O-LevelMathematicsAlgebra and graphs4024/22 · Oct/Nov 2024 · Q1010 Marks

The cost of apples is x cents per kilogram. Mina spends $9 on apples.

(a)Write down an expression for the mass, in kilograms, of apples Mina receives.[1]
(b)The cost of pears is 40 cents per kilogram more than the cost of apples. Mina spends $9 on pears. The mass of pears Mina receives is 0.75 kg less than the mass of apples. Form an equation in x and show that it simplifies to x²+40x-48000 = 0.[4]
(c)Solve the equation x²+40x-48 000 = 0. Show your working.[3]
(d)Narinder buys 1.5 kg of apples and 0.8 kg of pears. Work out the total amount he pays in dollars.[2]

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2024). The mark or mark type is shown in brackets.

[1] 900/x oe
[4] Correct expansion of brackets and rearrangement to x² + 40x – 48000 = 0
[B1] for 900/x - 900/(x+40) = 0.75 oe
[M1] FT their expressions with different algebraic denominators
[M1] FT elimination of fractions with different algebraic denominators or use of common denominator
[A1] A0 if any errors or omissions
[3] 200 and -240
[B2] for (x-200)(x+240)
[B1] for brackets giving two out of three terms correct
[B1] for partial factors x(x −200) + 240(x – 200) or x(x + 240) – 200(x + 240)
[B2] OR using formula: -40 ± √(40² - 4 × 1 × -48000) / 2 oe
[B1] OR √(40² - 4 × 1 × -48000) oe
[B1] OR -40 ± √their193600 / 2
[B2] OR complete the square: x+20 = ±220
[B1] OR for (x + 20)²
[2] 4.92
[M1] for 1.5 × their 200 + 0.8 × (their 200 + 40) or better

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