14 a With a reduction of 15%, the sale price M1 2 M1 for correct formula M (B) is × 0.85. A = A b P1 P1 for correct rearrangement of ÷ by 0.85 Yes, the new value will always be the c original value multiplied by a percentage, C1 C1 for clear explanation calculated from the percentage change. For a reduction, the multiplier is (100 – the percentage reduction)%, for an increase it is (100 + the percentage increase)%. Percentage change problem, for d C1 C1 for clarity of communication of question example: The cost of a new car was £A. In the new financial year, it increased by 5% to £B. Write a formula to describe the proportional change. = × 1.05 and = . B A A 4 15 a No, an increase to of 50% followed by C1 2 C1 for clear explanation with calculated justification oe M A × 1.5 × 1.5 = × 1.52 A A another increase of 50% gives 2.25A. = × 2.25 A Doubling would give 2A and 2A ≠ 2.25A. b An 80% discount off the price of gives A 80% discount gives a price of × 0.20. A a new price of 0.2A. 60% followed by 20% gives a price of P1 P1 for clear explanation with calculated justification oe A 60% discount off the price of A, × 0.4 × 0.8 = × 0.32. A A followed by a further 20% discount, gives a new price of 0.32A so the 80% discount is better value. c C1 C1 for clear explanation with calculated justification oe × 0.75 × 1.20 = 0.9A If the original cost is the cost after a A A, × 1.20 × 0.75 =0.9A discount of 25% is 0.75A and paying VAT A at 20% gives a new price of 0.9A. If VAT is added first, the price is 1.2A. A 25% reduction gives a new price of 0.9A. 3 Because multiplication is commutative, the final prices are the same. It makes no difference.
14 a b c d With a reduction of 15%, the sale price (B) is A × 0.85. A = Yes, the new value will always be the original value multiplied by a percentage, calculated from the percentage change. For a reduction, the multiplier is (100 – the percentage reduction)%, for an increase it is (100 + the percentage increase)%. Percentage change problem, for example: The cost of a new car was £A. In the new financial year, it increased by 5% to £B. Write a formula to describe the proportional change. B = A × 1.05 and A = . M1 P1 C1 C1 2 M1 for correct formula P1 for correct rearrangement of ÷ by 0.85 C1 for clear explanation C1 for clarity of communication of question M 4 15 a b c A × 1.5 × 1.5 = A × 1.52 = A × 2.25 80% discount gives a price of A × 0.20. 60% followed by 20% gives a price of A × 0.4 × 0.8 = A × 0.32. A × 0.75 × 1.20 = 0.9A A × 1.20 × 0.75 =0.9A No, an increase to A of 50% followed by another increase of 50% gives 2.25A. Doubling would give 2A and 2A ≠ 2.25A. An 80% discount off the price of A gives a new price of 0.2A. A 60% discount off the price of A, followed by a further 20% discount, gives a new price of 0.32A so the 80% discount is better value. If the original cost is A, the cost after a discount of 25% is 0.75A and paying VAT at 20% gives a new price of 0.9A. If VAT is added first, the price is 1.2A. A 25% reduction gives a new price of 0.9A. Because multiplication is commutative, the final prices are the same. It makes no difference. C1 P1 C1 2 C1 for clear explanation with calculated justification oe P1 for clear explanation with calculated justification oe C1 for clear explanation with calculated justification oe M 3
Higher_Skills_Ratio_MarkScheme_Edexcel.docx