ABC Education · 11+ Practice

Week 39 · Maths Practice Paper

20 questions · 90 marks · Suggested time: 60 minutes.

Question 1

[8 marks]

Write down the answers to these questions. (You may work them out in your head.)

(i)

57 + 26

(ii)

724 - 231

(iii)

459

(iv)

3²

(v)

thirty percent of seventy

(vi)

7.2 × 100

(vii)

456 + 389

(viii)

34 × 5

Question 2

[5 marks]

(a)

Write down all the prime numbers between 20 and 30

(b)

Write down the first three multiples of 15

(c)

Write down all the factors of 24

Question 3

[4 marks]

A box of 9 mangoes costs GBP 4.05.

(i)

What is the cost of one mango? Give your answer in pence.

(ii)

Sophie buys 3 boxes of mangoes and pays with a GBP 20 note. How much change should she receive?

Question 4

[2 marks]

At 9am one morning, the temperature inside a greenhouse was 19°C and the temperature outside was -3°C.

(i)

How many degrees warmer was it inside than outside?

(ii)

By 9pm, the temperature outside had risen by 5°C. What was the temperature outside at 9pm?

Question 5

[3 marks]

Fill in the boxes to make the following statements true.

(i)

6 + 5 × ? = 41

(ii)

4 × (7 - ?) = 16

(iii)

12 - (6 + ?) = -2

Question 6

[6 marks]

Shape P is drawn on the centimetre-square grid below. Its vertices are at (2,2), (4,2), (4,3), (3,4) and (2,3).

(i)

Shape P is reflected in the dashed line (y = 5). What are the new coordinates of the point (3,4)?

(ii)

Shape P is translated 3 units right and 2 units up. What are the new coordinates of the point (3,4)?

(iii)

Work out the area of shape P, with the correct units.

Question 7

[3 marks]

(a)(i)

Write down the value of the Roman numeral X

(a)(ii)

Write down the value of the Roman numeral D

(b)

Which year is written in Roman numerals as MMXIX?

Question 8

[10 marks]

(a)(i)

4867 + 2913

(a)(ii)

4867 - 2913

(a)(iii)

356 × 24

(a)(iv)

173811

(b)

Round 3142 to the nearest 100

Question 9

[2 marks]

Calculate the mean of these numbers.

11   16   9   19   10

Mean =

Question 10

[4 marks]

Here is a list of fractions:

98     34     45     69     511

Choose from the list

(i)

a fraction which is greater than 1

(ii)

a fraction equivalent to 75%

(iii)

a fraction equivalent to 0.8

(iv)

a fraction which is not in its simplest form

Question 11

[2 marks]

A bamboo plant is 120cm tall. How tall will it be if its height increases by 15%?

Answer:

Question 12

[4 marks]

Here are 5 number cards: 8, 7, 4, 3, 2. The cards can be put together to form numbers. Using all 5 cards, the largest number that could be made is 87432.

(i)(a)

Using all 5 cards, what is the largest possible even number?

(i)(b)

Using all 5 cards, what is the number which is closest to 50 000?

(ii)

Use exactly 2 of the cards to make the smallest possible prime number.

(iii)

Arrange any 4 of the cards to show a sum which gives the smallest possible answer.

Question 13

[3 marks]

Put these distances in order from smallest to largest.

34.6km     3.092km     3079m     3.907km

smallest to largest:

Question 14

[6 marks]

In triangle ABC, AB = 6.5cm, angle A = 50° and angle B = 90°.

(i)

Work out the size of angle C.

(ii)

Using trigonometry, work out the length of BC, to 1 decimal place. (Hint: tan(A) = BC / AB)

(iii)

Is triangle ABC scalene, isosceles or equilateral? Is it right-angled? Give a reason.

Question 15

[6 marks]

Two identical rectangles are each divided into 18 equal squares.

(a)

If 49 of the first rectangle were shaded, how many squares would be shaded?

(b)

If 56 of the second rectangle were shaded, how many squares would be shaded?

(c)

Which is larger: 49 or 56? Give a reason.

(d)

Arrange these fractions in order from smallest to largest: 1 29, 56, 79, 1118, 49

Question 16

[4 marks]

Work out

(i)

34 - 18

(ii)

37 × 4 (write your answer as a mixed number)

Question 17

[3 marks]

In a box of 36 pencils, one sixth are black, 25% are white and the rest are yellow. What fraction of the pencils is yellow?

Answer:

Question 18

[5 marks]

Jake hangs a lantern from two rods meeting at a point. Find the size of one of the shaded angles below, if both are the same size.

(a)

The diagram below shows two straight lines crossing. Find the sizes of the angles marked a, b and c.

(b)

(a)

Size of one shaded angle:

(b)

Sizes of angles a, b and c:

Question 19

[3 marks]

Tom measured the temperature of a greenhouse every 15 minutes and plotted his results on the graph below.

(i)

What was the lowest temperature recorded?

(ii)

At what time was the temperature 28°C?

(iii)

Tom measured the temperature again 3 hours 15 minutes after the last reading on the graph. At what time did he take this measurement?

Question 20

[7 marks]

Farmer Alan and Farmer Beth each have a rectangular field. Farmer Alan's field has an area of 27m² and its length is 9m. Farmer Beth's field has a perimeter of 22m and its width is 5m.

(i)

Work out the width of Farmer Alan's field.

(ii)

Work out the perimeter of Farmer Alan's field.

(iii)

Work out the length of Farmer Beth's field.

(iv)

Work out the area of Farmer Beth's field.