ABC Education · 11+ Practice

Week 56 · Maths Practice Paper

46 questions · 100 marks · Suggested time: 1 hour 15 minutes.

Question 1

[1 marks]

Work out 5378 + 2947

Question 2

[1 marks]

Work out 8213 − 3647

Question 3

[1 marks]

Work out 3617 × 8

Question 4

[1 marks]

Work out 5928 ÷ 6

Question 5

[1 marks]

Work out 49 of 117

Question 6

[1 marks]

Write down the next number in the sequence. 76, 68, 60, 52, ___

Question 7

[2 marks]

Write a number in each box to complete the statements.

(a)
18.6 × 100 = ___
(b)
___ ÷ 1000 = 2.35

Question 8

[1 marks]

Which number is two hundred less than five thousand and forty?

Question 9

[1 marks]

Write the missing sign ( =, < or > ) in the box. 16 × 4 ___ 9 × 7

Question 10

[1 marks]

The temperature inside a greenhouse is 11°C and the temperature outside is −6°C. How many degrees warmer is it inside than outside?

degrees

Question 11

[2 marks]

A regular decagon (10-sided shape) is divided into 10 equal triangles, meeting at its centre, like a pie.

(a)
How many of the triangles must be shaded to shade exactly 20% of the decagon?
(b)
What percentage of the decagon would be shaded if 7 of the triangles were shaded?

Question 12

[1 marks]

Maya's train to Leeds was scheduled to leave at 10:15 and to arrive at 11:05. However, the train left 6 minutes late and then took 53 minutes. At what time did Maya arrive?

Question 13

[1 marks]

Which number between 90 and 120 is a multiple of both 4 and 9?

Question 14

[1 marks]

Omar thinks of his favourite number. He multiplies it by 4, subtracts 7, and gets 29. What was his favourite number?

Question 15

[4 marks]

(a) When Farah calls out a number, Priya multiplies it by 4 and then subtracts 6, and writes down the result.

Farah calls outPriya writes down
7?
?30
?−2
Complete the table.
(b)
Two other girls play a similar game: −2 → −3, 0 → 3, 1 → 6, 3 → 12. Work out what the second girl does to each number the first girl calls out.

Question 16

[4 marks]

Hana has five number cards: 2, 3, 4, 5, 6. The cards can be placed together to form a number. For example, using three cards the smallest 3-digit multiple of 3 that can be made is 234.

(a)
Using three cards, what is the smallest 3-digit multiple of 6 that can be made?
(b)
Using two cards, what is the largest 2-digit prime number that can be made?
(c)
Using four cards, what is the largest 4-digit multiple of 5 that can be made?

Question 17

[4 marks]

The information on a pack of 'Chicken Curry' is shown per 100 g: Protein 12 g, Carbohydrate 20 g, Fat 6 g, Fibre 3 g, Salt 0.4 g.

(a)
How many grams of protein are in 100 g of 'Chicken Curry'?
(b)
What percentage of the 'Chicken Curry' is carbohydrate?
(c)
The mass of the fibre in a whole pack is 9 grams. What is the mass of 'Chicken Curry' in the whole pack?
(d)
What will be the mass of fat in the whole pack?

Question 18

[3 marks]

Mrs Ahmed asked all the children in Year 7 whether they play hockey. Class 7A: 16 play, 26 total. Class 7B: 18 do not play. Overall: 28 do not play, 54 total.

(a)
How many children are there in Class 7B?
(b)
How many children in Class 7A do not play hockey, how many in Class 7B play hockey, and what is the overall number who play?
(c)
What fraction of the children who do not play hockey are in Class 7B?

Question 19

[3 marks]

It is known that 236 × 145 = 34,220. Use this calculation to work out:

(a)
2.36 × 1.45
(b)
34,220 ÷ 2.36
(c)
23.6 × 72.5

Question 20

[5 marks]

In a magic square the sum of the numbers in each row, column and diagonal is the same. Complete the magic square below (it uses each of the numbers 1 to 16 once).

