Nadia buys a notebook for 2.75 pounds and a rubber for 0.60 pounds. She pays with a 5 pound note. How much change does she receive?
(Total for Question 1 is 2 marks)
2
A box contains 96 crayons. 3/8 of the crayons are broken. How many crayons are not broken?
(Total for Question 2 is 2 marks)
3
A swimming gala starts at 13:15 and finishes at 15:52. How long, in minutes, does the gala last?
(Total for Question 3 is 2 marks)
4
A rectangular allotment plot measures 26 m by 11 m. Find the perimeter of the plot.
(Total for Question 4 is 2 marks)
5
A sack of potatoes weighs 3.4 kg. A sack of carrots weighs 950 g. What is the total mass of both sacks, in kilograms?
(Total for Question 5 is 2 marks)
6
Find the mean of these six numbers: 4, 9, 7, 12, 10, 6
(Total for Question 6 is 2 marks)
7
The nth term of a sequence is given by 3n2 - 5. Find the 4th term of the sequence.
(Total for Question 7 is 2 marks)
8
Write these fractions in order, starting with the smallest: 3/4, 5/6, 7/9
(Total for Question 8 is 2 marks)
9
Three friends, Kwame, Layla and Rhys, share the cost of a party in the ratio 4:5:6. The total cost is 135 pounds. How much does Layla pay?
(Total for Question 9 is 3 marks)
10
Esme buys 3 identical magazines at 1.85 pounds each and a poster for 4.10 pounds. She pays with a 20 pound note. How much change does she receive?
(Total for Question 10 is 3 marks)
11
A patio is made up of two rectangular sections. The first section measures 7 m by 5 m and the second section measures 3 m by 2 m. Find the total area of the patio.
(Total for Question 11 is 3 marks)
12
A machine fills 32 identical bottles in 4 minutes, working at a constant rate. How many bottles does it fill in 15 minutes?
(Total for Question 12 is 3 marks)
13
Tariq paints 3/10 of a fence on Saturday and 2/5 of the fence on Sunday. What fraction of the fence is still unpainted?
(Total for Question 13 is 3 marks)
14
A pie chart shows how 252 visitors arrived at a museum. The sector for 'By car' has an angle of 100 degrees. How many visitors arrived by car?
(Total for Question 14 is 3 marks)
15
In 7 matches, a hockey team scored the following numbers of goals: 2, 3, 2, 4, 2, 5, 1.
(a)Find the range of the number of goals scored.(2)
(b)Find the mode of the number of goals scored.(2)
(Total for Question 15 is 4 marks)
16
A ferry travels 54 km in 3 hours at a constant speed.
(a)Find the ferry's average speed, in km/h.(2)
(b)At this speed, how long would it take the ferry to travel 30 km? Give your answer in minutes.(2)
(Total for Question 16 is 4 marks)
17
A youth club needs to transport 142 members to a residential trip. Each minibus seats 16 people. What is the smallest number of minibuses needed to carry everyone?
(Total for Question 17 is 3 marks)
18
The exterior angle at vertex B of triangle ABC is 118 degrees. Angle A = 61 degrees. Find the size of angle C.
(Total for Question 18 is 3 marks)
19
A fruit squash is made by mixing water, orange concentrate and lime concentrate in the ratio 8:3:1. A jug contains 480 ml of the squash in total. How much orange concentrate is in the jug?
(Total for Question 19 is 3 marks)
20
A shop increases the price of a bicycle by 25%. The new price is 275 pounds. Find the original price.
(Total for Question 20 is 3 marks)
21
A rectangular patio measures 6.4 m by 5.3 m. Paving slabs are sold only in packs that each cover 4 square metres, and whole packs must be bought to cover the entire patio. Each pack costs 27 pounds. Calculate the total cost of the paving slabs needed.
(Total for Question 21 is 4 marks)
22
A rectangle has length (3x + 2) cm and width (x - 3) cm. The perimeter of the rectangle is 46 cm. Find the value of x.
(Total for Question 22 is 4 marks)
23
A drawer contains 5 black socks and 3 white socks, and no other socks. Two socks are taken from the drawer at random, one after the other, without replacement. Work out the probability that both socks are black.
(Total for Question 23 is 4 marks)
24
The ratio of Rohan's age to his father's age is 2:7. In 3 years' time, the ratio of their ages will be 1:3. Find Rohan's present age.
(Total for Question 24 is 4 marks)
25
A market trader buys 8 crates of oranges. Each crate contains 60 oranges and costs the trader 15 pounds. She sells the oranges in bags of 4 for 2.20 pounds per bag, and sells every orange. Work out her total profit.
(Total for Question 25 is 5 marks)
26
Three cousins, Aaliyah, Jayden and Poppy, have ages this year in the ratio 2:3:7. In 6 years' time, the sum of their three ages will be 54.
