ABC Education · 11+ Practice

Week 25 · Maths Practice Paper

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

Question 1

[3 marks]

(a)

Write in figures: nine hundred and thirty-eight thousand and twenty-seven.

(b)

Write in words: 274600.

(c)

Round 615382 to the nearest 10000.

Question 2

[2 marks]

Calculate, using the correct order of operations:

(a)

10 + 3 × (7 - 3)² ÷ 8

(b)

(17 - 2) × 2 - 3²

Question 3

[3 marks]

(a)

Write 916 as a decimal.

(b)

Write 0.52 as a fraction in its simplest form.

(c)

Put these in order, smallest to largest: 25, 0.43, 44%, 920

Question 4

[2 marks]

A cookie dough recipe uses flour, sugar and butter in the ratio 6:2:3, making 550g in total.

(a)

How much flour is needed?

(b)

How much butter is needed?

Question 5

[2 marks]

Solve the following equations:

(a)

8x - 19 = 37

(b)

6(y - 4) = 18

Question 6

[3 marks]

A sequence has nth term 5n - 2.

(a)

Find the 9th term.

(b)

Find the first term greater than 100.

(c)

Is 148 a term in this sequence? Explain.

Question 7

[2 marks]

The angles of a triangle are x°, (x+45)° and (x+75)°.

(a)

Find x.

(b)

Find the size of the largest angle.

Question 8

[2 marks]

The quadrilateral below has a 70° angle, a right angle, and an exterior angle of 125° at the third corner (so the interior angle there is 55°). Calculate x and y.

x =

y =

Question 9

[2 marks]

For an isosceles trapezium:

(a)

How many lines of symmetry does it have?

(b)

What is its order of rotational symmetry?

Question 10

[2 marks]

For a pentagonal-based pyramid:

(a)

How many faces does it have?

(b)

How many edges does it have?

Question 11

[3 marks]

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

(a)

Find the coordinates of T.

(b)

Find the area of the rectangle.

(c)

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

Question 12

[2 marks]

A bag contains 8 rose, 3 violet and 1 ivory counter.

(a)

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

(b)

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

Question 13

[3 marks]

The bar chart shows the number of bushels of apples harvested each day of one week.

(a)

What is the total number of bushels harvested that week?

(b)

What is the mean number per day?

(c)

What is the median?

Question 14

[2 marks]

A workshop starts at 09:20 and ends at 12:05.

(a)

How long, in minutes, does the workshop last?

(b)

Write the workshop length as hours and minutes.

Question 15

[1 marks]

A car travels 114 miles in 1 hour 30 minutes. What is its average speed, in mph?

Question 16

[2 marks]

Grace is currently 4 times as old as her brother. In 2 years, the sum of their ages will be 44.

(a)

How old is Grace's brother now?

(b)

How old is Grace now?

Question 17

[2 marks]

(a)

Find the highest common factor (HCF) of 48 and 80.

(b)

Find the lowest common multiple (LCM) of 15 and 20.

Question 18

[2 marks]

A tent priced at £65 is increased in price by 40%, 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 72 students, 42 like robotics, 29 like coding, and 14 like both.

(a)

How many like neither activity?

(b)

How many like robotics only?

Question 20

[1 marks]

Find the missing digit d so that the six-digit number 3d6521 is divisible by 9.

Question 21

[2 marks]

Using the symbols ♪, ♫ and ☂ for three different numbers: ♪+☂=21, ♫+☂=17, ♪+♫=18.

(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 6:20?

Question 23

[1 marks]

How many different 3-digit codes, with no repeated digits, can be formed using the digits 1, 4, 6, 8 and 9?

Question 24

[2 marks]

Calculate 8⅓ - 5¾, giving your answer as a mixed number in its simplest form.

Question 25

[2 marks]

A rectangular garden measures 21m by 12m. A right-angled triangular pond with legs 9m and 6m 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+3) cm. Its perimeter is 31cm.

(a)

Find x.

(b)

Find the length of the base.

Question 27

[2 marks]

(a)

Convert 7100ml to litres.

(b)

Convert 5400g to kilograms.

Question 28

[2 marks]

6 workers can finish a job in 14 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 7 hours?

Question 29

[1 marks]

I am thinking of a number. When I subtract 7 from it and triple the result, I get 36. What is the number?

Question 30

[2 marks]

A stack of cards A, B and C are in the ratio 4:6:11. There are 28 more C cards than A cards.

(a)

How many A cards are there?

(b)

How many cards are there in total?