ABC Education · 11+ Practice

Week 33 · Maths Practice Paper

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

Question 1

[3 marks]

(a)

Write in figures: five hundred and sixty-two thousand and ninety.

(b)

Write in words: 718430.

(c)

Round 345921 to the nearest 10000.

Question 2

[2 marks]

Calculate, using the correct order of operations:

(a)

16 + 5 × (9 - 5)² ÷ 10

(b)

(35 - 19) × 2 - 3²

Question 3

[3 marks]

(a)

Write 35 as a decimal.

(b)

Write 0.84 as a fraction in its simplest form.

(c)

Put these in order, smallest to largest: 910, 0.93, 92%, 1920

Question 4

[2 marks]

A paint mix uses blue, green and white paint in the ratio 9:4:2, making 450ml in total.

(a)

How much blue paint is needed?

(b)

How much white paint is needed?

Question 5

[2 marks]

Solve the following equations:

(a)

11x - 21 = 34

(b)

8(y - 3) = 32

Question 6

[3 marks]

A sequence has nth term 7n + 4.

(a)

Find the 9th 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+10)° and (x+110)°.

(a)

Find x.

(b)

Find the size of the largest angle.

Question 8

[2 marks]

The quadrilateral below has a 115° angle, a right angle, and an exterior angle of 165° at the third corner (so the interior angle there is 15°). Calculate x and y.

x =

y =

Question 9

[2 marks]

For an S-shaped tetromino (four squares in an SZ arrangement):

(a)

How many lines of symmetry does it have?

(b)

What is its order of rotational symmetry?

Question 10

[2 marks]

For a nonagonal-based pyramid:

(a)

How many faces does it have?

(b)

How many edges does it have?

Question 11

[3 marks]

Three vertices of rectangle XYZA are X(-3,-4), Y(4,-4) and Z(4,0).

(a)

Find the coordinates of A.

(b)

Find the area of the rectangle.

(c)

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

Question 12

[2 marks]

A bag contains 8 coral, 3 teal and 1 amber counter.

(a)

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

(b)

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

Question 13

[3 marks]

The bar chart shows the number of goals a team scored in each of 5 matches.

(a)

What is the total number of goals scored?

(b)

What is the mean number of goals per match?

(c)

What is the median?

Question 14

[2 marks]

A festival opens at 10:05 and closes at 14:48.

(a)

How long, in minutes, is the festival open?

(b)

Write this length as hours and minutes.

Question 15

[1 marks]

A runner covers 30 miles in 5 hours. What is their average speed, in mph?

Question 16

[2 marks]

Isla is currently 7 times as old as her brother. In 2 years, the sum of their ages will be 44.

(a)

How old is Isla's brother now?

(b)

How old is Isla now?

Question 17

[2 marks]

(a)

Find the highest common factor (HCF) of 88 and 120.

(b)

Find the lowest common multiple (LCM) of 20 and 30.

Question 18

[2 marks]

A bag priced at £76 is increased in price by 25%, 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 115 students, 66 like swimming, 50 like diving, and 28 like both.

(a)

How many like neither sport?

(b)

How many like swimming only?

Question 20

[1 marks]

Find the missing digit d so that the six-digit number 8d5192 is divisible by 9.

Question 21

[2 marks]

Using the symbols ♛, ♜ and ♞ for three different numbers: ♛+♜=36, ♞+♜=31, ♛+♞=33.

(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 12:20?

Question 23

[1 marks]

How many different 4-digit codes, with no repeated digits, can be formed using the digits 1, 3, 5, 7 and 9?

Question 24

[2 marks]

Calculate 11⅙ - 8¾, giving your answer as a mixed number in its simplest form.

Question 25

[2 marks]

A rectangular garden measures 37m by 20m. A right-angled triangular pond with legs 17m and 12m 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 3x cm and a base of length (x+19) cm. Its perimeter is 54cm.

(a)

Find x.

(b)

Find the length of the base.

Question 27

[2 marks]

(a)

Convert 4400ml to litres.

(b)

Convert 8700g to kilograms.

Question 28

[2 marks]

25 workers can finish a job in 6 hours, all working at the same steady rate.

(a)

How long would it take 5 workers to finish the same job?

(b)

How many workers would be needed to finish the job in 3 hours?

Question 29

[1 marks]

I am thinking of a number. When I double it and add 17, I get 53. What is the number?

Question 30

[2 marks]

A tin of pennies A, B and C are in the ratio 9:12:28. There are 57 more C pennies than A pennies.

(a)

How many A pennies are there?

(b)

How many pennies are there in total?