Mixed Problem-Solving Paper D Worksheet with Answers

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11+ · GL ASSESSMENT

EP.M73 Mixed Problem-Solving Paper D

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

Total Marks

Name: _______________________________ Date: ____ / ____ / ______

Answer ALL questions. Show all your working.

1

Freddie has 45 stickers. He gives 8 stickers to his sister and then buys 12 more stickers from a shop. How many stickers does Freddie have now?

(Total for Question 1 is 2 marks)

2

Nadia buys 3 packets of crisps at 0.45 pounds each. She pays with a 2 pound coin. How much change does she receive?

(Total for Question 2 is 2 marks)

3

A film starts at 19:20 and finishes at 21:05. How long, in minutes, does the film last?

(Total for Question 3 is 2 marks)

4

A charity shop has 81 books on a shelf. 2/9 of the books are non-fiction. How many of the books are non-fiction?

(Total for Question 4 is 2 marks)

5

What is the highest common factor of 24 and 36?

(Total for Question 5 is 2 marks)

6

A carton holds 1.5 litres of orange juice. How many 200 ml glasses can be completely filled using 3 full cartons?

(Total for Question 6 is 2 marks)

7

A fruit drink is made by mixing apple juice and water in the ratio 2:3. How many millilitres of apple juice are needed to make 800 ml of the drink?

(Total for Question 7 is 2 marks)

8

A square has a perimeter of 36 cm. What is the area of the square?

(Total for Question 8 is 2 marks)

9

The rainfall recorded over 4 weeks was 12 mm, 18 mm, 9 mm and 25 mm. What is the range of the rainfall?

(Total for Question 9 is 2 marks)

10

The temperature at 6am was -4C. By midday it had risen by 11C. By 9pm it had fallen by 8C from the midday temperature. What was the temperature at 9pm?

(Total for Question 10 is 2 marks)

11

Tom starts with 20 pounds of pocket money. He spends 2/5 of it on a comic. He then spends 1/4 of what remains on sweets. How much money does he have left?

(Total for Question 11 is 3 marks)

12

A market trader packs apples into crates that each hold 35 apples. She has 482 apples to pack, and each crate must not be overfilled. What is the least number of crates needed, and how many spare spaces will be left in the final crate?

(Total for Question 12 is 3 marks)

13

A bottle of squash concentrate is mixed with water in a fixed ratio. To make 8 glasses of drink, 150 ml of concentrate is needed. How much concentrate is needed to make 28 glasses, using the same ratio?

(Total for Question 13 is 3 marks)

14

A train travels 180 km in 2 hours 30 minutes at a constant speed. At this speed, how far would it travel in 4 hours?

(Total for Question 14 is 3 marks)

15

A rectangular lawn measures 15 m by 9 m. A square flower bed with sides of 4 m is cut out of one corner of the lawn and is not grassed. What is the area of the lawn that remains grassed?

(Total for Question 15 is 3 marks)

16

The table shows the number of pets owned by pupils in a class: 0 pets - 6 pupils, 1 pet - 9 pupils, 2 pets - 7 pupils, 3 pets - 3 pupils. How many pupils are in the class, and what is the total number of pets owned by the class?

(Total for Question 16 is 3 marks)

17

A shop reduces the price of a jacket from 45 pounds by 20% in a sale. A customer also has a voucher for a further 3 pounds off the sale price. What is the final price of the jacket?

(Total for Question 17 is 3 marks)

18

Paint is made by mixing blue paint and white paint in the ratio 3:7. Priya has 6 litres of blue paint and wants to use all of it. How many litres of white paint does she need, and what is the total volume of paint produced?

(Total for Question 18 is 3 marks)

19

In a triangle, the second angle is twice the size of the first angle. The third angle is 20 degrees more than the first angle. Work out the size of each of the three angles.

(Total for Question 19 is 3 marks)

20

Entry to a fun fair costs 6.50 pounds per child and 9.20 pounds per adult. A group of 4 children and 3 adults visits the fair. Each of the 7 people also buys one drink costing 1.80 pounds. What is the total amount spent by the group?

(Total for Question 20 is 3 marks)

21

A rectangular garden is 12 m long and 7 m wide. A fence is needed around the whole garden except for a 2 m wide gate, which needs no fencing. What length of fencing is required?

