ABC Education · 11+ Practice

Week 28 · Maths Practice Paper

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

Question 1

[3 marks]

(a)

Write in figures: eight hundred and ninety-two thousand and sixteen.

(b)

Write in words: 436090.

(c)

Round 267834 to the nearest 10000.

Question 2

[2 marks]

Calculate, using the correct order of operations:

(a)

11 + 4 × (7 - 3)² ÷ 8

(b)

(26 - 11) × 2 - 3²

Question 3

[3 marks]

(a)

Write 1516 as a decimal.

(b)

Write 0.92 as a fraction in its simplest form.

(c)

Put these in order, smallest to largest: 910, 0.88, 87%, 1920

Question 4

[2 marks]

A paint mix uses red, yellow and white paint in the ratio 5:4:1, making 400ml in total.

(a)

How much red paint is needed?

(b)

How much white paint is needed?

Question 5

[2 marks]

Solve the following equations:

(a)

11x - 24 = 42

(b)

9(y - 2) = 45

Question 6

[3 marks]

A sequence has nth term 9n - 5.

(a)

Find the 6th term.

(b)

Find the first term greater than 100.

(c)

Is 175 a term in this sequence? Explain.

Question 7

[2 marks]

The angles of a triangle are x°, (x+20)° and (x+100)°.

(a)

Find x.

(b)

Find the size of the largest angle.

Question 8

[2 marks]

The quadrilateral below has a 55° angle, a right angle, and an exterior angle of 120° at the third corner (so the interior angle there is 60°). Calculate x and y.

x =

y =

Question 9

[2 marks]

For a shape like the letter H:

(a)

How many lines of symmetry does it have?

(b)

What is its order of rotational symmetry?

Question 10

[2 marks]

For an octagonal-based pyramid:

(a)

How many faces does it have?

(b)

How many edges does it have?

Question 11

[3 marks]

Three vertices of rectangle CDEF are C(-5,-3), D(1,-3) and E(1,2).

(a)

Find the coordinates of F.

(b)

Find the area of the rectangle.

(c)

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

Question 12

[2 marks]

A bag contains 6 copper, 3 bronze and 3 steel counters.

(a)

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

(b)

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

Question 13

[3 marks]

The bar chart shows the number of visitors (in hundreds) to a park each day of one week.

(a)

What is the total number of visitors (in hundreds) that week?

(b)

What is the mean number per day?

(c)

What is the median?

Question 14

[2 marks]

A trip starts at 06:40 and ends at 09:55.

(a)

How long, in minutes, does the trip last?

(b)

Write the trip 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]

Henry is currently 7 times as old as his niece. In 2 years, the sum of their ages will be 44.

(a)

How old is Henry's niece now?

(b)

How old is Henry now?

Question 17

[2 marks]

(a)

Find the highest common factor (HCF) of 80 and 100.

(b)

Find the lowest common multiple (LCM) of 14 and 35.

Question 18

[2 marks]

A rucksack priced at £38 is increased in price by 50%, 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 130 students, 75 like coding, 58 like robotics, and 35 like both.

(a)

How many like neither activity?

(b)

How many like coding only?

Question 20

[1 marks]

Find the missing digit d so that the six-digit number 5d9314 is divisible by 9.

Question 21

[2 marks]

Using the symbols ☾, ☀ and ☆ for three different numbers: ☾+☀=32, ☆+☀=27, ☾+☆=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 12:40?

Question 23

[1 marks]

How many different 2-digit codes, with no repeated digits, can be formed using the digits 1, 3, 5 and 7?

Question 24

[2 marks]

Calculate 6⅓ - 3⅚, giving your answer as a mixed number in its simplest form.

Question 25

[2 marks]

A rectangular garden measures 27m by 15m. A right-angled triangular pond with legs 12m 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+1) cm. Its perimeter is 29cm.

(a)

Find x.

(b)

Find the length of the base.

Question 27

[2 marks]

(a)

Convert 9800ml to litres.

(b)

Convert 2700g to kilograms.

Question 28

[2 marks]

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

(a)

How long would it take 9 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 subtract 5 from it and double the result, I get 38. What is the number?

Question 30

[2 marks]

A box of marbles A, B and C are in the ratio 4:9:16. There are 48 more C marbles than A marbles.

(a)

How many A marbles are there?

(b)

How many marbles are there in total?