(a)Find their three ages this year.(3)
(b)In how many years' time will Poppy's age be exactly double Aaliyah's age?(3)
(Total for Question 26 is 6 marks)
Mark scheme · EP.M74 Mixed Problem-Solving Paper E
Question 1
M1 2.75 + 0.60 = 3.35 (total spent)
A1 1.65 pounds cao
Answer: £1.65
Question 2
M1 96 / 8 = 12 (finds one eighth)
A1 60 cao
Answer: 60 crayons
Question 3
M1 13:15 to 15:15 = 2 hours (120 minutes), then adds the remaining 37 minutes to 15:52
A1 157 minutes cao
Answer: 157 minutes
Question 4
M1 26 + 11 = 37, or 2 x 26 + 2 x 11
A1 74 m cao
Answer: 74 m
Question 5
M1 3.4 kg = 3400 g (or 950 g = 0.95 kg)
A1 4.35 kg cao
Answer: 4.35 kg
Question 6
M1 4 + 9 + 7 + 12 + 10 + 6 = 48
A1 8 cao
Answer: 8
Question 7
M1 42 = 16, then 3 x 16 = 48
A1 43 cao
Answer: 43
Question 8
M1 converts all three fractions to a common denominator of 36 (27/36, 30/36, 28/36), or uses an equivalent correct comparison method
A1 3/4, 7/9, 5/6 cao (correct order)
Answer: 3/4, 7/9, 5/6
Question 9
M1 4 + 5 + 6 = 15 parts; 135 / 15 = 9 (finds the value of one part)
M1 5 x 9 (complete correct method for Layla's share)
A1 45 pounds cao
Answer: £45
Question 10
M1 3 x 1.85 = 5.55
M1 5.55 + 4.10 = 9.65
A1 10.35 pounds cao
Answer: £10.35
Question 11
M1 7 x 5 = 35 (area of the first section)
M1 3 x 2 = 6 (area of the second section)
A1 41 m2 cao
Answer: 41 m2
Question 12
M1 32 / 4 = 8 (bottles per minute)
M1 8 x 15 (complete correct method)
A1 120 cao
Answer: 120 bottles
Question 13
M1 converts to a common denominator: 3/10 stays as 3/10 and 2/5 = 4/10
M1 3/10 + 4/10 = 7/10 (total fraction painted)
A1 3/10 cao
Answer: 3/10
Question 14
M1 100/360 simplified to 5/18, or equivalent
M1 252 x 100/360 (complete correct method)
A1 70 cao
Answer: 70 visitors
Question 15
(a) M1 identifies the highest (5) and lowest (1) values
(a) A1 4 cao
(a) Answer: 4
(b) M1 identifies that 2 occurs most often (three times)
(b) A1 2 cao
(b) Answer: 2 goals
Question 16
(a) M1 54 / 3 (complete correct method)
(a) A1 18 km/h cao
(a) Answer: 18 km/h
(b) M1 30 / 18 = 5/3 hours (or equivalent, e.g. finds time per km then multiplies by 30)
(b) A1 100 minutes cao, ft their speed from (a)
(b) Answer: 100 minutes
Question 17
M1 attempts 142 / 16, e.g. 16 x 8 = 128
dM1 identifies a remainder of 14 people (142 - 128), who still need transport
A1 9 cao
Answer: 9 minibuses
Question 18
M1 uses the exterior angle theorem: angle A + angle C = 118 (or finds interior angle B = 180 - 118 = 62)
M1 substitutes angle A = 61 into the equation
A1 57 degrees cao
Answer: 57 degrees
Question 19
M1 8 + 3 + 1 = 12 parts; 480 / 12 = 40 (finds the value of one part)
M1 3 x 40 (complete correct method)
A1 120 ml cao
Answer: 120 ml
Question 20
M1 recognises the new price is 125% (or 1.25 x) of the original price
M1 275 / 1.25 (complete correct method)
A1 220 pounds cao
Answer: £220
Question 21
M1 6.4 x 5.3 = 33.92 (area of the patio)
M1 33.92 / 4 = 8.48, rounds up to 9 packs since whole packs must be bought to cover the entire patio
M1 9 x 27 (complete correct method)
A1 243 pounds cao
Answer: £243
Question 22
M1 sets up 2 x [(3x + 2) + (x - 3)] = 46, or equivalent
M1 simplifies to 8x - 2 = 46
M1 solves 8x = 48
A1 6 cao
Answer: x = 6
Question 23
M1 P(first sock is black) = 5/8
M1 P(second sock is black, given the first was black) = 4/7
M1 multiplies 5/8 x 4/7 = 20/56
A1 5/14 oe (accept 20/56) cao
Answer: 5/14
Question 24
M1 sets Rohan's age = 2x and his father's age = 7x now, from the ratio 2:7
M1 forms the equation (2x + 3)/(7x + 3) = 1/3, i.e. 3(2x + 3) = 7x + 3
M1 solves 6x + 9 = 7x + 3 to give x = 6
A1 12 cao
Answer: 12 years old
Question 25
M1 8 x 60 = 480 (total number of oranges)
M1 8 x 15 = 120 (total cost)
M1 480 / 4 = 120 (number of bags sold)
M1 120 x 2.20 = 264 (total revenue)
A1 144 pounds cao
Answer: £144
Question 26
(a) M1 2 + 3 + 7 = 12 parts; forms 12x + 18 = 54 (adding 6 years to each of the three ages)
(a) M1 solves 12x = 36 to give x = 3
(a) A1 Aaliyah = 6, Jayden = 9, Poppy = 21, all three correct cao
(a) Answer: Aaliyah 6, Jayden 9, Poppy 21
(b) M1 sets up the equation 21 + n = 2(6 + n), using Poppy's and Aaliyah's ages in n years' time