ABC Education · 11+ Practice

Week 15 · Maths Practice Paper

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

Question 1

[3 marks]

(a)

Write in figures: two hundred and six thousand and forty-five.

(b)

Write in words: 90807.

(c)

Round 68472 to the nearest thousand.

Question 2

[2 marks]

Calculate, using the correct order of operations:

(a)

6 + 4 × (9 - 5) ÷ 2

(b)

(15 - 3) × 2² - 7

Question 3

[3 marks]

(a)

Write 78 as a decimal.

(b)

Write 0.35 as a fraction in its simplest form.

(c)

Put these in order, smallest to largest: 35, 0.52, 58%, 1120

Question 4

[2 marks]

A recipe uses flour, sugar and butter in the ratio 5:3:2, making 400g of mixture in total.

(a)

How much flour is needed?

(b)

How much butter is needed?

Question 5

[2 marks]

Solve the following equations:

(a)

4x - 7 = 21

(b)

3(y + 2) = 27

Question 6

[3 marks]

A sequence has nth term 5n - 3.

(a)

Find the 10th term.

(b)

Find the first term greater than 100.

(c)

Is 152 a term in this sequence? Explain.

Question 7

[2 marks]

The angles of a triangle are x°, (x+10)° and (x+20)°.

(a)

Find x.

(b)

Find the size of the largest angle.

Question 8

[2 marks]

The quadrilateral below has a 100° angle, a right angle, and an exterior angle of 140° at the third corner (so the interior angle there is 40°). Calculate x and y.

x =

y =

Question 9

[2 marks]

For a regular hexagon:

(a)

How many lines of symmetry does it have?

(b)

What is its order of rotational symmetry?

Question 10

[2 marks]

For a triangular-based pyramid (a tetrahedron):

(a)

How many faces does it have?

(b)

How many edges does it have?

Question 11

[3 marks]

Three vertices of rectangle ABCD are A(2,5), B(6,5) and C(6,1).

(a)

Find the coordinates of D.

(b)

Find the area of the rectangle.

(c)

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

Question 12

[2 marks]

A bag contains 4 red, 5 blue and 3 green counters.

(a)

A counter is drawn at random. What is the probability it is green? Give your answer as a fraction in its simplest form.

(b)

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

Question 13

[3 marks]

The bar chart shows the number of books read by a class over one week.

(a)

What is the total number of books read that week?

(b)

What is the mean number of books read per day?

(c)

What is the range?

Question 14

[2 marks]

A train departs at 09:47 and arrives at 11:15.

(a)

How long, in minutes, is the journey?

(b)

Write the journey time as hours and minutes.

Question 15

[1 marks]

A car travels 126 miles in 2 hours 15 minutes. What is its average speed, in mph?

Question 16

[2 marks]

Sam is currently 3 times as old as his sister. In 4 years, he will be twice as old as her.

(a)

How old is Sam's sister now?

(b)

How old is Sam now?

Question 17

[2 marks]

(a)

Find the highest common factor (HCF) of 48 and 60.

(b)

Find the lowest common multiple (LCM) of 8 and 12.

Question 18

[2 marks]

A shirt priced at £40 is reduced by 15% in a sale, and then a further 10% is taken off the sale price.

(a)

What is the price after the first reduction?

(b)

What is the final price?

Question 19

[2 marks]

In a year group of 50 pupils, 28 play football, 19 play tennis, and 9 play both sports.

(a)

How many play neither sport?

(b)

How many play football only?

Question 20

[1 marks]

Find the missing digit d so that the six-digit number 42d738 is divisible by 9.

Question 21

[2 marks]

Using the symbols ★, ● and ▲ for three different numbers: ★+●=17, ▲+●=13, ★+▲=14.

(a)

Find ●.

(b)

Find ★.

Question 22

[1 marks]

What is the acute angle between the hour hand and minute hand of a clock at 4:20?

Question 23

[1 marks]

How many different two-digit numbers, with no repeated digits, can be formed using the digits 3, 5, 7 and 9?

Question 24

[2 marks]

Calculate 2¾ + 1⅚, giving your answer as a mixed number in its simplest form.

Question 25

[2 marks]

A rectangular garden measures 12m by 7m. A right-angled triangular flower bed with legs 4m and 3m is cut from one corner, as shown, and is no longer lawn.

(a)

What is the area of the flower bed?

(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+4) cm. Its perimeter is 32cm.

(a)

Find x.

(b)

Find the length of the base.

Question 27

[2 marks]

(a)

A tank holds 3.4 litres of water. How many millilitres is this?

(b)

Convert 2.5kg to grams.

Question 28

[2 marks]

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

(a)

How long would it take 6 workers, working at the same rate, to build the same wall?

(b)

How many workers would be needed to build the wall in 5 hours?

Question 29

[1 marks]

I am thinking of a number. When I double it and subtract 9, I get 37. What is the number?

Question 30

[2 marks]

A jar contains red, blue and green sweets in the ratio 2:3:5. There are 12 more green sweets than red sweets.

(a)

How many red sweets are there?

(b)

How many sweets are there in total?