Mixed Problem-Solving Paper A - Worksheets, Questions and Revision

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11+ · GL ASSESSMENT

EP.M57 Mixed Problem-Solving Paper A

GL ASSESSMENT GL-11PLUS-MATHS · Calculators not allowed · about 75 minutes

Total Marks

Name: _______________________________ Date: ____ / ____ / ______

Answer ALL questions. Show all your working.

A baker makes 15 trays of cupcakes. Each tray holds 12 cupcakes. She sells 134 cupcakes on Saturday. How many cupcakes are left unsold?

(Total for Question 1 is 2 marks)

Write down a number that is a multiple of both 6 and 8, and is less than 50.

(Total for Question 2 is 2 marks)

Sana has a bag of 40 marbles. She gives away 3/5 of the marbles to her cousins. How many marbles does she give away?

(Total for Question 3 is 2 marks)

A coach leaves the school car park at 08:38. The journey to a theme park takes 1 hour 47 minutes. At what time does the coach arrive?

(Total for Question 4 is 2 marks)

A rectangular field is 34 m long and 19 m wide. Find the perimeter of the field.

(Total for Question 5 is 2 marks)

Four friends kept a record of how many books they read over the summer holidays. Freya read 12 books, Ibrahim read 9 books and Priya read 15 books. Altogether, the four friends read 44 books. In September, Callum then read 3 more books, adding to his summer total. How many books had Callum read in total by the end of September?

(Total for Question 6 is 3 marks)

Two market stalls, Stall A and Stall B, split the cost of hiring a delivery van in the ratio 5:2. The total hire cost is 84 pounds. How much more does Stall A pay than Stall B?

(Total for Question 7 is 3 marks)

Deepa buys 4 keyrings at 1.65 pounds each and a birthday card for 2.30 pounds. She pays with a 10 pound note. How much change does she receive?

(Total for Question 8 is 3 marks)

Write these fractions in order, starting with the smallest: 2/3, 5/8, 7/12

(Total for Question 9 is 2 marks)

A bag of flour weighs 1.35 kg. A bag of sugar weighs 620 g. What is the total mass of both bags, in kilograms?

(Total for Question 10 is 2 marks)

A play area is made from a rectangle 10 m by 6 m, with a triangular section added along one of the 6 m sides. The triangle has the same 6 m base and a height of 4 m. Find the total area of the play area.

(Total for Question 11 is 3 marks)

The temperatures recorded at midday on five days in March were: 9C, 13C, 6C, 11C, 13C.

(a)Find the range of the temperatures.(2)

(b)Find the median temperature.(2)

(Total for Question 12 is 4 marks)

A machine in a factory produces 18 identical boxes in 3 minutes, working at a constant rate. How many boxes does it produce in 11 minutes?

(Total for Question 13 is 3 marks)

A minibus can carry 17 passengers. 130 people need to travel to a museum. What is the smallest number of minibuses needed to carry everyone?

(Total for Question 14 is 3 marks)

Ellie uses 1/4 of a length of rope to tie a parcel. Ravi uses 2/5 of the same rope to tie a different parcel. What fraction of the rope is left over?

(Total for Question 15 is 3 marks)

A cyclist travels 45 km in 2 hours 30 minutes at a constant speed.

(a)Find the cyclist's average speed, in km/h.(2)

(b)At this speed, how far would the cyclist travel in 40 minutes?(2)

(Total for Question 16 is 4 marks)

In triangle ABC, angle A = 54 degrees and angle B is twice the size of angle C. Find the size of angle C.

(Total for Question 17 is 3 marks)

A pie chart shows how 180 students at a school travel to school each morning. The sector for 'Walk' has an angle of 120 degrees. How many students walk to school?

(Total for Question 18 is 3 marks)

At a sports centre car park, the ratio of staff cars to visitor cars is 3:2, and the ratio of visitor cars to disabled-bay cars is 4:1. There are 110 cars in the car park altogether. How many disabled-bay cars are there?

(Total for Question 19 is 3 marks)

Olivia buys a pair of trainers costing 85 pounds. In a sale it is reduced by 20%. What is the sale price?

(Total for Question 20 is 3 marks)

A length of garden wire is 13 metres long. Femi cuts it into pieces that are each 3/4 metre long. How many complete pieces can he cut, and how much wire is left over?

(Total for Question 21 is 4 marks)

A rectangular lawn measures 12 m by 7.3 m. Turf is sold only in whole square metres, and enough must be bought to cover the whole lawn. Turf costs 4.50 pounds per square metre. What is the total cost of turfing the lawn?

(Total for Question 22 is 4 marks)

A closed cuboid box has length 15 cm, width 8 cm and height 6 cm.

(a)Find the volume of the box.(2)

(b)A shop assistant says the box can be exactly filled with cubes of side 2 cm, with no gaps and no cubes overlapping the edges. Is the shop assistant correct? Give a reason for your answer.(2)

(Total for Question 23 is 4 marks)

A box of raffle tickets contains 12 yellow tickets, 9 pink tickets and 3 orange tickets, and no others. One ticket is drawn at random. What is the probability that it is pink?

(Total for Question 24 is 3 marks)

Three consecutive whole numbers add up to 84. What is the largest of the three numbers?

(Total for Question 25 is 3 marks)

A school bake sale raises money from three types of cakes: cupcakes, brownies and flapjacks. Cupcakes and brownies were sold in the ratio 5:4. The number of brownies sold was 3/5 of the number of flapjacks sold. Altogether, 141 cakes were sold. How many of each type of cake were sold?

