ABC Education · 11+ Practice

Week 27 · Maths Practice Paper

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

Question 1

[3 marks]

(a)

Write in figures: seven hundred and four thousand and fifty-one.

(b)

Write in words: 359080.

(c)

Round 721463 to the nearest 100.

Question 2

[2 marks]

Calculate, using the correct order of operations:

(a)

7 + 6 × (9 - 5)² ÷ 16

(b)

(23 - 8) × 2 - 4²

Question 3

[3 marks]

(a)

Write 1316 as a decimal.

(b)

Write 0.84 as a fraction in its simplest form.

(c)

Put these in order, smallest to largest: 45, 0.83, 82%, 1720

Question 4

[2 marks]

A granola mix uses oats, honey and nuts in the ratio 7:2:3, making 480g in total.

(a)

How much oats is needed?

(b)

How much nuts is needed?

Question 5

[2 marks]

Solve the following equations:

(a)

10x - 23 = 37

(b)

8(y - 1) = 40

Question 6

[3 marks]

A sequence has nth term 8n - 3.

(a)

Find the 6th term.

(b)

Find the first term greater than 100.

(c)

Is 165 a term in this sequence? Explain.

Question 7

[2 marks]

The angles of a triangle are x°, (x+5)° and (x+55)°.

(a)

Find x.

(b)

Find the size of the largest angle.

Question 8

[2 marks]

The quadrilateral below has a 65° angle, a right angle, and an exterior angle of 130° at the third corner (so the interior angle there is 50°). Calculate x and y.

x =

y =

Question 9

[2 marks]

For a plus-shaped cross (like a plus sign):

(a)

How many lines of symmetry does it have?

(b)

What is its order of rotational symmetry?

Question 10

[2 marks]

For a heptagonal prism:

(a)

How many faces does it have?

(b)

How many edges does it have?

Question 11

[3 marks]

Three vertices of rectangle YZAB are Y(-2,-1), Z(4,-1) and A(4,3).

(a)

Find the coordinates of B.

(b)

Find the area of the rectangle.

(c)

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

Question 12

[2 marks]

A bag contains 5 azure, 4 amber and 3 jade counters.

(a)

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

(b)

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

Question 13

[3 marks]

The bar chart shows the number of birds spotted by a birdwatcher each day of one week.

(a)

What is the total number of birds spotted that week?

(b)

What is the mean number per day?

(c)

What is the median?

Question 14

[2 marks]

A hike starts at 07:30 and ends at 11:15.

(a)

How long, in minutes, does the hike last?

(b)

Write the hike length as hours and minutes.

Question 15

[1 marks]

A car travels 198 miles in 3 hours. What is its average speed, in mph?

Question 16

[2 marks]

Felix is currently 6 times as old as his niece. In 3 years, the sum of their ages will be 48.

(a)

How old is Felix's niece now?

(b)

How old is Felix now?

Question 17

[2 marks]

(a)

Find the highest common factor (HCF) of 72 and 120.

(b)

Find the lowest common multiple (LCM) of 10 and 25.

Question 18

[2 marks]

A jacket priced at £50 is increased in price by 60%, 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 120 students, 70 like photography, 52 like art, and 30 like both.

(a)

How many like neither activity?

(b)

How many like photography only?

Question 20

[1 marks]

Find the missing digit d so that the six-digit number 4d8235 is divisible by 9.

Question 21

[2 marks]

Using the symbols ♧, ♡ and ♤ for three different numbers: ♧+♡=30, ♤+♡=25, ♧+♤=27.

(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 3:15?

Question 23

[1 marks]

How many different 2-digit codes, with no repeated digits, can be formed using the digits 2, 4, 6 and 8?

Question 24

[2 marks]

Calculate 5⅙ - 2¾, giving your answer as a mixed number in its simplest form.

Question 25

[2 marks]

A rectangular garden measures 25m by 14m. A right-angled triangular pond with legs 10m and 7m 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+2) cm. Its perimeter is 30cm.

(a)

Find x.

(b)

Find the length of the base.

Question 27

[2 marks]

(a)

Convert 8600ml to litres.

(b)

Convert 3200g to kilograms.

Question 28

[2 marks]

16 workers can finish a job in 3 hours, all working at the same steady rate.

(a)

How long would it take 4 workers to finish the same job?

(b)

How many workers would be needed to finish the job in 2 hours?

Question 29

[1 marks]

I am thinking of a number. When I double it and add 13, I get 41. What is the number?

Question 30

[2 marks]

A tin of balls A, B and C are in the ratio 3:7:12. There are 36 more C balls than A balls.

(a)

How many A balls are there?

(b)

How many balls are there in total?