ABC Education · 11+ Practice

Week 21 · Maths Practice Paper

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

Question 1

[3 marks]

(a)

Write in figures: nine hundred and four thousand and twenty-three.

(b)

Write in words: 380509.

(c)

Round 247815 to the nearest 1000.

Question 2

[2 marks]

Calculate, using the correct order of operations:

(a)

11 + 2 × (6 - 2)² ÷ 4

(b)

(16 - 3) × 3 - 2²

Question 3

[3 marks]

(a)

Write 720 as a decimal.

(b)

Write 0.32 as a fraction in its simplest form.

(c)

Put these in order, smallest to largest: 34, 0.73, 72%, 1420

Question 4

[2 marks]

A jug of lemonade uses water, juice and sugar in the ratio 8:3:1, making 480ml in total.

(a)

How much water is needed?

(b)

How much sugar is needed?

Question 5

[2 marks]

Solve the following equations:

(a)

5x - 8 = 27

(b)

3(y + 4) = 33

Question 6

[3 marks]

A sequence has nth term 5n + 2.

(a)

Find the 11th term.

(b)

Find the first term greater than 100.

(c)

Is 137 a term in this sequence? Explain.

Question 7

[2 marks]

The angles of a triangle are x°, (x+5)° and (x+55)°.

(a)

Find x.

(b)

Find the size of the largest angle.

Question 8

[2 marks]

The quadrilateral below has a 105° angle, a right angle, and an exterior angle of 135° at the third corner (so the interior angle there is 45°). Calculate x and y.

x =

y =

Question 9

[2 marks]

For a regular dodecagon (12-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 cuboid:

(a)

How many faces does it have?

(b)

How many edges does it have?

Question 11

[3 marks]

Three vertices of rectangle ABCD are A(-3,-2), B(2,-2) and C(2,1).

(a)

Find the coordinates of D.

(b)

Find the area of the rectangle.

(c)

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

Question 12

[2 marks]

A bag contains 5 white, 4 black and 3 grey counters.

(a)

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

(b)

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

Question 13

[3 marks]

The bar chart shows the number of minutes of homework a pupil did each day of one week.

(a)

What is the total number of minutes that week?

(b)

What is the mean number of minutes per day?

(c)

What is the median?

Question 14

[2 marks]

A lesson starts at 10:15 and ends at 11:50.

(a)

How long, in minutes, does the lesson last?

(b)

Write the lesson length as hours and minutes.

Question 15

[1 marks]

A car travels 132 miles in 2 hours 45 minutes. What is its average speed, in mph?

Question 16

[2 marks]

Noah is currently 4 times as old as his cousin. In 5 years, the sum of their ages will be 45.

(a)

How old is Noah's cousin now?

(b)

How old is Noah now?

Question 17

[2 marks]

(a)

Find the highest common factor (HCF) of 45 and 75.

(b)

Find the lowest common multiple (LCM) of 8 and 10.

Question 18

[2 marks]

A ticket priced at £45 is increased in price by 30%, and then the new price is decreased by 10%.

(a)

What is the price after the increase?

(b)

What is the final price?

Question 19

[2 marks]

In a year group of 75 students, 42 like basketball, 33 like volleyball, and 15 like both.

(a)

How many like neither sport?

(b)

How many like basketball only?

Question 20

[1 marks]

Find the missing digit d so that the six-digit number 4d1653 is divisible by 9.

Question 21

[2 marks]

Using the symbols ♣, ♥ and ♠ for three different numbers: ♣+♥=19, ♠+♥=15, ♣+♠=16.

(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 7:20?

Question 23

[1 marks]

How many different 2-digit codes, with no repeated digits and the first digit not 0, can be formed using the digits 0, 1, 3, 5 and 7?

Question 24

[2 marks]

Calculate 4½ - 1⅝, giving your answer as a mixed number in its simplest form.

Question 25

[2 marks]

A rectangular garden measures 13m by 9m. A right-angled triangular pond with legs 6m and 5m 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+7) cm. Its perimeter is 37cm.

(a)

Find x.

(b)

Find the length of the base.

Question 27

[2 marks]

(a)

Convert 6700ml to litres.

(b)

Convert 4900g to kilograms.

Question 28

[2 marks]

9 workers can finish a job in 8 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 6 hours?

Question 29

[1 marks]

I am thinking of a number. When I add 12 to it and double the result, I get 50. What is the number?

Question 30

[2 marks]

A jar contains red, blue and green sweets in the ratio 3:5:9. There are 30 more green sweets than red sweets.

(a)

How many red sweets are there?

(b)

How many sweets are there in total?