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

26 original exam-style questions - 6 pages of questions with a full mark scheme - free printable PDF.

Download PDF Jump to mark scheme (page 7)Read the revision guide

Next in this strand

Revision Library

revisionlibrary.co.uk

11+ · GL ASSESSMENT

EP.M59 Mixed Problem-Solving Paper B

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

Total Marks

Name: _______________________________ Date: ____ / ____ / ______

Answer ALL questions. Show all your working.

Zoe buys a pencil case for 3.45 pounds and a ruler for 0.85 pounds. She pays with a 10 pound note. How much change does she receive?

(Total for Question 1 is 2 marks)

A box contains 54 sweets. 2/9 of the sweets are toffees. How many toffees are in the box?

(Total for Question 2 is 2 marks)

A train leaves the station at 07:52. The journey to the coast takes 2 hours 19 minutes. At what time does the train arrive?

(Total for Question 3 is 2 marks)

A rectangular allotment measures 22 m by 15 m. Find the perimeter of the allotment.

(Total for Question 4 is 2 marks)

Find the mean of these five numbers: 4, 7, 8, 10, 16

(Total for Question 5 is 2 marks)

Three market traders, Beth, Callan and Deja, share the cost of a stall pitch in the ratio 4:3:2. The total cost is 81 pounds. How much does Callan pay?

(Total for Question 6 is 3 marks)

Idris buys 3 identical notebooks at 2.15 pounds each and a pack of pens for 3.40 pounds. He pays with a 20 pound note. How much change does he receive?

(Total for Question 7 is 3 marks)

Write these fractions in order, starting with the largest: 3/5, 7/10, 5/8

(Total for Question 8 is 2 marks)

A parcel of books weighs 2.15 kg. A parcel of magazines weighs 480 g. What is the total mass of both parcels, in kilograms?

(Total for Question 9 is 2 marks)

A garden is formed from a rectangle 9 m by 6 m, with a right-angled triangular corner removed. The triangle removed has a base of 3 m and a height of 2 m. Find the remaining area of the garden.

(Total for Question 10 is 3 marks)

The rainfall recorded on six days was, in mm: 12, 15, 9, 15, 21, 8.

(a)Find the mode of the rainfall values.(2)

(b)Find the range of the rainfall values.(2)

(Total for Question 11 is 4 marks)

A conveyor belt moves 24 identical parcels every 4 minutes, working at a constant rate. How many parcels does it move in 15 minutes?

(Total for Question 12 is 3 marks)

A coach company must transport 158 passengers to a concert. Each coach seats 23 passengers. What is the smallest number of coaches needed to transport everyone?

(Total for Question 13 is 3 marks)

Farah paints 2/7 of a fence on Monday and 3/8 of the fence on Tuesday. What fraction of the fence is still unpainted?

(Total for Question 14 is 3 marks)

A train travels 84 km in 1 hour 45 minutes at a constant speed.

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

(b)At this speed, how long would it take to travel a further 20 km? Give your answer in minutes.(2)

(Total for Question 15 is 4 marks)

In triangle PQR, angle P = 38 degrees, and angle Q is 16 degrees more than angle R. Find the size of angle Q.

(Total for Question 16 is 3 marks)

A pie chart shows how 216 Year 6 pupils travel to a school trip. The sector for 'Coach' has an angle of 150 degrees. How many pupils travel by coach?

(Total for Question 17 is 3 marks)

A fruit punch is made by mixing orange juice, pineapple juice and lemonade. The ratio of orange juice to pineapple juice is 3:2, and the ratio of pineapple juice to lemonade is 4:5. Altogether, 3 litres of punch is made. How much lemonade is used?

(Total for Question 18 is 3 marks)

A laptop costs 460 pounds. In a sale it is reduced by 15%. What is the sale price?

(Total for Question 19 is 3 marks)

A roll of ribbon is 17 metres long. Nia cuts it into pieces that are each 5/8 metre long. How many complete pieces can she cut, and how much ribbon is left over?

