ABC Education · 11+ Practice

Week 20 · Maths Practice Paper

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

Question 1

[3 marks]

(a)

Write in figures: eight hundred and thirty thousand and forty-one.

(b)

Write in words: 270604.

(c)

Round 356789 to the nearest 100.

Question 2

[2 marks]

Calculate, using the correct order of operations:

(a)

14 + 4 × (9 - 6)² ÷ 12

(b)

(30 - 9) × 2 - 5²

Question 3

[3 marks]

(a)

Write 316 as a decimal.

(b)

Write 0.24 as a fraction in its simplest form.

(c)

Put these in order, smallest to largest: 25, 0.42, 41%, 920

Question 4

[2 marks]

A trail mix uses nuts, raisins and seeds in the ratio 5:2:3, making 500g in total.

(a)

How much nuts are needed?

(b)

How many seeds are needed?

Question 5

[2 marks]

Solve the following equations:

(a)

10x - 16 = 44

(b)

7(y - 1) = 35

Question 6

[3 marks]

A sequence has nth term 9n - 7.

(a)

Find the 6th term.

(b)

Find the first term greater than 150.

(c)

Is 185 a term in this sequence? Explain.

Question 7

[2 marks]

The angles of a triangle are x°, (x+35)° and (x+55)°.

(a)

Find x.

(b)

Find the size of the largest angle.

Question 8

[2 marks]

The quadrilateral below has a 75° angle, a right angle, and an exterior angle of 120° at the third corner (so the interior angle there is 60°). Calculate x and y.

x =

y =

Question 9

[2 marks]

For a regular nonagon (9-sided polygon):

(a)

How many lines of symmetry does it have?

(b)

What is the size of each interior angle?

Question 10

[2 marks]

For a cone:

(a)

How many faces does it have in total (flat and curved)?

(b)

How many vertices does it have?

Question 11

[3 marks]

Three vertices of rectangle NOPQ are N(-5,1), O(-1,1) and P(-1,-3).

(a)

Find the coordinates of Q.

(b)

Find the area of the rectangle.

(c)

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

Question 12

[2 marks]

A bag contains 9 red, 2 blue and 1 green counter.

(a)

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

(b)

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

Question 13

[3 marks]

The bar chart shows the runs scored by a batter in each of 5 innings.

(a)

What is the total number of runs scored?

(b)

What is the mean number of runs per innings?

(c)

What is the median?

Question 14

[2 marks]

A concert starts at 18:45 and ends at 21:10.

(a)

How long, in minutes, does the concert last?

(b)

Write the concert length as hours and minutes.

Question 15

[1 marks]

A car travels 175 miles in 3 hours 30 minutes. What is its average speed, in mph?

Question 16

[2 marks]

Ella is currently 7 times as old as her brother. In 5 years, the sum of their ages will be 58.

(a)

How old is her brother now?

(b)

How old is Ella now?

Question 17

[2 marks]

(a)

Find the highest common factor (HCF) of 56 and 98.

(b)

Find the lowest common multiple (LCM) of 16 and 20.

Question 18

[2 marks]

A speaker priced at £150 is increased in price by 10%, and then the new price is decreased by 20%.

(a)

What is the price after the increase?

(b)

What is the final price?

Question 19

[2 marks]

In a year group of 100 students, 60 like drama, 45 like debate, and 25 like both.

(a)

How many like neither activity?

(b)

How many like drama only?

Question 20

[1 marks]

Find the missing digit d so that the six-digit number 8d4725 is divisible by 9.

Question 21

[2 marks]

Using the symbols ♭, ♮ and ♯ for three different numbers: ♭+♮=29, ♯+♮=24, ♭+♯=25.

(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 1:50?

Question 23

[1 marks]

How many different 2-digit codes can be formed using the digits 0, 2, 4, 6 and 8 (with no repeated digits, and the first digit not 0)?

Question 24

[2 marks]

Calculate 9¼ - 6⅚, giving your answer as a mixed number in its simplest form.

Question 25

[2 marks]

A rectangular garden measures 20m by 12m. A right-angled triangular pond with legs 9m and 6m 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+5) cm. Its perimeter is 35cm.

(a)

Find x.

(b)

Find the length of the base.

Question 27

[2 marks]

(a)

Convert 9200ml to litres.

(b)

Convert 7300g to kilograms.

Question 28

[2 marks]

12 workers can finish a job in 8 hours, all working at the same steady rate.

(a)

How long would it take 6 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 divide it by 4 and subtract 5, I get 10. What is the number?

Question 30

[2 marks]

A collection of stickers has silver, gold and bronze in the ratio 3:5:8. There are 25 more bronze stickers than silver stickers.

(a)

How many silver stickers are there?

(b)

How many stickers are there in total?