3.7H Percentages: Higher Tier Practice

EDEXCEL Edexcel 1MA1 · Calculator allowed · about 75 minutes

Total Marks

Name: _______________________________ Date: ____ / ____ / ______

Answer ALL questions. Show all your working.

Write 15% as a fraction in its simplest form.

(Total for Question 1 is 2 marks)

A jacket costs 120 pounds. It is reduced by 25% in a sale and then a further 10% is taken off the reduced price. Work out the final price of the jacket.

(Total for Question 2 is 3 marks)

The population of a town increases by 8% each year. If the current population is 25 000, work out the population after 2 years. Give your answer to the nearest whole person.

(Total for Question 3 is 3 marks)

A school fundraiser collected 840 pounds. The organisers decide to give 12% to charity, use 35% for equipment, and split the remainder equally between two sports teams. Work out how much each sports team receives. Show your working.

(Total for Question 4 is 4 marks)

Show that increasing a number by 20% and then decreasing the result by 20% does not return to the original number. Use an algebraic approach with n as the original number and give the final expression in terms of n.

(Total for Question 5 is 4 marks)

A laptop is on sale at 15% off the marked price. After the sale the shop increases the sale price by 10% to return nearer to the original price. If the final price is 810 pounds, find the original marked price. Give your answer to the nearest penny.

(Total for Question 6 is 5 marks)

A recipe requires 250 g of flour. A baker wants to increase all ingredient quantities by 12.5% to make a larger batch. Work out the new required mass of flour, giving your answer in grams.

(Total for Question 7 is 4 marks)

A bank offers 6% compound interest per year, compounded annually. Sara invests 2000 pounds for 3 years. Work out the total interest earned after 3 years. Give your answer to the nearest pound.

(Total for Question 8 is 5 marks)

Mark scheme · 3.7H Percentages: Higher Tier Practice

Question 1

M1 express 15% as 15/100 or show method to convert percentage to fraction
A1 3/20 cao
Answer: 3/20

Question 2

M1 apply 25% reduction: 120 x 0.75 = 90 or equivalent method
M1 apply further 10% reduction: 90 x 0.9 = 81 (method)
A1 81.00 cao
Answer: 81.00

Question 3

M1 use 25 000 x 1.08 x 1.08 or 25 000 x 1.08²
M1 calculate 25 000 x 1.1664 = 29 160 oe
A1 29 160 cao (to nearest whole person)
Answer: 29 160

Question 4

M1 calculate amounts for charity and equipment: 840 x 0.12 = 100.8 and 840 x 0.35 = 294
M1 subtract from total to get remainder: 840 - 100.8 - 294 = 445.2
M1 divide remainder by 2: 445.2 / 2 = 222.6
A1 222.60 cao
Answer: 222.60

Question 5

M1 state after increase: n x 1.20 or 6/5 n
M1 state after decrease: (n x 1.20) x 0.80 or (6/5 n) x 4/5
M1 simplify to give (6/5 x 4/5) n = 24/25 n
A1 conclude 24/25 n, not equal to n, therefore does not return to original (cso)
Answer: 24/25 n

Question 6

M1 express sale price as 0.85 P where P is original price
M1 final price after 10% increase is 0.85 P x 1.10 = 0.935 P
M1 set 0.935 P = 810 and form equation P = 810 / 0.935
M1 calculate P = 866.309523... or equivalent
A1 866.31 to nearest penny cao
Answer: 866.31

Question 7

M1 identify percentage increase and write multiplier 1 + 12.5/100 = 1.125
M1 convert 12.5% to fraction 1/8 or show equivalent method
M1 calculate 250 x 1.125 = 281.25 (method)
A1 281.25 g cao
Answer: 281.25 g

Question 8

M1 use amount = 2000 x 1.06³
M1 calculate 2000 x 1.191016 = 2382.032 (or equivalent)
M1 interest = amount - principal = 2382.032 - 2000 = 382.032
M1 round to nearest pound = 382
A1 382 pounds cao
Answer: 382

Percentages: Higher Tier Practice - Worksheets, Questions and Revision