ABC Education · 11+ Practice

Week 29 · Maths Practice Paper

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

Question 1

[3 marks]

(a)

Write in figures: six hundred and seventy-three thousand and twenty-nine.

(b)

Write in words: 592340.

(c)

Round 835192 to the nearest 1000.

Question 2

[2 marks]

Calculate, using the correct order of operations:

(a)

12 + 3 × (9 - 6)² ÷ 9

(b)

(29 - 14) × 2 - 3²

Question 3

[3 marks]

(a)

Write 78 as a decimal.

(b)

Write 0.12 as a fraction in its simplest form.

(c)

Put these in order, smallest to largest: 14, 0.28, 27%, 310

Question 4

[2 marks]

A birdseed mix uses grass seed, clover and wildflower seed in the ratio 7:2:1, making 500g in total.

(a)

How much grass seed is needed?

(b)

How much wildflower seed is needed?

Question 5

[2 marks]

Solve the following equations:

(a)

12x - 25 = 47

(b)

10(y - 3) = 50

Question 6

[3 marks]

A sequence has nth term 10n - 6.

(a)

Find the 5th term.

(b)

Find the first term greater than 100.

(c)

Is 194 a term in this sequence? Explain.

Question 7

[2 marks]

The angles of a triangle are x°, (x+30)° and (x+90)°.

(a)

Find x.

(b)

Find the size of the largest angle.

Question 8

[2 marks]

The quadrilateral below has a 60° angle, a right angle, and an exterior angle of 135° at the third corner (so the interior angle there is 45°). 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 decagonal prism:

(a)

How many faces does it have?

(b)

How many edges does it have?

Question 11

[3 marks]

Three vertices of rectangle GHIJ are G(-3,3), H(2,3) and I(2,-2).

(a)

Find the coordinates of J.

(b)

Find the area of the rectangle.

(c)

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

Question 12

[2 marks]

A bag contains 4 slate, 5 sand and 3 rust counters.

(a)

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

(b)

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

Question 13

[3 marks]

The bar chart shows the number of eggs laid by a group of hens each day of one week.

(a)

What is the total number of eggs laid that week?

(b)

What is the mean number per day?

(c)

What is the median?

Question 14

[2 marks]

A rehearsal starts at 16:15 and ends at 18:50.

(a)

How long, in minutes, does the rehearsal last?

(b)

Write the rehearsal length as hours and minutes.

Question 15

[1 marks]

A cyclist travels 96 miles in 4 hours. What is their average speed, in mph?

Question 16

[2 marks]

Amelia is currently 8 times as old as her cousin. In 1 year, the sum of their ages will be 47.

(a)

How old is Amelia's cousin now?

(b)

How old is Amelia now?

Question 17

[2 marks]

(a)

Find the highest common factor (HCF) of 90 and 126.

(b)

Find the lowest common multiple (LCM) of 16 and 24.

Question 18

[2 marks]

A camera priced at £72 is increased in price by 25%, and then the new price is decreased by 40%.

(a)

What is the price after the increase?

(b)

What is the final price?

Question 19

[2 marks]

In a year group of 140 students, 80 like music, 60 like art, and 35 like both.

(a)

How many like neither subject?

(b)

How many like music only?

Question 20

[1 marks]

Find the missing digit d so that the six-digit number 6d1827 is divisible by 9.

Question 21

[2 marks]

Using the symbols ♛, ♚ and ♜ for three different numbers: ♛+♚=33, ♜+♚=28, ♛+♜=29.

(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 8:50?

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, 2, 4 and 6?

Question 24

[2 marks]

Calculate 7¼ - 4⅚, giving your answer as a mixed number in its simplest form.

Question 25

[2 marks]

A rectangular garden measures 29m by 16m. A right-angled triangular pond with legs 13m and 8m 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+8) cm. Its perimeter is 36cm.

(a)

Find x.

(b)

Find the length of the base.

Question 27

[2 marks]

(a)

Convert 4300ml to litres.

(b)

Convert 6600g to kilograms.

Question 28

[2 marks]

20 workers can finish a job in 6 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 4 hours?

Question 29

[1 marks]

I am thinking of a number. When I add 17 to it and halve the result, I get 22. What is the number?

Question 30

[2 marks]

A tub of sweets A, B and C are in the ratio 5:8:17. There are 36 more C sweets than A sweets.

(a)

How many A sweets are there?

(b)

How many sweets are there in total?