(Total for Question 21 is 3 marks)

22

Five pupils sat a spelling test out of 20. Four of the pupils scored 14, 17, 12 and 19. The mean score for all five pupils was 15. What was the fifth pupil's score?

(Total for Question 22 is 3 marks)

23

A bakery has two ovens running throughout the day. Oven A bakes 18 loaves every 30 minutes. Oven B bakes 20 loaves every 40 minutes.

(a)Work out the number of loaves each oven bakes per hour, and state which oven bakes at the faster rate.(2)

(b)Both ovens start baking at 09:00 and run continuously at these same rates until 17:00. How many more loaves will Oven A have baked than Oven B by 17:00?(3)

(Total for Question 23 is 5 marks)

24

A cinema sells tickets for 8.50 pounds each. On a Saturday evening, 3/4 of the 240 seats in the cinema are sold. The cinema also sells 60 tubs of popcorn at 3.20 pounds each during the showing. What is the total amount of money taken by the cinema for tickets and popcorn at this showing?

(Total for Question 24 is 4 marks)

25

A car travels at a constant speed and covers 63 km in 45 minutes. At the same speed, how many kilometres would it travel in 2 hours 20 minutes?

(Total for Question 25 is 4 marks)

26

A garden is made up of a rectangular lawn 10 m by 6 m and a semicircular flower bed attached to one of the 6 m sides, with a diameter of 6 m. Take π = 3.14. Work out the total area of the garden, giving your answer to the nearest whole square metre.

(Total for Question 26 is 4 marks)

27

A school is organising a trip. Each coach seats 48 pupils and costs 180 pounds to hire. There are 260 pupils going on the trip, and every pupil must have a seat, so coaches are hired in whole numbers only. The total cost is shared equally between all 260 pupils. Work out the total cost of hiring the coaches, and the amount each pupil must pay, giving your final answer to the nearest penny.

(Total for Question 27 is 4 marks)

Mark scheme · EP.M73 Mixed Problem-Solving Paper D

Question 1

M1 45 - 8 = 37 found
A1 49 cao
Answer: 49 stickers

Question 2

M1 3 * 0.45 = 1.35 found
A1 0.65 pounds cao
Answer: £0.65

Question 3

M1 19:20 to 21:05 split into 1 hour (to 20:20) plus 45 minutes (to 21:05), or equivalent
A1 105 minutes cao
Answer: 105 minutes

Question 4

M1 81 / 9 = 9 found
A1 18 cao
Answer: 18 books

Question 5

M1 lists factors of 24 and/or 36, or uses prime factorisation
A1 12 cao
Answer: 12

Question 6

M1 3 * 1.5 = 4.5 litres (= 4500 ml) found
A1 22 cao (accept 22 glasses with 100 ml left over)
Answer: 22 glasses

Question 7

M1 800 / 5 = 160 (value of 1 part) found
A1 320 cao ft
Answer: 320 ml

Question 8

M1 36 / 4 = 9 (side length) found
A1 81 cm² cao ft
Answer: 81 cm²

Question 9

M1 identifies the highest (25 mm) and lowest (9 mm) values
A1 16 mm cao
Answer: 16 mm

Question 10

M1 -4 + 11 = 7 (midday temperature) found
A1 -1C cao ft
Answer: -1C

Question 11

M1 2/5 * 20 = 8 pounds (comic), leaving 12 pounds found
M1 1/4 * 12 = 3 pounds (sweets) found
A1 9 pounds cao ft
Answer: £9

Question 12

M1 attempts 482 / 35, e.g. 35 * 13 = 455
dM1 identifies a remainder of 27 apples (482 - 455), which still need a crate
A1 14 crates and 8 spare spaces both correct cao
Answer: 14 crates, with 8 spare spaces

Question 13

M1 28 / 8 = 3.5 (scale factor) found
M1 150 * 3.5 (complete correct method)
A1 525 ml cao
Answer: 525 ml

Question 14

M1 2 hours 30 minutes = 2.5 hours
M1 180 / 2.5 = 72 km/h (speed) found
A1 288 km cao
Answer: 288 km

