ABC Education · 11+ Practice

Week 22 · Maths Practice Paper

30 questions · 60 marks · Suggested time: 50 minutes.

Question 1

[3 marks]

(a)

Write in figures: six hundred and fifteen thousand and eight.

(b)

Write in words: 492050.

(c)

Round 583421 to the nearest 10000.

Question 2

[2 marks]

Calculate, using the correct order of operations:

(a)

9 + 3 × (10 - 6)² ÷ 12

(b)

(19 - 4) × 2 - 3²

Question 3

[3 marks]

(a)

Write 920 as a decimal.

(b)

Write 0.36 as a fraction in its simplest form.

(c)

Put these in order, smallest to largest: 45, 0.79, 77%, 1720

Question 4

[2 marks]

A smoothie mix uses banana, mango and yogurt in the ratio 5:4:3, making 480ml in total.

(a)

How much banana is needed?

(b)

How much yogurt is needed?

Question 5

[2 marks]

Solve the following equations:

(a)

4x - 9 = 23

(b)

5(y - 2) = 25

Question 6

[3 marks]

A sequence has nth term 6n + 1.

(a)

Find the 8th term.

(b)

Find the first term greater than 100.

(c)

Is 151 a term in this sequence? Explain.

Question 7

[2 marks]

The angles of a triangle are x°, (x+20)° and (x+70)°.

(a)

Find x.

(b)

Find the size of the largest angle.

Question 8

[2 marks]

The quadrilateral below has a 100° angle, a right angle, and an exterior angle of 145° at the third corner (so the interior angle there is 35°). Calculate x and y.

x =

y =

Question 9

[2 marks]

For a kite:

(a)

How many lines of symmetry does it have?

(b)

What is its order of rotational symmetry?

Question 10

[2 marks]

For a hexagonal prism:

(a)

How many faces does it have?

(b)

How many edges does it have?

Question 11

[3 marks]

Three vertices of rectangle EFGH are E(-2,3), F(3,3) and G(3,-1).

(a)

Find the coordinates of H.

(b)

Find the area of the rectangle.

(c)

Find the coordinates of E after it is reflected in the x-axis.

Question 12

[2 marks]

A bag contains 6 teal, 3 maroon and 1 silver counter.

(a)

A counter is drawn at random. What is the probability it is silver?

(b)

4 more teal counters are added. What is the new probability of drawing teal, as a fraction in its simplest form?

Question 13

[3 marks]

The bar chart shows the number of cups of tea sold by a café over one week.

(a)

What is the total number of cups sold that week?

(b)

What is the mean number sold per day?

(c)

What is the median?

Question 14

[2 marks]

A football match kicks off at 15:10 and ends at 16:47.

(a)

How long, in minutes, does the match last?

(b)

Write the match length as hours and minutes.

Question 15

[1 marks]

A car travels 143 miles in 2 hours 45 minutes. What is its average speed, in mph?

Question 16

[2 marks]

Leah is currently 3 times as old as her brother. In 7 years, the sum of their ages will be 54.

(a)

How old is Leah's brother now?

(b)

How old is Leah now?

Question 17

[2 marks]

(a)

Find the highest common factor (HCF) of 63 and 84.

(b)

Find the lowest common multiple (LCM) of 9 and 24.

Question 18

[2 marks]

A speaker priced at £70 is increased in price by 40%, and then the new price is decreased by 25%.

(a)

What is the price after the increase?

(b)

What is the final price?

Question 19

[2 marks]

In a year group of 85 students, 50 like history, 38 like geography, and 20 like both.

(a)

How many like neither subject?

(b)

How many like history only?

Question 20

[1 marks]

Find the missing digit d so that the six-digit number 5d2748 is divisible by 9.

Question 21

[2 marks]

Using the symbols ★, ● and ▲ for three different numbers: ★+●=22, ▲+●=17, ★+▲=19.

(a)

Find ●.

(b)

Find ★.

Question 22

[1 marks]

What is the smaller of the two angles between the hour hand and minute hand of a clock at 4:40?

Question 23

[1 marks]

How many different 2-digit codes, with no repeated digits, can be formed using the digits 1, 2, 4, 6 and 8?

Question 24

[2 marks]

Calculate 5⅓ - 2¾, giving your answer as a mixed number in its simplest form.

Question 25

[2 marks]

A rectangular garden measures 15m by 9m. A right-angled triangular pond with legs 6m and 4m is dug in one corner, as shown, and is no longer lawn.

(a)

What is the area of the pond?

(b)

What is the area of the remaining lawn?

Question 26

[2 marks]

An isosceles triangle has two equal sides of length 2x cm and a base of length (x+9) cm. Its perimeter is 39cm.

(a)

Find x.

(b)

Find the length of the base.

Question 27

[2 marks]

(a)

Convert 3900ml to litres.

(b)

Convert 8200g to kilograms.

Question 28

[2 marks]

7 workers can finish a job in 12 hours, all working at the same steady rate.

(a)

How long would it take 3 workers to finish the same job?

(b)

How many workers would be needed to finish the job in 4 hours?

Question 29

[1 marks]

I am thinking of a number. When I subtract 9 from it and triple the result, I get 33. What is the number?

Question 30

[2 marks]

A box contains beads A, B and C in the ratio 2:3:7. There are 25 more C beads than A beads.

(a)

How many A beads are there?

(b)

How many beads are there in total?