ABC Education · 11+ Practice

Week 32 · Maths Practice Paper

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

Question 1

[3 marks]

(a)

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

(b)

Write in words: 407290.

(c)

Round 692418 to the nearest 1000.

Question 2

[2 marks]

Calculate, using the correct order of operations:

(a)

15 + 4 × (6 - 2)² ÷ 8

(b)

(27 - 9) × 2 - 5²

Question 3

[3 marks]

(a)

Write 58 as a decimal.

(b)

Write 0.64 as a fraction in its simplest form.

(c)

Put these in order, smallest to largest: 710, 0.68, 67%, 1320

Question 4

[2 marks]

A smoothie mix uses strawberry, banana and milk in the ratio 7:2:3, making 480ml in total.

(a)

How much strawberry is needed?

(b)

How much milk is needed?

Question 5

[2 marks]

Solve the following equations:

(a)

10x - 19 = 31

(b)

7(y - 2) = 21

Question 6

[3 marks]

A sequence has nth term 6n + 7.

(a)

Find the 8th term.

(b)

Find the first term greater than 100.

(c)

Is 145 a term in this sequence? Explain.

Question 7

[2 marks]

The angles of a triangle are x°, (x+25)° and (x+95)°.

(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 160° at the third corner (so the interior angle there is 20°). Calculate x and y.

x =

y =

Question 9

[2 marks]

For a scalene triangle:

(a)

How many lines of symmetry does it have?

(b)

What is its order of rotational symmetry?

Question 10

[2 marks]

For a decagonal-based pyramid:

(a)

How many faces does it have?

(b)

How many edges does it have?

Question 11

[3 marks]

Three vertices of rectangle TUVW are T(-5,2), U(0,2) and V(0,-3).

(a)

Find the coordinates of W.

(b)

Find the area of the rectangle.

(c)

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

Question 12

[2 marks]

A bag contains 7 cocoa, 3 vanilla and 2 mint counters.

(a)

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

(b)

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

Question 13

[3 marks]

The bar chart shows the number of laps a swimmer swam each day of one week.

(a)

What is the total number of laps swum that week?

(b)

What is the mean number per day?

(c)

What is the median?

Question 14

[2 marks]

A rehearsal starts at 17:25 and ends at 20:10.

(a)

How long, in minutes, does the rehearsal last?

(b)

Write the rehearsal length as hours and minutes.

Question 15

[1 marks]

A jogger runs 27 miles in 4 hours 30 minutes. What is their average speed, in mph?

Question 16

[2 marks]

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

(a)

How old is Daniel's niece now?

(b)

How old is Daniel now?

Question 17

[2 marks]

(a)

Find the highest common factor (HCF) of 75 and 105.

(b)

Find the lowest common multiple (LCM) of 6 and 10.

Question 18

[2 marks]

A necklace priced at £64 is increased in price by 50%, 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 105 students, 60 like Latin, 42 like Greek, and 25 like both.

(a)

How many like neither language?

(b)

How many like Latin only?

Question 20

[1 marks]

Find the missing digit d so that the six-digit number 7d1935 is divisible by 9.

Question 21

[2 marks]

Using the symbols ♙, ♘ and ♗ for three different numbers: ♙+♘=27, ♗+♘=22, ♙+♗=23.

(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 1:40?

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, 2, 4, 6 and 8?

Question 24

[2 marks]

Calculate 10¼ - 7⅚, giving your answer as a mixed number in its simplest form.

Question 25

[2 marks]

A rectangular garden measures 35m by 19m. A right-angled triangular pond with legs 16m and 11m 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+17) cm. Its perimeter is 52cm.

(a)

Find x.

(b)

Find the length of the base.

Question 27

[2 marks]

(a)

Convert 6100ml to litres.

(b)

Convert 7900g to kilograms.

Question 28

[2 marks]

24 workers can finish a job in 5 hours, all working at the same steady rate.

(a)

How long would it take 8 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 add 21 to it and halve the result, I get 25. What is the number?

Question 30

[2 marks]

A jar of beads A, B and C are in the ratio 8:11:25. There are 51 more C beads than A beads.

(a)

How many A beads are there?

(b)

How many beads are there in total?