Amara buys a notebook for £2.35 and a pencil case for £1.20. She pays with a £5 note. How much change does she get?
A) £1.35
B) £1.45
C) £1.55
D) £2.65
E) £3.80
(Total for Question 1 is 1 mark)
2
A piece of ribbon is 3.6 m long. Priya cuts it into pieces that are each 40 cm long. How many complete pieces can she cut?
(Total for Question 2 is 1 mark)
3
On 14/03, a coach carrying Year 6 pupils leaves the school at 09:45 for a trip to a science museum. The journey takes 1 hour 50 minutes. What time does the coach arrive at the museum?
A) 10:35
B) 11:15
C) 11:25
D) 11:35
E) 12:35
(Total for Question 3 is 1 mark)
4
Nadia has a fruit bowl at home. The ratio of apples to oranges in the bowl is 3:2. There are 12 apples in the bowl. How many oranges are there?
(Total for Question 4 is 1 mark)
5
Find the mean of these five numbers: 3, 5, 7, 9, 16.
A) 7
B) 8
C) 9
D) 10
E) 16
(Total for Question 5 is 1 mark)
6
Kwame buys 3 identical footballs. Each football costs £8.75. He pays with two £20 notes. How much change does he receive?
(Total for Question 6 is 2 marks)
7
A rectangular school garden is 9.5 m long and 6 m wide. What is the perimeter of the garden, in metres?
A) 15.5 m
B) 29 m
C) 30 m
D) 31 m
E) 57 m
(Total for Question 7 is 2 marks)
8
A cinema showing starts at 14:20 and finishes at 16:05. The film itself lasts 1 hour 35 minutes. How many minutes of adverts and trailers are shown before the film starts?
(Total for Question 8 is 2 marks)
9
Three friends, Ffion, Rhys and Nia, share a prize of £72 in the ratio 4:3:2. How much does Rhys receive?
A) £16
B) £24
C) £32
D) £36
E) £8
(Total for Question 9 is 2 marks)
10
A pancake recipe for 4 people needs 200 g of flour. Sanjay is cooking pancakes for 10 people. How much flour does he need, in grams?
(Total for Question 10 is 2 marks)
11
Grace scored 6, 8, 7 and 9 marks out of 10 in four spelling tests. What must she score in her fifth test so that her mean score across all five tests is 8?
A) 8
B) 9
C) 10
D) 11
E) 12
(Total for Question 11 is 2 marks)
12
Divya is 3 times as old as her brother Callum. In 4 years' time, Divya will be 25. How old is Callum now?
(Total for Question 12 is 2 marks)
13
Yasmin is comparing two bottles of juice in a shop: a 750 ml bottle for £1.80, and a 1.2 litre bottle for £2.64. Which bottle offers better value for money, and what is its price per 100 ml?
A) 750 ml bottle at 20p per 100 ml
B) 750 ml bottle at 24p per 100 ml
C) 1.2 litre bottle at 22p per 100 ml
D) 1.2 litre bottle at 24p per 100 ml
E) Both are the same value, at 22p per 100 ml
(Total for Question 13 is 2 marks)
14
A recipe needs 1.25 kg of flour. Osei has three bags of flour, each weighing 400 g. Does he have enough flour, and by how many grams is he short or over?
(Total for Question 14 is 2 marks)
15
A ferry timetable shows departures every 35 minutes, starting at 08:15. What is the departure time of the 5th ferry of the day?
A) 09:50
B) 10:00
C) 10:25
D) 10:35
E) 11:10
(Total for Question 15 is 2 marks)
16
On a map, a scale of 1:25000 is used. Two towns are 8 cm apart on the map. What is the real distance between the towns, in kilometres?
(Total for Question 16 is 2 marks)
17
Zainab cycles at a steady speed of 15 km/h to visit a friend. How far does she travel in 40 minutes?
A) 6 km
B) 8 km
C) 9 km
D) 10 km
E) 12 km
(Total for Question 17 is 2 marks)
18
The mean age of 6 members of a chess club is 13 years. One new member, Harjit, joins the club, and the mean age of all 7 members becomes 14 years. How old is Harjit?
(Total for Question 18 is 2 marks)
19
Tariq thinks of a number. He doubles it, then adds 7, and the result is 29. What number did Tariq think of?
A) 9
B) 10
C) 11
D) 18
E) 22
(Total for Question 19 is 2 marks)
20
Meera is saving for a bike that costs £145. She has already saved £58, and she saves £12 more from her pocket money each week.
(a)How much more money does Meera need to save?(1)
(b)How many full weeks will it take her to save enough money for the bike?(2)
(Total for Question 20 is 3 marks)
21
A charity bake sale raises £150 in total. The money is split between two school classes in the ratio 7:8, and each class then divides its own share equally among 5 local charities. How much does each charity in the class with the larger share receive?
A) £10
B) £14
C) £16
D) £20
E) £30
(Total for Question 21 is 2 marks)
22
On 02/08, Amina drives from her home to visit her grandmother, a total distance of 132 km. She leaves home at 10:20 and drives the first 84 km at an average speed of 56 km/h, before stopping for a 15 minute break.
