O-LevelMathematicsAlgebra and graphs4024/12 · Oct/Nov 2025 · Q2210 Marks

Ade and Maha make cards. One day they each work for 4 hours making cards. Ade takes x minutes to make one card.

(a)Show that the number of cards Ade makes in 4 hours is given by 240/x.[1]
(b)Maha takes 2 minutes less than Ade to make one card. Maha and Ade make a total of 70 cards in 4 hours. Form an equation and show that it simplifies to 7x² - 62x + 48 = 0.[4]
(c)Solve by factorisation. 7x² - 62x + 48 = 0[3]
(d)Work out the number of cards Maha makes in 1 hour.[2]

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2025). The mark or mark type is shown in brackets.

[1] (a) 60 × 4 / x leading to 240 / x
[4] (b) 240/x + 240/(x-2) = 70 oe
[4] (b) M1 Correct use of common denominator or correct removal of fractions from *their* 3-term equation with two fractions with different algebraic denominators
[4] (b) M1 Correct elimination of fractions and expansion of brackets from *their* 3-term equation with two fractions with different algebraic denominators
[4] (b) A1 A0 if any errors or omissions once an equation has been formed
[3] (c) (7x-6)(x-8)
[3] (c) M2 M1 for (7x+a)(x+b) where ab = 48 or 7b + a = -62 or for partial factorisation x(7x-6)-8(7x-6) or 7x(x-8)-6(x-8)
[3] (c) B1 for 6/7 and 8
[2] (d) 10
[2] (d) M1 for 60/(their 8-2) where their 8 > 2
[2] (d) If 0 scored, SC1 for answer 40

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