ABC Education · 11+ Practice

Week 17 · Maths Practice Paper

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

Question 1

[3 marks]

(a)

Write in figures: five hundred and eighty thousand and twelve.

(b)

Write in words: 203400.

(c)

Round 725499 to the nearest hundred.

Question 2

[2 marks]

Calculate, using the correct order of operations:

(a)

9 + 2 × (11 - 4)² ÷ 7

(b)

(18 - 5) × 2² - 9

Question 3

[3 marks]

(a)

Write 916 as a decimal.

(b)

Write 0.44 as a fraction in its simplest form.

(c)

Put these in order, smallest to largest: 45, 0.77, 78%, 1720

Question 4

[2 marks]

A fruit salad uses apples, oranges and grapes in the ratio 4:5:7, making 480g in total.

(a)

How much apple is needed?

(b)

How much grape is needed?

Question 5

[2 marks]

Solve the following equations:

(a)

7x - 9 = 40

(b)

5(y - 3) = 20

Question 6

[3 marks]

A sequence has nth term 6n - 4.

(a)

Find the 9th term.

(b)

Find the first term greater than 100.

(c)

Is 146 a term in this sequence? Explain.

Question 7

[2 marks]

The angles of a triangle are x°, (x+20)° and (x+40)°.

(a)

Find x.

(b)

Find the size of the largest angle.

Question 8

[2 marks]

The quadrilateral below has a 95° 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 octagon:

(a)

How many lines of symmetry does it have?

(b)

What is the size of each interior angle?

Question 10

[2 marks]

For a square-based pyramid:

(a)

How many faces does it have?

(b)

How many edges does it have?

Question 11

[3 marks]

Three vertices of rectangle EFGH are E(-4,-1), F(2,-1) and G(2,3).

(a)

Find the coordinates of H.

(b)

Find the area of the rectangle.

(c)

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

Question 12

[2 marks]

A bag contains 7 black, 2 white and 3 pink counters.

(a)

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

(b)

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

Question 13

[3 marks]

The bar chart shows the number of pizza slices sold by a café over one week.

(a)

What is the total number of slices sold that week?

(b)

What is the mean number sold per day?

(c)

What is the median?

Question 14

[2 marks]

A film starts at 19:50 and ends at 21:35.

(a)

How long, in minutes, does the film last?

(b)

Write the film length as hours and minutes.

Question 15

[1 marks]

A car travels 95 miles in 2 hours 30 minutes. What is its average speed, in mph?

Question 16

[2 marks]

Zoe is currently 4 times as old as her cousin Ben. In 5 years, the sum of their ages will be 50.

(a)

How old is Ben now?

(b)

How old is Zoe now?

Question 17

[2 marks]

(a)

Find the highest common factor (HCF) of 54 and 72.

(b)

Find the lowest common multiple (LCM) of 6 and 14.

Question 18

[2 marks]

A bike priced at £80 is increased in price by 15%, 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 70 students, 40 like art, 30 like music, and 15 like both.

(a)

How many like neither subject?

(b)

How many like art only?

Question 20

[1 marks]

Find the missing digit d so that the six-digit number 3d5824 is divisible by 9.

Question 21

[2 marks]

Using the symbols ♪, ♫ and ☂ for three different numbers: ♪+♫=23, ☂+♫=18, ♪+☂=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 8:20?

Question 23

[1 marks]

How many different 4-digit codes, with no repeated digits, can be formed using the digits 1, 2, 3, 4, 5 and 6?

Question 24

[2 marks]

Calculate 6¼ - 3⅚, giving your answer as a mixed number in its simplest form.

Question 25

[2 marks]

A rectangular garden measures 14m by 8m. A right-angled triangular pond with legs 6m 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 2x cm and a base of length (x+9) cm. Its perimeter is 39cm.

(a)

Find x.

(b)

Find the length of the base.

Question 27

[2 marks]

(a)

Convert 5600ml to litres.

(b)

Convert 4250g to kilograms.

Question 28

[2 marks]

6 workers can finish a job in 10 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 5 hours?

Question 29

[1 marks]

I am thinking of a number. When I multiply it by 4 and subtract 6, I get 50. What is the number?

Question 30

[2 marks]

A jar contains red, blue and green marbles in the ratio 2:5:7. There are 20 more green marbles than red marbles.

(a)

How many red marbles are there?

(b)

How many marbles are there in total?