ABC Education · 11+ Practice

Week 16 · Maths Practice Paper

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

Question 1

[3 marks]

(a)

Write in figures: four hundred and seventeen thousand and sixty-two.

(b)

Write in words: 305090.

(c)

Round 154382 to the nearest 10000.

Question 2

[2 marks]

Calculate, using the correct order of operations:

(a)

8 + 3 × (7 - 2)² ÷ 5

(b)

(20 - 6) × 3 - 4²

Question 3

[3 marks]

(a)

Write 58 as a decimal.

(b)

Write 0.28 as a fraction in its simplest form.

(c)

Put these in order, smallest to largest: 710, 0.68, 66%, 1320

Question 4

[2 marks]

A paint mix uses blue, yellow and white paint in the ratio 3:4:5, making 480ml of mixture 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)

6x + 5 = 41

(b)

2(3y - 4) = 22

Question 6

[3 marks]

A sequence has nth term 4n + 3.

(a)

Find the 12th term.

(b)

Find the first term greater than 150.

(c)

Is 99 a term in this sequence? Explain.

Question 7

[2 marks]

The angles of a triangle are x°, 2x° and 3x°.

(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 150° at the third corner (so the interior angle there is 30°). Calculate x and y.

x =

y =

Question 9

[2 marks]

For a regular pentagon:

(a)

How many lines of symmetry does it have?

(b)

What is the size of each interior angle?

Question 10

[2 marks]

For a cube:

(a)

How many faces does it have?

(b)

How many vertices does it have?

Question 11

[3 marks]

Three vertices of rectangle PQRS are P(-3,2), Q(1,2) and R(1,-2).

(a)

Find the coordinates of S.

(b)

Find the area of the rectangle.

(c)

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

Question 12

[2 marks]

A bag contains 6 yellow, 3 green and 1 blue counter.

(a)

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

(b)

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

Question 13

[3 marks]

The bar chart shows the number of ice creams sold by a shop over one week.

(a)

What is the total number of ice creams sold that week?

(b)

What is the mean number sold per day?

(c)

What is the median?

Question 14

[2 marks]

A meeting starts at 14:35 and ends at 16:10.

(a)

How long, in minutes, does the meeting last?

(b)

Write the meeting length as hours and minutes.

Question 15

[1 marks]

A car travels 84 miles in 1 hour 45 minutes. What is its average speed, in mph?

Question 16

[2 marks]

Mia is currently twice as old as her brother Leo. In 6 years, the sum of their ages will be 42.

(a)

How old is Leo now?

(b)

How old is Mia now?

Question 17

[2 marks]

(a)

Find the highest common factor (HCF) of 36 and 84.

(b)

Find the lowest common multiple (LCM) of 9 and 15.

Question 18

[2 marks]

A jacket priced at £60 is increased in price by 20%, 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 60 students, 32 study French, 25 study Spanish, and 10 study both.

(a)

How many study neither language?

(b)

How many study French only?

Question 20

[1 marks]

Find the missing digit d so that the six-digit number 5d1362 is divisible by 9.

Question 21

[2 marks]

Using the symbols ♦, ♣ and ♠ for three different numbers: ♦+♣=21, ♠+♣=16, ♦+♠=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 5:10?

Question 23

[1 marks]

How many different 3-digit codes, with no repeated digits, can be formed using the digits 1, 2, 3, 4 and 5?

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 5m 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 3x cm and a base of length (x+4) cm. Its perimeter is 46cm.

(a)

Find x.

(b)

Find the length of the base.

Question 27

[2 marks]

(a)

Convert 4200ml to litres.

(b)

Convert 3750g to kilograms.

Question 28

[2 marks]

5 painters can paint a fence in 12 hours, all working at the same steady rate.

(a)

How long would it take 3 painters to paint the same fence?

(b)

How many painters would be needed to paint the fence in 4 hours?

Question 29

[1 marks]

I am thinking of a number. When I triple it and add 8, I get 50. What is the number?

Question 30

[2 marks]

A jar contains red, blue and yellow marbles in the ratio 3:4:6. There are 15 more blue marbles than red marbles.

(a)

How many red marbles are there?

(b)

How many marbles are there in total?