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GCSE · EDEXCEL

3.8D Percentage Change: Fluency and Exam Drill

EDEXCEL 1MA1 · Calculator allowed · about 80 minutes

Total Marks

Name: _______________________________ Date: ____ / ____ / ______

Answer ALL questions. Show all your working.

A quantity increases from 50 to 63. Work out the percentage increase.

(Total for Question 1 is 2 marks)

A quantity decreases from 120 to 84. Work out the percentage decrease.

(Total for Question 2 is 2 marks)

A train ticket cost 45 pounds last year. This year it costs 51.75 pounds. Work out the percentage increase in the price of the ticket.

(Total for Question 3 is 3 marks)

A blender was priced at 68 pounds. In a sale it is now priced at 57.80 pounds. Work out the percentage decrease in the price of the blender.

(Total for Question 4 is 3 marks)

Marcus buys a bicycle for 140 pounds and sells it for 168 pounds. Work out Marcus's percentage profit.

(Total for Question 5 is 3 marks)

Elif buys a laptop for 480 pounds and sells it for 372 pounds. Work out Elif's percentage loss.

(Total for Question 6 is 3 marks)

A cafe's weekly takings rise from 2150 pounds to 2310 pounds. Work out the percentage increase in the takings. Give your answer correct to 1 decimal place.

(Total for Question 7 is 3 marks)

A charity's donations fall from 18400 pounds to 16950 pounds. Work out the percentage decrease in donations. Give your answer correct to 3 significant figures.

(Total for Question 8 is 3 marks)

Two football clubs both increased their season ticket prices. Club A: from 24 pounds to 27.60 pounds. Club B: from 30 pounds to 34.20 pounds. Work out which club had the greater percentage increase. You must show your working.

(Total for Question 9 is 4 marks)

Increase 250 pounds by 18%.

(Total for Question 10 is 3 marks)

Decrease 340 pounds by 35%.

(Total for Question 11 is 3 marks)

Tariq buys a 4 kg bag of sweets for 10 pounds. He repackages it into 80 g bags and sells each bag for 45p. Work out Tariq's percentage profit.

(Total for Question 12 is 4 marks)

Nadia buys 90 second-hand paperback books for 45 pounds. She is unable to sell 15 of them and donates them to a charity shop. She sells each of the remaining books for 90p. Work out Nadia's percentage profit.

(Total for Question 13 is 4 marks)

Using p pounds for the original price of an item, show that increasing the price by 15% and then decreasing the new price by 15% is equivalent overall to a decrease of 2.25% on the original price.

(Total for Question 14 is 4 marks)

A shop increases the price of a kettle by 25%. In a clearance sale, the new price is then reduced by 20%. The original price of the kettle was 32 pounds.

(a)Work out the sale price of the kettle.(3)

(b)Comment on how the sale price compares with the original price of 32 pounds, and explain why this happens.(1)

(Total for Question 15 is 4 marks)

A car's value decreased by 22% over one year. At the end of the year it was worth 10530 pounds. Work out the value of the car at the start of the year.

(Total for Question 16 is 4 marks)

A trader buys a batch of 200 garden ornaments for a total of 900 pounds. She also pays a delivery charge of 60 pounds. She wants to make an overall percentage profit of 45% on her total costs, including delivery. Work out the price she should charge for each ornament, if she sells all 200 of them.

(Total for Question 17 is 4 marks)

The price of a laptop is increased by 30%. It is then reduced by y% in a clearance sale. The final price is 4% more than the original price. Work out the value of y.

(Total for Question 18 is 4 marks)

A company's revenue increased by 12% in its first year of trading, then increased by a further 8% in its second year. At the end of the second year, the revenue was 302400 pounds. Work out the company's revenue before either increase, that is, at the start of the first year.

(Total for Question 19 is 4 marks)

A piece of machinery depreciates in value by the same percentage each year. After 2 years its value is 2178 pounds. After 3 years its value is 1960.20 pounds. Work out the annual percentage rate of depreciation. Give your answer correct to 1 decimal place.

(Total for Question 20 is 4 marks)

A shop's revenue changed over three consecutive years. Year 1 to Year 2: increased by 15%. Year 2 to Year 3: decreased by 8%. Year 3 to Year 4: increased by r%. Over the three years, from Year 1 to Year 4, the overall percentage change in revenue was an increase of 26.96%. Work out the value of r.

