ABC Education · 11+ Practice

Week 23 · Maths Practice Paper

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

Question 1

[3 marks]

(a)

Write in figures: seven hundred and twelve thousand and thirty-six.

(b)

Write in words: 368210.

(c)

Round 294817 to the nearest 1000.

Question 2

[2 marks]

Calculate, using the correct order of operations:

(a)

6 + 4 × (8 - 3)² ÷ 10

(b)

(21 - 5) × 2 - 3²

Question 3

[3 marks]

(a)

Write 1120 as a decimal.

(b)

Write 0.48 as a fraction in its simplest form.

(c)

Put these in order, smallest to largest: 34, 0.71, 73%, 1420

Question 4

[2 marks]

A concrete mix uses sand, cement and water in the ratio 4:2:1, making 350kg in total.

(a)

How much sand is needed?

(b)

How much water is needed?

Question 5

[2 marks]

Solve the following equations:

(a)

6x - 13 = 29

(b)

4(y + 3) = 32

Question 6

[3 marks]

A sequence has nth term 3n + 5.

(a)

Find the 14th term.

(b)

Find the first term greater than 100.

(c)

Is 98 a term in this sequence? Explain.

Question 7

[2 marks]

The angles of a triangle are x°, (x+30)° and (x+60)°.

(a)

Find x.

(b)

Find the size of the largest angle.

Question 8

[2 marks]

The quadrilateral below has a 110° angle, a right angle, and an exterior angle of 140° at the third corner (so the interior angle there is 40°). Calculate x and y.

x =

y =

Question 9

[2 marks]

For a (non-rectangular, non-rhombus) parallelogram:

(a)

How many lines of symmetry does it have?

(b)

What is its order of rotational symmetry?

Question 10

[2 marks]

For a pentagonal prism:

(a)

How many faces does it have?

(b)

How many edges does it have?

Question 11

[3 marks]

Three vertices of rectangle HIJK are H(-4,2), I(0,2) and J(0,-3).

(a)

Find the coordinates of K.

(b)

Find the area of the rectangle.

(c)

Find the coordinates of H after it is reflected in the y-axis.

Question 12

[2 marks]

A bag contains 4 navy, 5 peach and 3 olive counters.

(a)

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

(b)

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

Question 13

[3 marks]

The bar chart shows the number of books returned to a library over one week.

(a)

What is the total number of books returned that week?

(b)

What is the mean number returned per day?

(c)

What is the median?

Question 14

[2 marks]

A train leaves at 08:55 and arrives at 10:20.

(a)

How long, in minutes, is the journey?

(b)

Write the journey time as hours and minutes.

Question 15

[1 marks]

A car travels 117 miles in 1 hour 30 minutes. What is its average speed, in mph?

Question 16

[2 marks]

Oscar is currently 4 times as old as his sister. In 6 years, the sum of their ages will be 57.

(a)

How old is Oscar's sister now?

(b)

How old is Oscar now?

Question 17

[2 marks]

(a)

Find the highest common factor (HCF) of 66 and 110.

(b)

Find the lowest common multiple (LCM) of 14 and 21.

Question 18

[2 marks]

A game console priced at £55 is increased in price by 20%, and then the new price is decreased by 30%.

(a)

What is the price after the increase?

(b)

What is the final price?

Question 19

[2 marks]

In a year group of 95 students, 55 like chess, 40 like debate, and 22 like both.

(a)

How many like neither activity?

(b)

How many like chess only?

Question 20

[1 marks]

Find the missing digit d so that the six-digit number 6d4137 is divisible by 9.

Question 21

[2 marks]

Using the symbols ♦, ♣ and ♠ for three different numbers: ♦+♣=24, ♠+♣=18, ♦+♠=20.

(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 10:10?

Question 23

[1 marks]

How many different 3-digit codes, with no repeated digits, can be formed using the digits 2, 3, 5, 7 and 9?

Question 24

[2 marks]

Calculate 6¼ - 3⅚, giving your answer as a mixed number in its simplest form.

Question 25

[2 marks]

A rectangular garden measures 17m by 10m. A right-angled triangular pond with legs 7m 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+10) cm. Its perimeter is 40cm.

(a)

Find x.

(b)

Find the length of the base.

Question 27

[2 marks]

(a)

Convert 5200ml to litres.

(b)

Convert 6800g to kilograms.

Question 28

[2 marks]

11 workers can finish a job in 6 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 2 hours?

Question 29

[1 marks]

I am thinking of a number. When I double it and subtract 11, I get 23. What is the number?

Question 30

[2 marks]

A collection of coins A, B and C are in the ratio 3:4:8. There are 30 more C coins than A coins.

(a)

How many A coins are there?

(b)

How many coins are there in total?