(Total for Question 26 is 5 marks)

Mark scheme · EP.M57 Mixed Problem-Solving Paper A

Question 1

M1 15 x 12 = 180 (or equivalent complete method)
A1 46 cao
Answer: 46 cupcakes

Question 2

M1 lists multiples of 6 and/or 8, or identifies the lowest common multiple (24)
A1 24 or 48 oe
Answer: 24 (or 48)

Question 3

M1 40 / 5 = 8 (finds one fifth)
A1 24 cao
Answer: 24 marbles

Question 4

M1 adds 1 hour to reach 09:38, or converts to a total of 107 minutes added
A1 10:25 (accept 10.25 am / 10:25 am) cao
Answer: 10:25

Question 5

M1 34 + 19 = 53, or 2 x 34 + 2 x 19
A1 106 m cao
Answer: 106 m

Question 6

M1 12 + 9 + 15 = 36
M1 44 - 36 = 8 (Callum's summer total)
A1 11 cao, from 8 + 3
Answer: 11 books

Question 7

M1 84 / 7 = 12 (finds the value of one part)
M1 5 x 12 = 60 and 2 x 12 = 24 (or 3 x 12 for the difference directly)
A1 36 pounds cao
Answer: £36

Question 8

M1 4 x 1.65 = 6.60
M1 6.60 + 2.30 = 8.90
A1 1.10 pounds cao
Answer: £1.10

Question 9

M1 converts all three fractions to a common denominator of 24 (16/24, 15/24, 14/24), or uses an equivalent correct comparison method
A1 7/12, 5/8, 2/3 cao (correct order)
Answer: 7/12, 5/8, 2/3

Question 10

M1 1.35 kg = 1350 g (or 620 g = 0.62 kg)
A1 1.97 kg cao
Answer: 1.97 kg

Question 11

M1 10 x 6 = 60 (rectangle area)
M1 0.5 x 6 x 4 = 12 (triangle area)
A1 72 m² cao
Answer: 72 m²

Question 12

(a) M1 identifies the highest (13C) and lowest (6C) values
(a) A1 7C cao
(a) Answer: 7C
(b) M1 orders the values correctly: 6, 9, 11, 13, 13
(b) A1 11C cao
(b) Answer: 11C

Question 13

M1 18 / 3 = 6 (boxes per minute)
M1 6 x 11 (complete correct method)
A1 66 cao
Answer: 66 boxes

Question 14

M1 attempts 130 / 17, e.g. 17 x 7 = 119
dM1 identifies a remainder of 11 people (130 - 119), who still need transport
A1 8 cao
Answer: 8 minibuses

Question 15

M1 converts to a common denominator: 1/4 = 5/20 and 2/5 = 8/20
M1 5/20 + 8/20 = 13/20 (total rope used)
A1 7/20 cao
Answer: 7/20

Question 16

(a) M1 2 hours 30 minutes = 2.5 hours
(a) A1 18 km/h cao
(a) Answer: 18 km/h
(b) M1 40 minutes = 2/3 hour (or equivalent, e.g. 18/60 x 40)
(b) A1 12 km cao, ft their speed from (a)
(b) Answer: 12 km

Question 17

M1 180 - 54 = 126 (sum of angles B and C)
M1 sets up 2C + C = 126, i.e. 3C = 126
A1 42 degrees cao
Answer: 42 degrees

Question 18

M1 120/360 simplified to 1/3, or equivalent
M1 180 x 120/360 (complete correct method)
A1 60 cao
Answer: 60 students

Question 19

M1 combines the ratios using a common value for visitor cars: staff:visitor:disabled = 6:4:1
M1 6 + 4 + 1 = 11 parts; 110 / 11 = 10
A1 10 cao
Answer: 10 disabled-bay cars

Question 20

M1 10% of 85 = 8.50
M1 20% of 85 = 17 (doubles 10%, or uses 85 x 0.2)
A1 68 pounds cao
Answer: £68

Question 21

M1 13 / (3/4) = 13 x 4/3 = 52/3, or equivalent method
M1 identifies 17 as the greatest whole number of pieces (since 52/3 = 17 and 1/3)
A1 17 pieces cao
A1 0.25 m (1/4 m) left over cao
Answer: 17 pieces, with 0.25 m (1/4 m) left over

Question 22

M1 12 x 7.3 = 87.6 (area of the lawn)
M1 rounds up to 88 square metres, since the whole lawn must be covered
M1 88 x 4.50 (complete correct method)
A1 396 pounds cao
Answer: £396

Question 23

(a) M1 15 x 8 = 120 (or another correct pairing of two dimensions)
(a) A1 720 cm³ cao
(a) Answer: 720 cm³
(b) B1 states 'No' (the shop assistant is not correct)
(b) B1 correct reason: 15 is not divisible by 2 (15 / 2 = 7.5, not a whole number), so whole 2 cm cubes cannot exactly fill the length oe
(b) Answer: No; 15 is not a multiple of 2, so the length cannot be exactly filled by whole 2 cm cubes

Question 24

M1 12 + 9 + 3 = 24 (total number of tickets)
M1 9/24 identified as the probability before simplifying
A1 3/8 oe (accept 0.375 or 37.5%) cao
Answer: 3/8

Question 25

M1 84 / 3 = 28 (or forms 3n + 3 = 84)
M1 identifies the three numbers as 27, 28, 29
A1 29 cao
Answer: 29

Question 26

M1 sets cupcakes = 5k and brownies = 4k, from the ratio 5:4
M1 forms flapjacks = 4k x 5/3 = 20k/3, from brownies = 3/5 of flapjacks
dM1 recognises k must be a multiple of 3 for whole numbers of cakes, and rewrites as cupcakes = 15m, brownies = 12m, flapjacks = 20m
dM1 forms 15m + 12m + 20m = 141, i.e. 47m = 141, so m = 3
A1 cupcakes = 45, brownies = 36, flapjacks = 60, all three correct cao
Answer: 45 cupcakes, 36 brownies, 60 flapjacks

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