ABC Education

ABC Education · 11+ Practice

Week 45 · Maths Practice Paper

26 questions · 100 marks · Suggested time: 1 hour.

Question 1

[9 marks]

Work out:

(a)
2024 − 678
(b)
58 × 79
(c)
74.4 ÷ 6
(d)
19.6 + 7.85

Question 2

[6 marks]

Fill in the missing numbers in these sequences:

(a)
18, 25, 32, ___, 46, ___
(b)
11, 6, 1, ___, ___
(c)
128, -64, 32, -16, ___, ___

Question 3

[3 marks]

Fill in the blanks to make the calculation correct.

(a)
20 − 8 + 9 = ___
(b)
24 − (___ × 3) = 9
(c)
20 − (-4)² = ___

Question 4

[4 marks]

The perimeter of the rectangle below is 18cm.

3 cm
(a)
Find the width of the rectangle.
(b)
Find the area of the rectangle.
(c)
A 6cm square is cut into 3 identical 6cm × 2cm strips, which are rearranged into a staircase shape, each strip offset by 2cm from the last. What is the perimeter of the new shape?

Question 5

[3 marks]

4 identical right-angled triangles, each with legs 4cm and 3cm (area 6cm² each), can be arranged edge-to-edge to form different quadrilaterals.

(a)
If arranged into a rectangle, what is the rectangle's area?
(b)
If arranged into a non-rectangular parallelogram instead, what is that shape's area?

Question 6

[3 marks]
(a)
Round 728 to the nearest 100
(b)
Round 846 to the nearest 10
(c)
A number has been rounded to the nearest 10 to give 420. What is the smallest whole number it could possibly have been?

Question 7

[4 marks]
(a)
Calculate 0.5 + 14 + 13100
(b)
Write 3960 as a decimal

Question 8

[3 marks]

Find:

(a)
One quarter of £140
(b)
35% of £620

Question 9

[4 marks]

A sleeper train travels from London to Glasgow. The train departs at 10:47pm and arrives at 5:38am.

(a)
How long does the journey take?
(b)
A different train travels from London to Manchester at constant speed. The journey takes 2 hours 45 minutes and the distance travelled is 220 miles. Calculate the speed of the train.

Question 10

[4 marks]

You are given the following five numbers: 40, 25, 35, 50, 30

(a)
Find the mean of these five numbers.
(b)
Find the median.
(c)
Find the range.
(d)
A sixth number is added to the list and the mean changes to 40. What was this sixth number?

Question 11

[3 marks]

The diagram shows a triangle and a line. The two angles marked y° are equal.

116°y°y°x°
(a)
Work out the value of x
(b)
Work out the value of y

Question 12

[2 marks]

A shape has vertices at (1,2), (1,5), (3,5), (3,3), (2,3) and (2,2). It is reflected in the vertical line x = 4. What are the coordinates of the reflected vertices?

Question 13

[4 marks]

A(-3,3) and B(5,-3) are two points on a coordinate grid.

(a)
Find the coordinates of the midpoint of AB.
(b)
Point D(2,3) is midway between the points C(-1,-2) and E. Find the coordinates of the point E.

Question 14

[6 marks]

A set of solid towers are made by adding layers, where Tower N has 2N² − 2N + 1 cubes in total (Tower 1 has 1 cube).

→
Tower N has 2N² − 2N + 1 cubes (Tower 1 has 1 cube).
(a)
How many cubes are needed to build Tower 2?
(b)
How many cubes are needed to build Tower 3?
(c)
Without drawing it, how many cubes would be needed to build Tower 5?
(d)
Which tower number would contain 145 cubes?

Question 15

[4 marks]

The square numbers between 1 and 100 inclusive are 1, 4, 9, 16, 25, 36, 49, 64, 81, 100. Circle A contains the factors of 360. Circle B contains the multiples of 4.

(a)
Which square numbers go in the overlap of both circles?
(b)
Which square numbers are in Circle A only?
(c)
Which square numbers are in Circle B only?
(d)
Which square numbers are outside both circles?

Question 16

[4 marks]

The table shows the maths and science scores for 9 pupils: Nina (4,12), Omar (8,12), Priya (12,15), Jake (15,11), Alex (6,9), Chloe (10,6), Liam (4,4), Jade (7,2), Ethan (14,2). (Scores are given as maths, science.)

(a)
Who had the highest score in maths?
(b)
Who is good at science and poor at maths?
(c)
The two scores are added together for each pupil. Who has the highest total?

Question 17

[3 marks]

16 cards have letters on them: P (×3), M (×2), O (×2), R (×3), T (×2), Y (×4). A card is chosen at random.

(a)
Which letter is most likely to be taken?
(b)
Give one other letter that has the same probability of being chosen as an M.

Question 18

[3 marks]

A regular hexagon has lines drawn connecting points one-third of the way along each edge, forming a six-pointed star shape in the middle. What fraction of the hexagon's area is the star?

Question 19

[2 marks]

11 lamp posts are equally spaced along a road. The distance from the first to the fourth is 90m. How far is it from the first to the last (11th)?

m

Question 20

[3 marks]

A staircase-shaped figure has perimeter 50cm, made up of a top edge of 6cm, a bottom edge of 12cm, and 8 equal-length staircase segments, each labelled x. Find x.

x =
cm

Question 21

[5 marks]

The instruction x ⊕ y means subtract x from y and then multiply by 4. For example, 2 ⊕ 6 = (6 − 2) × 4 = 16.

(a)
Work out the value of 18 ⊕ 25
(b)
Work out the value of 12 ⊕ 7
(c)
Work out the value of a if 5 ⊕ a = 8
(d)
Work out the value of b if b ⊕ 6 = 8
(e)
Work out the value of c if c ⊕ 6 = 8 ⊕ c

Question 22

[3 marks]

A square has vertices at (2,1), (5,1), (5,4) and (2,4). It is rotated 90° clockwise about the origin.

What are the new coordinates of the vertex originally at (5,4)?

Question 23

[4 marks]

For each of the following questions you need to find a whole number between 0 and 100 that has all of the following properties.

(a)
When divided by 4 the remainder is 3. It is divisible by 9. When divided by 5 the remainder is 3. What is the number?
(b)
It is odd. It is divisible by 5. When divided by 3 the remainder is 1. When divided by 7 the remainder is 4. What is the number?

Question 24

[5 marks]

In this subtraction, P, Q, R, S and T represent single digits.

  9 Q 4 S T
− P 2 R 8 5
-----------
  3 3 3 3 3
P =, Q =, R =, S =, T =

Question 25

[3 marks]

Anastasia thinks of a positive integer, which Barry then doubles. Next, Charlie multiplies Barry's number by five. Finally, Damien multiplies Charlie's number by three. The sum of these four numbers (Anastasia's, Barry's, Charlie's and Damien's) is a perfect square. What is the smallest number that Anastasia could have thought of?

Question 26

[3 marks]

Calum and his friend cycle from A to C, passing through B. During the trip he asks his friend how far they have cycled. His friend replies 'one third as far as it is from here to B'. Fifteen miles later, Calum asks him how far they still have to cycle to reach C. His friend replies again 'one third as far as it is from here to B'. How far from A will Calum have cycled when he reaches C?

miles