(Total for Question 21 is 4 marks)

Mark scheme · 3.8D Percentage Change: Fluency and Exam Drill

Question 1

M1 13 seen (63 - 50), or equivalent method
A1 26% cao
Answer: 26%

Question 2

M1 36 seen (120 - 84), or equivalent method
A1 30% cao
Answer: 30%

Question 3

M1 6.75 seen (51.75 - 45)
M1 6.75/45 x 100 (oe)
A1 15% cao
Answer: 15%

Question 4

M1 10.20 seen (68 - 57.80)
M1 10.20/68 x 100 (oe)
A1 15% cao
Answer: 15%

Question 5

M1 28 seen (168 - 140)
M1 28/140 x 100 (oe)
A1 20% cao
Answer: 20%

Question 6

M1 108 seen (480 - 372)
M1 108/480 x 100 (oe)
A1 22.5% cao
Answer: 22.5%

Question 7

M1 160 seen (2310 - 2150)
M1 160/2150 x 100 (oe)
A1 awrt 7.4%
Answer: 7.4%

Question 8

M1 1450 seen (18400 - 16950)
M1 1450/18400 x 100 (oe)
A1 awrt 7.88% (3sf)
Answer: 7.88%

Question 9

M1 3.60 seen (27.60 - 24) and 4.20 seen (34.20 - 30)
M1 Club A: 3.60/24 x 100 (= 15%)
M1 Club B: 4.20/30 x 100 (= 14%)
A1 Club A, with correct comparison (15% > 14%), ft from their two percentages
Answer: Club A (15% increase vs 14% increase)

Question 10

M1 finds 18% of 250 (= 45), or uses multiplier 1.18
M1 adds their 18% to 250 (oe)
A1 295 (pounds) cao
Answer: 295 pounds

Question 11

M1 finds 35% of 340 (= 119), or uses multiplier 0.65
M1 subtracts their 35% from 340 (oe)
A1 221 (pounds) cao
Answer: 221 pounds

Question 12

M1 4000/80 = 50 (bags)
M1 50 x 0.45 = 22.50 (total revenue)
dM1 22.50 - 10 = 12.50 (profit), dependent on both M1s
A1 125% cao
Answer: 125%

Question 13

M1 90 - 15 = 75 (books sold)
M1 75 x 0.90 = 67.50 (total revenue)
dM1 67.50 - 45 = 22.50 (profit), dependent on both M1s
A1 50% cao
Answer: 50%

Question 14

M1 forms the increased price, 1.15p (oe)
M1 multiplies their increased value by 0.85 (dep on M1)
A1 obtains 0.9775p oe
B1 correct conclusion: 0.9775p is 97.75% of p, i.e. an overall decrease of 2.25%, with supporting working shown
Answer: Overall equivalent to a 2.25% decrease (multiplier 0.9775)

Question 15

(a) M1 32 x 1.25 (= 40)
(a) M1 their 40 x 0.8 (oe)
(a) A1 32 (pounds) cao
(a) Answer: 32 pounds
(b) B1 states the sale price equals the original price, because the combined multiplier 1.25 x 0.8 = 1, so the two percentage changes exactly cancel out
(b) Answer: The sale price equals the original price (1.25 x 0.8 = 1, so the changes exactly cancel)

Question 16

M1 recognises 10530 represents 78% (0.78) of the value at the start of the year
M1 sets up start value x 0.78 = 10530 (oe)
M1 10530/0.78 (oe)
A1 13500 (pounds) cao
Answer: 13500 pounds

Question 17

M1 900 + 60 = 960 (total cost)
M1 960 x 1.45 (oe, total revenue needed = 1392)
M1 1392/200 (oe)
A1 6.96 (pounds) cao
Answer: 6.96 pounds (per ornament)

Question 18

M1 sets up 1.3(1 - y/100) = 1.04 (oe)
M1 (1 - y/100) = 1.04/1.3 = 0.8 (oe, evaluated)
M1 y/100 = 1 - 0.8 = 0.2 (oe)
A1 y = 20, cao
Answer: y = 20

Question 19

M1 recognises the combined multiplier 1.12 x 1.08 = 1.2096 (oe)
M1 sets up original x 1.2096 = 302400 (oe)
M1 302400/1.2096 (oe)
A1 250000 (pounds) cao
Answer: 250000 pounds

Question 20

M1 recognises that dividing the year-3 value by the year-2 value gives the annual multiplier (1 - r/100), independent of the original value
M1 1960.20/2178 correctly set up and evaluated
A1 0.9 (or 90%) for the multiplier
A1 10.0% cao (1dp)
Answer: 10.0% per annum

Question 21

M1 combines the first two multipliers: 1.15 x 0.92 = 1.058 (oe)
M1 sets up 1.058(1 + r/100) = 1.2696 (oe)
M1 (1 + r/100) = 1.2696/1.058 = 1.2 (oe, evaluated)
A1 r = 20, cao
Answer: r = 20

Percentage Change: Fluency and Exam Drill - Worksheets, Questions and Revision