(Total for Question 20 is 4 marks)

A rectangular wall measures 5.5 m by 3.2 m. Tins of paint each cover 4 square metres, and only whole tins can be bought, with enough needed to cover the whole wall. Each tin costs 13.50 pounds. What is the total cost of painting the wall?

(Total for Question 21 is 4 marks)

A closed cuboid water tank has length 1.2 m, width 0.8 m and height 0.5 m.

(a)Find the volume of the tank, in cubic metres.(2)

(b)1 cubic metre = 1000 litres. The tank is filled using a hose that delivers water at 15 litres per minute. How long does it take to fill the tank completely?(2)

(Total for Question 22 is 4 marks)

A box contains 8 red pens, 5 blue pens and 7 black pens, and no others. One pen is drawn at random. What is the probability that it is NOT black?

(Total for Question 23 is 3 marks)

Three consecutive odd numbers add up to 87. What is the smallest of the three numbers?

(Total for Question 24 is 3 marks)

A school fun run raises money from entry fees, a raffle and a cake stall. Entry fees and raffle money were collected in the ratio 7:3. The raffle money raised was 2/5 of the amount raised by the cake stall. Altogether, entry fees, raffle and cake stall raised 525 pounds. How much did each raise?

(Total for Question 25 is 5 marks)

A rectangular lawn is twice as long as it is wide. A path of width 1 m is built all the way around the outside of the lawn, so that the lawn and path together form a larger rectangle. The area of the path alone is 40 m². Find the dimensions of the original lawn.

(Total for Question 26 is 5 marks)

Mark scheme · EP.M59 Mixed Problem-Solving Paper B

Question 1

M1 3.45 + 0.85 = 4.30
A1 5.70 pounds cao
Answer: £5.70

Question 2

M1 54 / 9 = 6 (finds one ninth)
A1 12 cao
Answer: 12 toffees

Question 3

M1 adds 2 hours to reach 09:52, or converts to a total of 139 minutes added
A1 10:11 (accept 10.11 am / 10:11 am) cao
Answer: 10:11

Question 4

M1 22 + 15 = 37, or 2 x 22 + 2 x 15
A1 74 m cao
Answer: 74 m

Question 5

M1 4 + 7 + 8 + 10 + 16 = 45
A1 9 cao
Answer: 9

Question 6

M1 4 + 3 + 2 = 9 parts; 81 / 9 = 9 (finds the value of one part)
M1 3 x 9 (complete correct method for Callan's share)
A1 27 pounds cao
Answer: £27

Question 7

M1 3 x 2.15 = 6.45
M1 6.45 + 3.40 = 9.85
A1 10.15 pounds cao
Answer: £10.15

Question 8

M1 converts all three fractions to a common denominator of 40 (24/40, 28/40, 25/40), or uses an equivalent correct comparison method
A1 7/10, 5/8, 3/5 cao (correct order)
Answer: 7/10, 5/8, 3/5

Question 9

M1 2.15 kg = 2150 g (or 480 g = 0.48 kg)
A1 2.63 kg cao
Answer: 2.63 kg

Question 10

M1 9 x 6 = 54 (rectangle area)
M1 0.5 x 3 x 2 = 3 (triangle area removed)
A1 51 m² cao
Answer: 51 m²

Question 11

(a) M1 identifies that 15 occurs twice, more often than any other value
(a) A1 15 mm cao
(a) Answer: 15 mm
(b) M1 identifies the highest (21 mm) and lowest (8 mm) values
(b) A1 13 mm cao
(b) Answer: 13 mm

Question 12

M1 24 / 4 = 6 (parcels per minute)
M1 6 x 15 (complete correct method)
A1 90 cao
Answer: 90 parcels

Question 13

M1 attempts 158 / 23, e.g. 23 x 6 = 138
dM1 identifies a remainder of 20 passengers (158 - 138), who still need transport
A1 7 cao
Answer: 7 coaches

