Calculation Problems: Fluency and Exam Drill (Part 2) - Worksheets, Questions and Revision

16 original exam-style questions - 5 pages of questions with a full mark scheme - free printable PDF.

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GCSE · Calculation

2.1DB Calculation Problems: Fluency and Exam Drill (Part 2)

EDEXCEL 1MA1 · Calculator allowed · about 60 minutes

Total Marks

Name: _______________________________ Date: ____ / ____ / ______

Answer ALL questions. Show all your working.

Erin buys a sandwich for £2.15, a drink for £1.10 and a snack bar for £0.85. Work out the total amount Erin spends.

(Total for Question 1 is 1 mark)

A cinema charges £8.50 for an adult ticket and £5.75 for a child ticket. Work out the total cost for 2 adult tickets and 3 child tickets.

(Total for Question 2 is 2 marks)

A ribbon is 3.2 m long. Work out the length of the ribbon in centimetres.

(Total for Question 3 is 1 mark)

A carton contains 900 ml of orange juice. Yusuf drinks 2/5 of the carton. Work out how much juice, in millilitres, Yusuf drinks.

(Total for Question 4 is 2 marks)

A school trip needs to transport 134 students. Each minibus can carry 15 students. Work out the least number of minibuses needed to transport all the students.

(Total for Question 5 is 2 marks)

A raffle raises £540. The money is shared between the school fund and the charity fund in the ratio 5:4. Work out how much money the charity fund receives.

(Total for Question 6 is 3 marks)

Aisha and Ben each go for a run. The table shows the distance each of them ran and the time each of them took.

Runner	Distance (km)	Time (minutes)
Aisha	15	50
Ben	21	60

Work out which runner had the greater average speed. You must show your working.

(Total for Question 7 is 3 marks)

A garden centre sells packs of plant food at £4.20 each. Priti buys 6 packs and uses a voucher that reduces the total cost by £3.50. Work out the total amount Priti pays.

(Total for Question 8 is 3 marks)

After a 12% pay rise, Priya's new weekly wage is £392. Work out her original weekly wage, before the rise.

(Total for Question 9 is 3 marks)

A supermarket sells rice in two sizes: a 500 g bag for £1.20, and a 2 kg bag for £4.32. Work out which bag gives better value for money. You must show your working.

(Total for Question 10 is 3 marks)

A plumber charges a call-out fee of £45 plus £30 per hour worked. Show that the total cost of a job lasting 2.5 hours is £120.

(Total for Question 11 is 2 marks)

A student's working to find 15% of £84 is shown below.

84 / 15 = 5.6
So 15% of £84 is £5.60

Identify the error in the student's method, then work out the correct value of 15% of £84.

(Total for Question 12 is 3 marks)

Noah invests £2,500 in a savings account paying compound interest at 2.5% per year.
(a) Work out the value of his savings after 2 years.
(b) Work out the total interest earned over the 2 years.

(a)(a) Work out the value of his savings after 2 years.(3)

(b)(b) Work out the total interest earned over the 2 years.(1)

(Total for Question 13 is 4 marks)

The diagram shows the shape of a garden, made from two rectangles put together to form an L-shape. All corners are right angles. Diagram NOT drawn accurately.

Work out the cost of fencing the whole perimeter of the garden, if fencing costs £14.50 per metre.

Figure (to be drawn): An L-shaped garden formed from two rectangles joined together, all interior angles right angles, NOT drawn accurately. Labelled edges, starting at the bottom-left corner and travelling clockwise: bottom edge 12 m (going right); lower right-hand edge 6 m (going up); then the outline steps left 4 m; then continues up an unlabelled edge to the top-right area; then left along an unlabelled top edge back to the top-left corner; then down the left-hand edge 9 m to close the shape back at the bottom-left corner.

(Total for Question 14 is 4 marks)

A school trip costs a total of £2,850. 2/5 of the total cost is for coach travel. Of the money remaining after paying for the coach, 30% is spent on entry tickets, and the rest is shared equally between 4 accompanying tutors as a contingency allowance. Work out how much each tutor receives.

(Total for Question 15 is 4 marks)

A cleaning fluid mixes chemical A and chemical B in the ratio 2:5 by volume. A batch of the fluid contains 7.5 litres more chemical B than chemical A. Work out the total volume of the batch.

(Total for Question 16 is 4 marks)

Mark scheme · 2.1DB Calculation Problems: Fluency and Exam Drill (Part 2)

Question 1

B1 £4.10 cao
Answer: £4.10. Working check: 2.15 + 1.10 + 0.85 = 4.10.

Question 2

M1 finds the cost of the adult tickets and the cost of the child tickets, e.g. 2 x 8.50 = 17.00 and 3 x 5.75 = 17.25 (method)
A1 £34.25 cao
Answer: £34.25. Working check: 2 x 8.50 = 17.00; 3 x 5.75 = 17.25; 17.00 + 17.25 = 34.25.

Question 3

B1 320 cm cao
Answer: 320 cm. Working check: 3.2 x 100 = 320.

Question 4

M1 finds one fifth of 900: 900 / 5 = 180 (method)
A1 360 ml cao
Answer: 360 ml. Working check: 900 / 5 = 180; 180 x 2 = 360.

