ABC Education · 11+ Practice

Week 35 · Maths Practice Paper

20 questions · 60 marks · Suggested time: 1 hour.

Question 1

[3 marks]

Calculate the following, showing your working.

(a)

47 - 103 + 31

(b)

7355

(c)

42 × 11

Question 2

[3 marks]

Convert the following fractions to decimals.

(a)

710

(b)

2350

(c)

1824

Question 3

[2 marks]

Fill in each box with either a + or - to make the calculations true.

(a)

9 [?] 15 = -6

(b)

-4 [?] 7 [?] 12 = -9

Question 4

[2 marks]

Fill in each box with a number to make the calculations true.

(a)

(15 + [?]) × 4 = 100

(b)

[?] - 83 = 11

Question 5

[2 marks]

A plank of wood is 5.4 metres long. Two lengths are cut from the plank: 95cm and 1420mm. What length of wood is left? Give your answer in cm.

Answer:

Question 6

[2 marks]

Place the following fractions in order from smallest to largest.

512, 38, 724, 14

smallest to largest:

Question 7

[4 marks]

For each item on sale, calculate the reduced price.

(a)

A muffin originally costing GBP 2.50 has been reduced by 18%.

(b)

A bagel originally costing 60p has been reduced by 15%.

Question 8

[2 marks]

A factory makes wooden cubes with sides of 4cm. They are packed into a large box measuring 24cm by 16cm by 20cm. How many wooden cubes can be packed into one large box?

Answer:

Question 9

[6 marks]

Evaluate the following, giving your answer in its simplest form.

(a)

37 ÷ 5

(b)

2 14 × 4 23

(c)

13 + 15 - 16

Question 10

[3 marks]

The table below shows a timetable for four trains. Trains B and C do not stop at every station.

Station	A	B	C	D
Leeds	08:15	08:40	09:05	10:30
Wakefield	08:28	08:53	09:18	10:43
Sheffield	08:50	-	09:38	11:05
Chesterfield	09:10	-	09:50	11:25
Derby	09:28	09:35	-	11:43
Nottingham	09:55	09:58	10:15	12:10

(a)

What time does the 08:40 train from Leeds arrive in Nottingham?

(b)

Which train is fastest from Leeds to Nottingham?

(c)

You arrive at Wakefield at 09:05. How long will you have to wait for a train to Derby?

Question 11

[3 marks]

Priya has a map of a village. The scale on the map is such that 1cm represents 20m.

(a)

On the map, the library is 6cm from the park. What is the real distance from the library to the park?

(b)

Priya estimates her house is 800m from the library. On the map, how many cm would represent this distance?

Question 12

[6 marks]

Write down the next two numbers in each of the following sequences.

(a)

0.05, 0.12, 0.19, ...

(b)

4, 12, 36, ...

(c)

0.2, 940, 14, ...

Question 13

[6 marks]

Solve for x in the following equations.

(a)

7x + 4 = 39

(b)

12(x - 4) = 60

(c)

23 x + 7 = 23

Question 14

[2 marks]

Let p be a prime number greater than 2.

(a)

Circle one expression below which could also be a prime number: 3p 5p p+2 p²

(b)

Give a reason for your answer above.

Question 15

[3 marks]

A farmer keeps rabbits in the plot shown below. If each rabbit requires 4m², what is the maximum number of rabbits the farmer can keep?

Answer:

Question 16

[3 marks]

Mia's car uses 32 litres of fuel to travel 128 miles. She wants to drive from Bristol to Newcastle, a distance of 316 miles. How much fuel will she need?

Answer:

Question 17

[2 marks]

On a pair of balance scales: 2 triangles and 1 hexagon together weigh 46g. 1 triangle and 1 hexagon together weigh 29g. What is the weight of one triangle?

Answer:

Question 18

[2 marks]

Mia is five years younger than Leo. In three years' time, Leo will be twice as old as Mia. Find Leo's present age. Show your working.

Answer:

Question 19

[2 marks]

Two identical large triangles are each divided into smaller triangles of equal size, as shown. Every upward-pointing small triangle is shaded. Triangle 1 is divided into 4 rows; Triangle 2 is divided into 5 rows.

Triangle 1 (4 rows)

Triangle 2 (5 rows)

Which has the larger shaded area? You must give a reason for your answer.

Question 20

[2 marks]

The board shown has cells arranged in a 6 by 5 grid, with one cell (marked x) that cannot be used. Starting at S and finishing at F, every move goes one cell right or one cell up. How many shortest paths (9 moves) are there from S to F that avoid the marked cell? Show your working.

Answer: