE of these is incorrect: (5) C × F = 24, (6) D × E = 36, (7) F × A = E, (8) B ÷ C = A, (9) A × B = E, (10) E − D = 9. Which one is incorrect, and what should the answer be?