O-LevelMathematicsNumber4024/21 · Oct/Nov 2016 · Q912 Marks

On Monday, Abdul sold 140 boxes of matches at 30 cents per box.

(a)Calculate the income, in dollars, Abdul received on Monday.[1]
(b)On Tuesday, the price per box decreased by 10% and the number of boxes sold increased by 30%. Calculate the percentage change in the income.[3]
(c)(i)On Wednesday, the price of a box was y cents less than it was on Monday. Abdul sold 4y more boxes on Wednesday than he did on Monday. Write down an expression, in terms of y, for the income received on Wednesday. Give your answer in dollars.[2]
(c)(ii)Given that this income is equal to $40, write down an equation in y and show that it simplifies to y² + 5y – 50 = 0.[2]
(c)(iii)Solve the equation y² + 5y - 50 = 0.[3]
(c)(iv)Hence find the number of boxes sold on Wednesday.[1]

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2016). The mark or mark type is shown in brackets.

[1] (a) 42
[3] (b) 17 B2 for 0.9 × 1.3 or for answer 117 or B1 for 27 x 182 or 0.27 × 182 and M1 for (their 4914– their 4200) / their 4200 × 100 oe
[2] (c)(i) (30 - y) × (140 + 4y) / 100 oe isw B1 for (30-y) or (140 + 4y) soi
[2] (c)(ii) Forms equation (30 - y) × (140 + 4y) / 100 = 40 then correct working leading to y² + 5y - 50 = 0 AG B1 FT for 4200 – 140y + 120y –4y² = 4000 or better FT equating their product from (ii) with 40, eliminating fraction and expanding brackets
[3] (c)(iii) y=-10, 5 B2 for (y + 10 )( y – 5 ) or B1 for (y + a )( y + b ) where ab = -50 or a + b = 5 OR B1 for √225 soi and B1 for (-5 ± √their225) / 2 oe
[1] (c)(iv) 160 cao

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