(a)At what time does Amina finish the first 84 km of the journey, before her break?(1)
(b)She then drives the remaining distance at an average speed of 48 km/h. At what time does she arrive at her grandmother's house?(2)
(Total for Question 22 is 3 marks)
23
A school orders 240 revision guides. 3/8 of the guides are for maths, 1/3 are for english, and the rest are for science. How many more maths guides are ordered than science guides?
A) 10
B) 20
C) 30
D) 40
E) 70
(Total for Question 23 is 3 marks)
24
A school hall has 8 rows of chairs, with the same number of chairs in each row. If 3 more chairs were added to each row, the hall would hold 224 chairs in total.
(a)How many chairs are currently in each row?(2)
(b)If instead 2 chairs were removed from each row (from the original number), how many chairs would the hall hold in total?(1)
(Total for Question 24 is 3 marks)
25
Five friends, Declan, Ellie, Kofi, Zara and Yusuf, each contribute money to a joint birthday gift, in the ratio 2:3:3:4:8 respectively. The mean contribution across all five friends is £12. How much did Zara contribute?
A) £3
B) £6
C) £9
D) £12
E) £24
(Total for Question 25 is 3 marks)
Mark scheme · EP.M21 Worded Problems Set A
Question 1
B1 B) £1.45, from £5.00 - £3.55
Answer: B) £1.45
Question 2
B1 9 pieces, with correct conversion 3.6 m = 360 cm shown or implied
Answer: 9 pieces
Question 3
B1 D) 11:35
Answer: D) 11:35
Question 4
B1 8 oranges
Answer: 8 oranges
Question 5
B1 B) 8, from a total of 40 divided by 5 numbers
Answer: B) 8
Question 6
M1 finds total cost 3 x £8.75 = £26.25
A1 £13.75, from £40.00 - £26.25
Answer: £13.75
Question 7
M1 9.5 + 6 = 15.5 (half the perimeter), or equivalent method
A1 D) 31 m
Answer: D) 31 m
Question 8
M1 finds total time slot = 105 minutes (1h45) and film length = 95 minutes (1h35), in consistent units
A1 10 minutes
Answer: 10 minutes
Question 9
M1 total parts = 4 + 3 + 2 = 9, one part = 72 / 9 = £8
A1 B) £24 (3 x £8)
Answer: B) £24
Question 10
M1 finds flour per person = 200 / 4 = 50 g
A1 500 g
Answer: 500 g
Question 11
M1 target total = 8 x 5 = 40; current total = 6 + 8 + 7 + 9 = 30
A1 C) 10 (40 - 30)
Answer: C) 10
Question 12
M1 finds Divya's current age = 25 - 4 = 21
A1 7 years old
Answer: 7 years old
Question 13
M1 finds both unit prices: 750 ml = 24p per 100 ml, 1.2 litre = 22p per 100 ml
A1 C) 1.2 litre bottle at 22p per 100 ml
Answer: C) 1.2 litre bottle at 22p per 100 ml
Question 14
M1 total flour available = 3 x 400 = 1200 g, and 1.25 kg converted to 1250 g
A1 50 g short (not enough), with a correct conclusion
Answer: No, he is 50 g short (he has 1200 g but needs 1250 g).
Question 15
M1 the 5th ferry is 4 intervals after the 1st, so 4 x 35 = 140 minutes after 08:15
A1 D) 10:35
Answer: D) 10:35
Question 16
M1 8 x 25000 = 200000 cm (real distance in cm)
A1 2 km, with correct conversion from cm
Answer: 2 km
Question 17
M1 40 minutes = 2/3 hour
A1 D) 10 km (15 x 2/3)
Answer: D) 10 km
Question 18
M1 finds total age before (6 x 13 = 78) and total age after (7 x 14 = 98)
A1 20 years old
Answer: 20 years old
Question 19
M1 sets up 2x + 7 = 29, or equivalent, and finds 29 - 7 = 22
A1 C) 11 (22 / 2)
Answer: C) 11
Question 20
(a) B1 £87
(a) Answer: £87
(b) M1 87 / 12 = 7.25, or repeated addition/multiplication of 12 up to at least 84
(b) A1 8 weeks, with recognition that 7 weeks (£84) is not enough
(b) Answer: 8 weeks
Question 21
M1 total parts = 15, one part = £10, larger share (8 parts) = £80
A1 C) £16 (£80 / 5 charities)
Answer: C) £16
Question 22
(a) B1 11:50
(a) Answer: 11:50
(b) M1 finds departure time after the break (11:50 + 0:15 = 12:05) and the remaining journey time (48 / 48 = 1 hour)
(b) A1 13:05 (or 1:05 pm)
(b) Answer: 13:05
Question 23
M1 maths = 3/8 x 240 = 90 and english = 1/3 x 240 = 80
M1 science = 240 - 90 - 80 = 70
A1 B) 20 (90 - 70)
Answer: B) 20
Question 24
(a) M1 224 / 8 = 28 (chairs per row if 3 were added to each row)
(a) A1 25 chairs per row
(a) Answer: 25 chairs per row
(b) B1 184 chairs
(b) Answer: 184 chairs
Question 25
M1 total contributed = mean x 5 = 12 x 5 = £60
M1 total ratio parts = 2 + 3 + 3 + 4 + 8 = 20, one part = 60 / 20 = £3