Percentage Changes

Notes on the Worksheets

Worksheet 1: Programme Questions

The worksheet can be used to review the programme and expand on the mathematical content.

1. The discount on Ben's medallion is 25%, or a quarter. Other easy fraction equivalents could be revised.

2. Katie finds 10% + 5% mentally. Other mental methods could be explored. For example, how can you find 20%, 40%, 70%, 25%, 75%?

3. Ben saved £9. This was compared with Katie's saving of £35 from a '50% off' deal.

4. The original prices were:

• trainers: £60
• T-shirt: £15
• computer game: £40

His total saving was £40. Students could use the method shown in the programme to calculate Ben's overall percentage saving and compare it to Katie's 37.5%.

5. The question asked for an answer to three significant figures. The need to note and follow such instructions in the exam and to round answers appropriately could be developed here.

6. The correct formula was stated as:

(percentage change) = ^(change) / _(original) x 100%

The formula was used to find Katie's percentage saving, to find the percentage increase in football attendances, and to express a '6 for 5' deal as a percentage change.

7. 'Buy one, get one free' represents 100% extra free. What percentage is free for other deals like '3 for the price of 2', '4 for 3', '5 for 4' and so on?

8. Katie had three tins of meat for the price of two, or 'buy two, get a third free', or '50% extra free'. Alternative ways of stating deals could be discussed. What does 'buy two, get one free' mean?

9. The bottle contains 150ml of shampoo. This includes 15% extra free. Can students calculate how much was in the original bottle? Given that manufacturers often round quantities, what was likely to have been the actual size of the original?

10. Ben takes three extra bags to the checkout. If the large offer pack contains 15 bags, what is the 'extra free' deal here, expressed as a percentage? What if the offer pack contained 12 bags? What if it was 2 extra free bags in a pack of 12?

Worksheet 2: Tick or Trash

Question 1

Student A is correct.

Student B has failed to recognise that the sale price represents 85%, the original price being 100%.

The use of 1.15 as a multiplier may not be familiar to some students (Student B found 115% of £750).

Question 2

Student B is correct. Student A has found the discount but not the sale price as asked for in the question. This student has also neglected to write the answer in the conventional way as an amount of money.

Worksheet 3: Exam Practise Questions (Edexcel)

This is a selection of past exam questions from Edexcel, targeted at the middle ability range. You can use the sequence as it stands or select individual questions to suit your needs.

Given below is the mark scheme for each question, which will help you to see how marks are allocated and what the examiner is especially looking out for. The mark schemes use the following abbreviations:

Question 1

(a) Working: ^{2 x 12} / ₅

Answer: £4.80

(b) i) 0.3

ii) Working: 0.3 x 12 (oe)

Answer: £3.60

(c) Working: ^0.84 / ₁₂ or 0.07, ^0.84 / ₁₂ x 100 (oe)

Answer: 7%

(d) Working: ^0.24 / ₁₂, ² / ₁₀₀

Answer: ¹ / ₅₀

Notes:

(a) M1. A1 cao.

(b) B1. M1. A1 cao.

(c) M1 for ^0.84 / ₁₂ (oe) (can be implied). A1 cao.

(d) M1 ^0.24 / ₁₂ (oe). A2 cao (A1 for correct vulgar fraction not in simplest form or for 0.02 or 2%).

Question 2

i) 30 - (30 x ¹⁵ / ₁₀₀) = £25.50

ii) 36 x ² / ₃ = £24

iii) 22 + (22 x ^17.5 / ₁₀₀) = £25.85

Question 3

(a) 330 - (330 ÷ 4) (oe) = £247.50

(b) 320 - (20 ÷ 100) x 320 (oe) = £256

(c) 210 + (17.5 ÷ 100 x 210) (oe) = £246.75

Notes:

(a) M1 for 330 - (330 ÷ 4) or 330 x 3 ÷ 4. A1 cao (accept 247.5).

(b) M1 for 320 - (20 ÷ 100) x 320 or (80 ÷ 100) x 320. A1 cao

(c) M1 for 210 + (17.5 ÷ 100 x 210) or (117.5 ÷ 100) x 210. A1 cao.

SC: B2 for all three of (a) £82.50, (b) £64, (c) £36.75.

Question 4

7.5 x ^17.5 / ₁₀₀ = 1.31

7.5 + 1.31 = 8.81

8.81 - 8.75 = 6p

Notes:

M1 7.5 x 17.5 or 7.5 x 117.5 or 0.175 seen or 1.175 seen. A1 cao for 8.81.... B1 ft '£8.81' - £8.75 = 6p (dep on previous M1).

Question 5

(a) 30 x 30 x 20 = 18000cm³

(b) 30 x 30 x 21.6 = 19440

(19440 - 'a') ÷ 'a' x 100 = 8%

or 30 x 30 x 1.6 ÷ 'a' x 100

or (21.6 - 20) ÷ 20 x 100 = 8%

Notes:

(a) M1 for 30 x 30 x 20. A1 cao.

(b) M1 for 19440 or 30 x 30 x 21.6 or 30 x 30 x 1.6 or 1440 or (21.6 - 20) ÷ 20 or (21.6 - 20) x 100. A1 cao.

Question 6

(a) £9.40

(b) 120 x 5 ÷ 8 = 75

OR

120 ÷ 8, x 5 = 75

(c) ³ / ₈ x 100 = 37¹/₂%

OR

⁴⁵ / ₁₂₀ x 100 = 37¹/₂%

Notes:

(a) M1 8 x 1.175 (oe).

(b) M1 for ÷ 8. M1 for x 5 (dep). A1 cao.

(c) M1 for ³ / ₈ x 100 or (120 - '75' =) ⁴⁵ / ₁₂₀ x 100. A1 cao. NB: M1A0 for 0.37, 0.38, 37%, 38%, 0.375

Question 7

(a) ²⁰ / ₁₀₀ x 240 = 1.92

(b) 2.70 - ¹ / ₃ x 2.70

2.70 - 0.90 = £1.80

Question 8

(a) 2 x p x 6 or p x 12 = 37.7 cm

(b) 12 x ¹³⁰ / ₁₀₀;

12 + 12 x ³⁰ / ₁₀₀ = 15.6 cm

Question 9

(a) i) 450 x 0.8 or

450 - (0.2 x 450) (oe) = £360

ii) 0.8 x '360' or 288 seen

0.8 x '288' (oe) = £230.40

(b) ^80P / ₁₀₀ = 300 oe or P = ¹⁰⁰ / ₈₀ x 300 (oe)

Notes:

(a) i) M1. A1 cao.

ii) M1. M1 (dep on previous M1). A1 cao (accept 230.4).

(b) M1. A1 cao.

Question 10

740 x 5 ÷ 100 = £37

65 x 12 = £780

817 - 740

Answer = £77

Notes:

M1 for 740 x 5 ÷ 100 or £37 seen. M1 for 65 x 12 or £780 seen (indep). A1 for £77.00 cao.

SC: B2 for £817.