ABC Education · 11+ Practice

Week 26 · Maths Practice Paper

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

Question 1

[3 marks]

(a)

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

(b)

Write in words: 823070.

(c)

Round 489215 to the nearest 1000.

Question 2

[2 marks]

Calculate, using the correct order of operations:

(a)

9 + 5 × (8 - 4)² ÷ 16

(b)

(28 - 9) × 2 - 3²

Question 3

[3 marks]

(a)

Write 516 as a decimal.

(b)

Write 0.16 as a fraction in its simplest form.

(c)

Put these in order, smallest to largest: 310, 0.32, 31%, 720

Question 4

[2 marks]

A trail mix uses chocolate, nuts and dried fruit in the ratio 4:3:3, making 500g in total.

(a)

How much chocolate is needed?

(b)

How much dried fruit is needed?

Question 5

[2 marks]

Solve the following equations:

(a)

9x - 22 = 32

(b)

7(y - 3) = 28

Question 6

[3 marks]

A sequence has nth term 7n - 3.

(a)

Find the 7th term.

(b)

Find the first term greater than 100.

(c)

Is 144 a term in this sequence? Explain.

Question 7

[2 marks]

The angles of a triangle are x°, (x+15)° and (x+75)°.

(a)

Find x.

(b)

Find the size of the largest angle.

Question 8

[2 marks]

The quadrilateral below has a 120° angle, a right angle, and an exterior angle of 155° at the third corner (so the interior angle there is 25°). Calculate x and y.

x =

y =

Question 9

[2 marks]

For a regular 5-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 hexagonal-based pyramid:

(a)

How many faces does it have?

(b)

How many edges does it have?

Question 11

[3 marks]

Three vertices of rectangle UVWX are U(-4,4), V(1,4) and W(1,-1).

(a)

Find the coordinates of X.

(b)

Find the area of the rectangle.

(c)

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

Question 12

[2 marks]

A bag contains 9 plum, 2 mint and 1 honey counter.

(a)

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

(b)

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

Question 13

[3 marks]

The bar chart shows the number of cakes baked each day of one week.

(a)

What is the total number of cakes baked that week?

(b)

What is the mean number per day?

(c)

What is the median?

Question 14

[2 marks]

A filming session starts at 13:10 and ends at 16:02.

(a)

How long, in minutes, does the session last?

(b)

Write the session length as hours and minutes.

Question 15

[1 marks]

A car travels 207 miles in 4 hours 30 minutes. What is its average speed, in mph?

Question 16

[2 marks]

Ruby is currently 5 times as old as her brother. In 1 year, the sum of their ages will be 44.

(a)

How old is Ruby's brother now?

(b)

How old is Ruby now?

Question 17

[2 marks]

(a)

Find the highest common factor (HCF) of 60 and 90.

(b)

Find the lowest common multiple (LCM) of 18 and 24.

Question 18

[2 marks]

A dress priced at £40 is increased in price by 50%, and then the new price is decreased by 30%.

(a)

What is the price after the increase?

(b)

What is the final price?

Question 19

[2 marks]

In a year group of 110 students, 65 like dance, 48 like drama, and 25 like both.

(a)

How many like neither activity?

(b)

How many like dance only?

Question 20

[1 marks]

Find the missing digit d so that the six-digit number 2d7416 is divisible by 9.

Question 21

[2 marks]

Using the symbols ♭, ♯ and ♮ for three different numbers: ♭+♯=28, ♮+♯=23, ♭+♮=25.

(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 9:30?

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, 3, 5, 7 and 9?

Question 24

[2 marks]

Calculate 9¼ - 6⅚, giving your answer as a mixed number in its simplest form.

Question 25

[2 marks]

A rectangular garden measures 23m by 13m. A right-angled triangular pond with legs 10m 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+5) cm. Its perimeter is 33cm.

(a)

Find x.

(b)

Find the length of the base.

Question 27

[2 marks]

(a)

Convert 6300ml to litres.

(b)

Convert 7800g to kilograms.

Question 28

[2 marks]

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

(a)

How long would it take 5 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 add 9 to it and triple the result, I get 42. What is the number?

Question 30

[2 marks]

A jar of beads A, B and C are in the ratio 5:6:13. There are 40 more C beads than A beads.

(a)

How many A beads are there?

(b)

How many beads are there in total?