Question 14

M1 converts to a common denominator: 2/7 = 16/56 and 3/8 = 21/56
M1 16/56 + 21/56 = 37/56 (total fraction painted)
A1 19/56 cao
Answer: 19/56

Question 15

(a) M1 1 hour 45 minutes = 1.75 hours
(a) A1 48 km/h cao
(a) Answer: 48 km/h
(b) M1 48 km/h = 0.8 km per minute (or equivalent, e.g. 20/48 hours)
(b) A1 25 minutes cao, ft their speed from (a)
(b) Answer: 25 minutes

Question 16

M1 180 - 38 = 142 (sum of angles Q and R)
M1 sets up 2R + 16 = 142, i.e. 2R = 126
A1 79 degrees cao
Answer: 79 degrees

Question 17

M1 150/360 simplified to 5/12, or equivalent
M1 216 x 150/360 (complete correct method)
A1 90 cao
Answer: 90 pupils

Question 18

M1 combines the ratios using a common value for pineapple juice: orange:pineapple:lemonade = 6:4:5
M1 6 + 4 + 5 = 15 parts; 3 / 15 = 0.2 (litres per part)
A1 1 litre cao
Answer: 1 litre

Question 19

M1 10% of 460 = 46
M1 15% of 460 = 46 + 23 = 69 (or 460 x 0.15)
A1 391 pounds cao
Answer: £391

Question 20

M1 17 / (5/8) = 17 x 8/5 = 136/5, or equivalent method
M1 identifies 27 as the greatest whole number of pieces (since 136/5 = 27.2)
A1 27 pieces cao
A1 0.125 m (1/8 m) left over cao
Answer: 27 pieces, with 0.125 m (1/8 m) left over

Question 21

M1 5.5 x 3.2 = 17.6 (area of the wall)
M1 rounds up to 5 tins, since 17.6 / 4 = 4.4 and the whole wall must be covered
M1 5 x 13.50 (complete correct method)
A1 67.50 pounds cao
Answer: £67.50

Question 22

(a) M1 1.2 x 0.8 = 0.96 (or another correct pairing of two dimensions)
(a) A1 0.48 m³ cao
(a) Answer: 0.48 m³
(b) M1 0.48 m³ = 480 litres (uses 1 m³ = 1000 litres)
(b) A1 32 minutes cao, ft their volume from (a)
(b) Answer: 32 minutes

Question 23

M1 8 + 5 + 7 = 20 (total number of pens)
M1 20 - 7 = 13 (number that are not black), or 8 + 5 = 13
A1 13/20 oe (accept 0.65 or 65%) cao
Answer: 13/20

Question 24

M1 87 / 3 = 29 (or forms 3n + 6 = 87)
M1 identifies the three numbers as 27, 29, 31
A1 27 cao
Answer: 27

Question 25

M1 sets entry = 7k and raffle = 3k, from the ratio 7:3
M1 forms cake stall = 3k x 5/2 = 7.5k, from raffle = 2/5 of cake stall
dM1 recognises k must be even for whole-pound amounts, and rewrites as entry = 14j, raffle = 6j, cake stall = 15j (with k = 2j)
dM1 forms 14j + 6j + 15j = 525, i.e. 35j = 525, so j = 15
A1 entry = 210 pounds, raffle = 90 pounds, cake stall = 225 pounds, all three correct cao
Answer: Entry fees £210, raffle £90, cake stall £225

Question 26

M1 lets the lawn be w by 2w, and forms the outer rectangle (2w + 2) by (w + 2), from a 1 m path on every side
M1 expands the outer area to 2w² + 6w + 4
dM1 subtracts the lawn area 2w² to find the path area = 6w + 4, or equivalent complete method
dM1 sets 6w + 4 = 40 and solves to w = 6
A1 lawn measures 6 m by 12 m, both dimensions correct cao
Answer: Width 6 m, length 12 m

Mark my answers