ABC Education · 11+ Practice

Week 40 · Maths Practice Paper

18 questions · 110 marks · Suggested time: 55 minutes.

Question 1

[9 marks]

Work out:

(a)

246 + 87

(b)

273 − 58

(c)

614 − 97

(d)

62 × 8

(e)

42 × 26

(f)

315 ÷ 9

(g)

391 ÷ 17

Question 2

[5 marks]

Find the perimeter and area of this shape (a right-angled trapezium):

Perimeter =

Area =

cm²

Question 3

[5 marks]

Calculate, giving your answer as simply as possible:

(a)

715 + 515

(b)

110 + 35

Question 4

[4 marks]

Find:

(a)

35% of £80

(b)

A fifth of £80

(c)

80% of a half of £80

Question 5

[4 marks]

Find the missing angles (diagrams not to scale):

a =

b =

c =

d =

Question 6

[8 marks]

Find the next 2 numbers in the following sequences:

(a)

4, 9, 14, 19, 24, ___, ___

(b)

5, 10, 20, 40, ___, ___

(c)

4, 6, 10, 16, 24, ___, ___

(d)

16, 311, 518, 727, ___, ___

Question 7

[6 marks]

Complete the table below, giving fractions in their lowest terms.

Fraction	Decimal	Percentage
?	?	25%
?	0.4	?
7/10	?	?
9/20	?	?

Question 8

[9 marks]

The table shows part of the railway timetable from Leeds to Derby. Some trains stop at every station and others are express trains. All stopping trains take the same time between each station as each other.

	Express	Stopping	Express	Stopping	Express	Stopping
Leeds	10:12	10:35	11:15	11:38	12:05	12:26
Wakefield		10:53		11:56
Sheffield		11:04		12:07
Chesterfield		11:10		12:13
Derby	10:50	11:28	11:53	12:31	12:43

(a)

How many minutes does it take to travel between Leeds and Sheffield (on the stopping service)?

(b)

Complete the times for the stopping train that leaves Leeds at 12:26 (Wakefield, Sheffield, Chesterfield, Derby).

(c)

How much longer does the stopping train take than the express train for the journey from Leeds to Derby?

(d)

Tom arrives at the airport next to Leeds station at 09:40. It takes him 20 minutes to collect his baggage, then 30 minutes to get to Leeds station. How long does he have to wait for the next train?

Question 9

[6 marks]

Find the area of each of the following shapes: (i) a right-angled triangle with legs 6cm and 4cm, (ii) a parallelogram with base 5cm and height 4cm, (iii) a kite with diagonals 9cm and 6cm, (iv) a trapezium with parallel sides 4cm and 8cm and height 5cm.

(i)

cm²

(ii)

cm²

(iii)

cm²

(iv)

cm²

Question 10

[10 marks]

James was given £18 to buy supplies for the school year. He chose to spend it on pens and pencils. Each pen costs £1.35 and each pencil costs 70p.

(a)

If James buys 6 pens and 8 pencils, how much money will he have left?

(b)

If instead James buys a set of 6 pencils first, what is the maximum number of pens he can then buy?

(c)

If instead James ends up with £3.00 left of his money, how many pens and how many pencils did he buy?

Question 11

[6 marks]

15 campers eat 24 biscuits in 3 days.

(a)

How many campers will eat 48 biscuits in 3 days?

(b)

How many days will it take 5 campers to eat 24 biscuits?

(c)

How many biscuits will 10 campers eat in 6 days?

Question 12

[3 marks]

Put these numbers in order from smallest to largest:

55%      1925      710      0.72

Question 13

[5 marks]

There are four unknown positive whole numbers. The mean of the two smallest numbers is 2. The mean of the three smallest numbers is 5. The mean of all four numbers is 7. All the numbers are different and odd. What are the four numbers?

Question 14

[2 marks]

Twelve green bottles are hanging on a wall. If the first bottle fell at 6:05am and the others fell down at 4-minute intervals, at what time would the last (12th) bottle fall?

Question 15

[2 marks]

A shape has a line of symmetry along the line y = x. One part of the shape (above the line) has a horizontal edge running from (1,4) to (1,6). What are the coordinates of the corresponding reflected points on the other side of the line of symmetry?

Question 16

[9 marks]

Here are five cards with numbers printed on them. The cards can be placed in order to form a 5-digit number — for example, the smallest number possible using all 5 cards is 13569.

(a)

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

(b)

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

(c)

Using only two of the cards, what is the largest possible prime number?

(d)

Arrange any three of the number cards to give the largest possible answer to a two-digit × one-digit multiplication.

Question 17

[9 marks]

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

(a)

It is divisible by 9. When divided by 7 the remainder is 3. When divided by 4 the remainder is 1. What is the number?

(b)

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?

(c)

When divided by 2 the remainder is 1. When divided by 3 the remainder is 2. It is divisible by 5. When divided by 7 the remainder is 2. What is the number?

Question 18

[8 marks]

In a magic triangle, each of the numbers 1 to 6 is placed once — three at the corners and three at the midpoints of the sides — so that each side of the triangle adds up to the same total. The corners hold the numbers 1, 2 and 3, as shown.

(a)

What is the fixed side-total?

(b)

What number sits on the edge connecting the corners holding 2 and 3?