ABC Education · 11+ Practice

Week 64 · Maths Practice Paper

22 questions · 60 marks · Suggested time: 1 hour.

Question 1

[8 marks]

For this question, put answers only in the spaces on the right.

3.65 × 10,000 =

17² =

The square root of 81 is

The cube root of 216 is

5³ =

210350 in its simplest form is

35% of 80 =

47 × 36 =

Question 2

[1 marks]

A calculator display shows 37 as a decimal: 0.428571429 (10 digits). Complete the box to show how the calculator would display the answer to 29000, given that 29 displays as 0.222222222 (you don't need to use the same digit style, but use 10 digits).

Question 3

[2 marks]

I buy 8 drinks at 65p each, and 6 sandwiches at £1.35 each. How much change do I get from a £20 note?

Question 4

[2 marks]

The letters of the word 'MATHS' are placed on a grid at these positions: M(2,5), A(3,5), T(4,5), H(5,5), S(6,5). Reflect each letter's position in the vertical line x = 8. Give the new coordinates in order.

Question 5

[2 marks]

Zoe is given £360. She gives 16 to her sister and 14 of what remains to her brother. How much does she keep herself?

Question 6

[3 marks]

The midday temperature was 15°C. The midnight temperature was −8°C.

(i)

What was the midday temperature in °F? (F = C × 95 + 32)

(ii)

What was the midnight temperature in °C?

(iii)

What was the difference in temperature between midday and midnight, in °C?

Question 7

[2 marks]

How many minutes are there between 8:47 am and 2:15 pm?

minutes

Question 8

[3 marks]

(i)

A design is made from 8 identical hexagons; 3 of them are shaded. What fraction is shaded, in simplest form?

(ii)

How many more hexagons need to be shaded so that 34 of the design is shaded?

(iii)

A large rectangle is divided into 10 equal squares (2 rows of 5); 7 are shaded. What fraction is shaded?

Question 9

[3 marks]

(i)

Write 15% as a fraction in its simplest form.

(ii)

Zoe sends 9 text messages each day. A £5 credit buys her 120 text messages. Today she received an extra 20% free text messages when she bought her £5 credit. How many days should the credit last? Show your working.

Question 10

[1 marks]

In a sponsored walk: Priya took 3 hours 52 minutes; Rosa took 226 minutes; Sam took 3¾ hours. Who was quickest and who was the slowest?

Question 11

[4 marks]

Two overlapping rectangles: a smaller rectangle 10cm by 8cm overlaps a larger rectangle 15cm by 18cm, with the overlap measuring 4cm by 6cm.

(i)

Calculate the area of the larger rectangle only.

(ii)

Calculate the total shaded area that the rectangles cover (combined, not double-counting the overlap).

Question 12

[2 marks]

A rectangle measures 80cm by 20cm, and a square has an equal perimeter to the rectangle. What is the difference in their areas?

cm²

Question 13

[1 marks]

Calculate the size of the missing angle in a triangle with two known angles of 28° and 97°.

Question 14

[3 marks]

Two straight lines cross to form an X-shape, creating two triangles on opposite sides of the crossing point (vertically opposite there). One triangle has base angles 72° and 17°. The other triangle has one base angle of 19° and the other base angle labelled 'a'.

(a)

Find the value of a.

(b)

Would you describe 250°? Acute, obtuse or reflex?

Question 15

[2 marks]

A right-angled triangle has legs 6cm and 8cm, and hypotenuse 10cm.

(i)

Calculate the perimeter of the triangle.

(ii)

Calculate the area of the triangle.

Question 16

[4 marks]

A box measures 18cm by 9cm by 12cm.

(i)

Calculate the volume of the box.

(ii)

A string is tied around the box with a bow at the top (going around both ways, plus the bow). If the bow uses 6cm of string, calculate the total length of string used (2×length + 2×width + 4×height + bow).

Question 17

[7 marks]

20, 21, 22, 23, 24, 25, 26, 27, 28. Write one number from 20 to 28 that satisfies each description below (some numbers may be used more than once).

(i)

Prime?

(ii)

A cube number?

(iii)

A square number?

(iv)

A Fibonacci number? (1, 1, 2, 3, 5, 8, 13, 21, ...)

(v)

A triangular number? (1, 3, 6, 10, 15, 21, 28, ...)

(vi)

A perfect number? (factors, not including itself, add up to itself; e.g. 6 = 1+2+3)

(vii)

A powerful number? (every prime factor's square also divides it; e.g. 16 = 2⁴)

Question 18

[1 marks]

What is 5 − ((6 + 6) ÷ 6)?

Question 19

[2 marks]

2431 = a × b × c, where a, b and c are prime numbers, with c bigger than b, and b bigger than a. Find a, b and c.

Question 20

[2 marks]

Given that 3184 × 99 = 315,216, find:

(i)

315,216 ÷ 99

(ii)

318.4 × 99

Question 21

[3 marks]

The symbol ☆ has a special meaning: a ☆ b means multiply b by (a + b). For example, 3 ☆ 5 = 5 × (3+5) = 5 × 8 = 40.

(a)

Work out 3 ☆ 7

(b)

Work out 3 ☆ (2 ☆ 4)

(c)

Work out the value of p such that p ☆ 5 = 90

Question 22

[2 marks]

Four bells ring at intervals of 3, 9, 5 and 13 seconds. If they are all rung at the same time, how many seconds will pass before they all ring at the same time again?

seconds