ABC Education · 11+ Practice

Week 30 · Maths Practice Paper

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

Question 1

[3 marks]

(a)

Write in figures: seven hundred and forty-one thousand and thirteen.

(b)

Write in words: 683020.

(c)

Round 194637 to the nearest 10000.

Question 2

[2 marks]

Calculate, using the correct order of operations:

(a)

13 + 2 × (10 - 6)² ÷ 8

(b)

(31 - 13) × 2 - 4²

Question 3

[3 marks]

(a)

Write 38 as a decimal.

(b)

Write 0.08 as a fraction in its simplest form.

(c)

Put these in order, smallest to largest: 15, 0.22, 21%, 720

Question 4

[2 marks]

A bird-food mix uses seeds, nuts and dried berries in the ratio 8:3:1, making 480g in total.

(a)

How much seeds is needed?

(b)

How much dried berries is needed?

Question 5

[2 marks]

Solve the following equations:

(a)

13x - 28 = 63

(b)

11(y - 4) = 33

Question 6

[3 marks]

A sequence has nth term 11n - 7.

(a)

Find the 5th term.

(b)

Find the first term greater than 100.

(c)

Is 202 a term in this sequence? Explain.

Question 7

[2 marks]

The angles of a triangle are x°, (x+40)° and (x+80)°.

(a)

Find x.

(b)

Find the size of the largest angle.

Question 8

[2 marks]

The quadrilateral below has a 75° 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 a regular 6-pointed star:

(a)

How many lines of symmetry does it have?

(b)

What is its order of rotational symmetry?

Question 10

[2 marks]

For a heptagonal-based pyramid:

(a)

How many faces does it have?

(b)

How many edges does it have?

Question 11

[3 marks]

Three vertices of rectangle KLMN are K(-2,-3), L(3,-3) and M(3,1).

(a)

Find the coordinates of N.

(b)

Find the area of the rectangle.

(c)

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

Question 12

[2 marks]

A bag contains 6 birch, 4 elm and 2 oak counters.

(a)

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

(b)

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

Question 13

[3 marks]

The bar chart shows the number of cyclists counted each hour over one week's survey.

(a)

What is the total number of cyclists counted?

(b)

What is the mean number per hour?

(c)

What is the median?

Question 14

[2 marks]

An exam starts at 09:00 and ends at 11:33.

(a)

How long, in minutes, does the exam last?

(b)

Write the exam length as hours and minutes.

Question 15

[1 marks]

A car travels 135 miles in 3 hours. What is its average speed, in mph?

Question 16

[2 marks]

Charlie is currently 9 times as old as his niece. In 1 year, the sum of their ages will be 52.

(a)

How old is Charlie's niece now?

(b)

How old is Charlie now?

Question 17

[2 marks]

(a)

Find the highest common factor (HCF) of 100 and 140.

(b)

Find the lowest common multiple (LCM) of 12 and 16.

Question 18

[2 marks]

A pair of headphones priced at £48 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 150 students, 88 like gymnastics, 62 like athletics, and 40 like both.

(a)

How many like neither sport?

(b)

How many like gymnastics only?

Question 20

[1 marks]

Find the missing digit d so that the six-digit number 8d3654 is divisible by 9.

Question 21

[2 marks]

Using the symbols ♞, ♟ and ♝ for three different numbers: ♞+♟=35, ♝+♟=30, ♞+♝=31.

(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 5:40?

Question 23

[1 marks]

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

Question 24

[2 marks]

Calculate 8⅙ - 5¾, giving your answer as a mixed number in its simplest form.

Question 25

[2 marks]

A rectangular garden measures 31m by 17m. A right-angled triangular pond with legs 14m and 9m 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+13) cm. Its perimeter is 48cm.

(a)

Find x.

(b)

Find the length of the base.

Question 27

[2 marks]

(a)

Convert 3400ml to litres.

(b)

Convert 9100g to kilograms.

Question 28

[2 marks]

21 workers can finish a job in 4 hours, all working at the same steady rate.

(a)

How long would it take 7 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 subtract 9, I get 41. What is the number?

Question 30

[2 marks]

A tin of coins A, B and C are in the ratio 6:9:19. There are 39 more C coins than A coins.

(a)

How many A coins are there?

(b)

How many coins are there in total?