151412679811532
Fill in the five missing numbers.

Question 21

[2 marks]

Nasreen buys a box containing a selection of three types of biscuit. There are 10 chocolate biscuits. A third of the other biscuits are shortbread. There are 16 jaffa cakes.

(a)
How many shortbread biscuits are there?
(b)
How many biscuits are in the box altogether?

Question 22

[1 marks]

In a box of shapes there are 4 times as many hearts as stars, and 3 times as many moons as hearts. If there are 60 hearts, how many shapes are there altogether?

Question 23

[1 marks]

Which bus takes the shortest time from Denby to Fairfield, and by how many minutes? Bus X: departs 9:15, arrives 10:42. Bus Y: departs 9:50, arrives 11:05.

Question 24

[1 marks]

Nadia's marks on five mental arithmetic tests are: 14, 17, 11, 16, 22. What is her mean (average) mark?

Question 25

[1 marks]

A number line runs from 30 to 34, split into 20 equal small divisions (each worth 0.2). An arrow points to the 7th small division after the 31 mark. What number is the arrow pointing to?

Question 26

[1 marks]

A parallelogram (which is not a rectangle) has area 12 cm² and a base of 4 cm. What is its perpendicular height?

cm

Question 27

[1 marks]

Which is more likely: rolling a multiple of 3 with a fair six-sided die, or drawing a heart from a standard 52-card deck?

Question 28

[2 marks]

A shape has vertices at (2,1), (5,1), (5,3), (3,3), (3,5) and (2,5). Reflect it in the line y = x. Give the reflected coordinates.

Question 29

[2 marks]

In a long jump competition, the distances jumped were: Grace 1.85 m, Holly 1.5 m, Ivy 0.7 m, Jade 1.65 m, Kira 1.15 m.

(a)
By how many centimetres did Grace jump further than Ivy?
(b)
What is the mean distance jumped, in metres?

Question 30

[4 marks]

Penny places 5p coins, touching, in a straight line. She hopes to make a line of coins measuring 500 metres. A 5p coin has a diameter of 20 mm.

(a)
How long, in metres, is a line of 25 coins?
(b)
What is the total value, in pounds, of 25 coins?
(c)
How many coins will Penny need for a 500 metre line?
(d)
What is the total value of a 500 metre line of coins?

Question 31

[2 marks]

Zara was born on 14 March 2005 and her mother, Farah, was born on the same date 24 years earlier.

(a)
What is Zara's age, on 1st January, in 2017?
(b)
In which year, on 1st January, will Farah's age be three times Zara's age?

Question 32

[2 marks]

Six girls took a maths test. Their marks were: 19, 21, 12, 7, 15, 21. Zoe's mark was 8 more than Yara's mark and 6 less than Wren's mark.

(a)
What is the difference between the highest and lowest marks?
(b)
What was Zoe's mark?

Question 33

[3 marks]

Leah checks the time when she sets off on her journey to school: her clock's hour hand points exactly halfway between 7 and 8, and its minute hand points exactly at the 6.

(a)
Write the time as a 12-hour time.
(b)
At twenty-five minutes past eight, Leah stops to buy a snack. Write 'twenty-five minutes past eight' as a 12-hour clock time.
(c)
Leah spends 8 minutes at the shop before walking another 19 minutes to school. At what time does she reach school?

Question 34

[4 marks]

The diagram shows information about girls in Year 7 who play netball and/or hockey: netball & hockey: 10, netball & not hockey: 8, not netball & hockey: 6, not netball & not hockey: 6.

(a)
How many girls are in Year 7?
(b)
How many girls play both sports?
(c)
What percentage of the girls play hockey but not netball?
(d)
What fraction of the girls who play netball also play hockey?

Question 35

[1 marks]

The diagram shows two squares: a larger square with perimeter 24 cm, and a smaller square drawn inside it by joining the midpoints of its sides. What is the area of the smaller square?

cm²

Question 36

[2 marks]

Bertie the Bee flies in straight lines from P, 12 cm to Q, and then from Q to R, which is 12 cm due south of P.

(a)
In which direction does Bertie fly to get from Q to R?
(b)
Bertie then flies from R back to P. Estimate the total distance that Bertie flies.