Question 15

M1 15 * 9 = 135 m² (lawn area) found
M1 4 * 4 = 16 m² (flower bed area) found
A1 119 m² cao ft
Answer: 119 m²

Question 16

B1 25 pupils cao (6 + 9 + 7 + 3)
M1 method for total pets shown: (0 * 6) + (1 * 9) + (2 * 7) + (3 * 3)
A1 32 pets cao
Answer: 25 pupils; 32 pets in total

Question 17

M1 10% of 45 = 4.50, so 20% = 9 pounds (discount) found
M1 45 - 9 = 36 pounds (sale price) found
A1 33 pounds cao ft
Answer: £33

Question 18

M1 6 / 3 = 2 litres (value of 1 part) found
M1 7 * 2 = 14 litres (white paint) found
A1 20 litres total cao ft
Answer: 14 litres of white paint; 20 litres in total

Question 19

M1 forms x + 2x + (x + 20) = 180, or equivalent
M1 4x + 20 = 180, so x = 40 found
A1 40 degrees, 80 degrees and 60 degrees all correct cao
Answer: 40 degrees, 80 degrees, 60 degrees

Question 20

M1 4 * 6.50 = 26 and 3 * 9.20 = 27.60 (entry costs) found
M1 7 * 1.80 = 12.60 (drinks) found
A1 66.20 pounds cao ft
Answer: £66.20

Question 21

M1 2 * (12 + 7) = 38 m (perimeter) found
M1 38 - 2 (subtracts the gate width) shown
A1 36 m cao ft
Answer: 36 m

Question 22

M1 15 * 5 = 75 (total needed for 5 pupils) found
M1 14 + 17 + 12 + 19 = 62 (sum of four known scores) found
A1 13 cao ft
Answer: 13

Question 23

(a) M1 Oven A: 18 / 30 * 60 = 36 per hour (or equivalent) found
(a) A1 Oven B: 20 / 40 * 60 = 30 per hour found, and correctly states Oven A is faster cao
(a) Answer: Oven A: 36 loaves per hour; Oven B: 30 loaves per hour; Oven A is faster
(b) M1 09:00 to 17:00 = 8 hours found
(b) M1 Oven A: 36 * 8 = 288 and Oven B: 30 * 8 = 240 found, ft their rates from part (a)
(b) A1 48 cao ft
(b) Answer: 48 more loaves

Question 24

M1 3/4 * 240 = 180 (seats sold) found
M1 180 * 8.50 = 1530 pounds (ticket revenue) found
M1 60 * 3.20 = 192 pounds (popcorn revenue) found
A1 1722 pounds cao ft
Answer: £1722

Question 25

M1 63 / 45 * 60 = 84 km/h (speed per hour) found
M1 2 hours 20 minutes converted to 7/3 hours (or 140 minutes)
dM1 84 * 7/3 (dep on both previous marks) method shown
A1 196 km cao
Answer: 196 km

Question 26

M1 10 * 6 = 60 m² (rectangle area) found
M1 radius = 3 m found
dM1 0.5 * 3.14 * 3 * 3 = 14.13 m² (semicircle area, dep on radius) found
A1 74 m² cao ft (awrt 74)
Answer: 74 m²

Question 27

M1 260 / 48 = 5.41... found, rounded up to 6 coaches
M1 6 * 180 = 1080 pounds (total cost) found
dM1 1080 / 260 (dep on total cost) method shown
A1 4.15 pounds cao ft (awrt)
Answer: £1080 total; £4.15 per pupil

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

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EP.M73 Mixed Problem-Solving Paper D

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Question 3

Question 4

Question 5

Question 6

Question 7

Question 8

Question 9

Question 10

Question 11

Question 12

Question 13

Question 14

Question 15

Question 16

Question 17

Question 18

Question 19

Question 20

Question 21

Question 22

Question 23

Question 24

Question 25

Question 26

Question 27

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Question 3

Question 4

Question 5

Question 6

Question 7

Question 8

Question 9

Question 10

Question 11

Question 12

Question 13

Question 14

Question 15

Question 16

Question 17

Question 18

Question 19

Question 20

Question 21

Question 22

Question 23

Question 24

Question 25

Question 26

Question 27