Question 5

M1 divides 134 by 15 (method), e.g. 134 / 15 = 8.9(3...)
A1 9 cao (rounds up to a whole number of minibuses)
Answer: 9 minibuses. Working check: 134 / 15 = 8.93 (2 dp); 8 minibuses only hold 120 students, so 9 minibuses are needed.

Question 6

M1 finds the total number of parts: 5 + 4 = 9
M1 finds the value of one part: 540 / 9 = 60
A1 £240 cao
Answer: £240. Working check: 540 / 9 = 60; charity fund = 4 x 60 = 240; school fund = 5 x 60 = 300; 240 + 300 = 540.

Question 7

M1 finds Aisha's average speed: 15 / (50/60) = 18 km/h (oe)
M1 finds Ben's average speed: 21 / (60/60) = 21 km/h (oe)
A1 correct conclusion that Ben has the greater average speed (21 km/h > 18 km/h) cao
Answer: Ben has the greater average speed (21 km/h compared with Aisha's 18 km/h). Working check: Aisha 15 / (50/60) = 18; Ben 21 / (60/60) = 21.

Question 8

M1 finds the cost of 6 packs: 6 x 4.20 (oe)
M1 subtracts the £3.50 voucher from the total (method)
A1 £21.70 cao
Answer: £21.70. Working check: 6 x 4.20 = 25.20; 25.20 - 3.50 = 21.70.

Question 9

M1 recognises £392 represents 112% of the original wage (oe, e.g. sets up 1.12 x w = 392)
M1 divides 392 by 1.12 (method)
A1 £350 cao
Answer: £350. Working check: 350 x 1.12 = 392.

Question 10

M1 finds a price per unit mass for the 500 g bag, e.g. 1.20 / 500 x 100 = £0.24 per 100 g (oe)
M1 finds a price per unit mass for the 2 kg bag, e.g. 4.32 / 2000 x 100 = £0.216 per 100 g (oe, allow consistent units)
A1 correct conclusion that the 2 kg bag is better value, since £0.216 per 100 g is less than £0.24 per 100 g, cao
Answer: The 2 kg bag is better value for money. Working check: 500 g bag = 1.20 / 500 = £0.0024 per gram (£0.24 per 100 g); 2 kg bag = 4.32 / 2000 = £0.00216 per gram (£0.216 per 100 g); 0.216 is less than 0.24.

Question 11

M1 30 x 2.5 = 75 seen (oe)
A1 45 + 75 = 120 shown correctly (cso)
Answer: £120 (shown). Working check: 30 x 2.5 = 75; 45 + 75 = 120.

Question 12

B1 identifies the error: the student divided 84 by 15 instead of finding 15% (15/100) of 84, e.g. by multiplying by 0.15 (oe)
M1 correct method: 84 x 0.15 (oe 84 x 15/100)
A1 £12.60 cao
Answer: The error: the student divided by 15 instead of multiplying by 15% (0.15). Correct value: £12.60. Working check: 84 x 0.15 = 12.60.

Question 13

(a) M1 uses the multiplier 1.025
(a) M1 applies the multiplier twice: 2500 x 1.025 x 1.025 (oe 2500 x 1.025²)
(a) A1 £2626.56 cao (awrt to the nearest penny)
(a) Answer: £2626.56 (awrt)
(b) B1 £126.56 cao (ft from part (a): answer to (a) minus 2500)
(b) Answer: £126.56

Question 14

M1 finds the missing top edge: 12 - 4 = 8 m (oe)
M1 finds the missing middle edge: 9 - 6 = 3 m (oe)
M1 finds the total perimeter: 12 + 6 + 4 + 3 + 8 + 9 = 42 m (method, ft from the two found lengths)
A1 £609.00 cao
Answer: £609.00. Working check: missing lengths 12 - 4 = 8 m and 9 - 6 = 3 m; perimeter = 12 + 6 + 4 + 3 + 8 + 9 = 42 m; 42 x 14.50 = 609.00.

Question 15

M1 coach cost = 2/5 x 2850 = £1140 (oe)
M1 remaining after coach = 2850 - 1140 = £1710 (oe, ft)
M1 entry tickets = 30% of 1710 = £513; remaining after tickets = 1710 - 513 = £1197 (oe, ft)
A1 £299.25 cao (1197 / 4)
Answer: £299.25. Working check: coach = 2/5 x 2850 = 1140; remaining = 2850 - 1140 = 1710; tickets = 0.30 x 1710 = 513; remaining = 1710 - 513 = 1197; 1197 / 4 = 299.25.

Question 16

M1 finds the difference in parts: 5 - 2 = 3
M1 finds the value of one part: 7.5 / 3 = 2.5 litres
M1 finds the total number of parts: 2 + 5 = 7
A1 17.5 litres cao (7 x 2.5)
Answer: 17.5 litres. Working check: 1 part = 7.5 / 3 = 2.5; chemical A = 2 x 2.5 = 5; chemical B = 5 x 2.5 = 12.5; total = 5 + 12.5 = 17.5; difference = 12.5 - 5 = 7.5 (matches the given information).

Question 16

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Calculation Problems: Fluency and Exam Drill (Part 2) - Worksheets, Questions and Revision

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