Question 37

[2 marks]

A matchbox measures 2 cm high, 3 cm wide and 6 cm long.

(a)
What is the maximum number of matchboxes that could fit, in one layer, onto a tray that is 24 cm long and 18 cm wide?
(b)
What is the maximum number of matchboxes that could be fitted into a storage box measuring 24 cm by 18 cm by 20 cm?

Question 38

[1 marks]

A rhombus is drawn on a grid with vertices at (2,5), (5,9), (8,5) and (5,1). Three points are listed: X (5,2), Y (5,10), Z (3,4). Write the letter names of the points that lie inside the rhombus.

Question 39

[1 marks]

To convert ounces and pounds to kilograms: 16 ounces = 1 pound, 2.2 pounds = 1 kg. A newborn panda cub weighs about 40 ounces. Which of these gives the best approximation of its mass in kilograms: 0.5 kg, 1 kg, 1.5 kg, 2 kg, 2.5 kg, or 3 kg?

Question 40

[5 marks]

A sequence of patterns is made from small squares arranged in a bigger square. Pattern n has n² small squares, perimeter 4n, and (n+1)² dots.

Pattern number1234
Number of small squares14??
Perimeter (cm)48??
Number of dots49??
(a)
How many small squares are in Pattern 5?
(b)
Complete the table.
(c)
How many small squares are there in Pattern 7?
(d)
What is the perimeter of Pattern 12?
(e)
Which pattern has 100 dots?

Question 41

[2 marks]

Two icebergs, X and Y, are floating in the ocean. On 1 January, iceberg X weighs 5 tonnes (5000 kg) but loses 40 kg every day.

(a)
After how many days will iceberg X weigh 4600 kg?
(b)
On 1 January, iceberg Y weighs 5600 kg and loses 70 kg every day. After how many days will the two icebergs have the same mass?

Question 42

[3 marks]

In a tower of bricks, the number on a brick is found from the two bricks supporting it.

(a)
If each brick is the SUM of the two below it, and the bottom row is 5, 3, 2, 4, what number is on the top brick?
(b)
If each brick is instead the PRODUCT of the two below it, and the bottom row is 5, 3, 2, 4, what number is on the top brick?
(c)
In a product-tower with 3 rows (bottom row of 3 bricks, then 2, then 1), the top brick is 48 and all the numbers in the tower are different whole numbers. What number is on the middle brick of the bottom row?

Question 43

[3 marks]

A number machine works to the rule 'cube each digit and then add the cubes together'. For example, input 25 gives output 133 (2³ + 5³ = 8 + 125 = 133).

(a)
Work out the output for input 34.
(b)
What is the smallest three-digit input that would give output 2?
(c)
Input 407 gives output 407. Which two numbers between 300 and 400 also have this property (their output equals their input)?

Question 44

[4 marks]

Nadia has three spinners, X, Y and Z, each with 4 sections.

(a)
Spinner X: however many times it is spun and the scores added, you always get an even total. Write a different number (choosing from 1 to 9) in each of its 4 sections.
(b)
Spinner Y: the result is always a prime number. Write a different number (choosing from 1 to 9) in each section.
(c)
Spinner Z: there is an equal chance of getting a cube number or a multiple of 3. Write a different number (choosing from 1 to 8) in each section.
(d)
If each spinner is spun 100 times and the 100 scores added, which spinner is likely to score the highest total, and why?

Question 45

[4 marks]

A bird has 2 legs, a cat has 4 legs, an insect has 6 legs, and a spider has 8 legs. Priya looks at some animals and counts all their legs — she counts 50 legs. There are 3 times as many birds as spiders, and 3 times as many cats as insects.

Birds
Cats
Insects
Spiders

Question 46

[6 marks]

Tia adds three consecutive prime numbers: 5 + 7 + 11 = 23. She notices the sum of three consecutive primes often gives another prime number.

(a)(i)
17 + 19 + 23 = ?
(a)(ii)
Which three consecutive primes sum to 71?
(a)(iii)
Which three consecutive primes sum to 83?
(b)
Which two groups of three consecutive prime numbers, between 10 and 50, have a sum which is NOT prime?