O-LevelMathematicsAlgebra and graphs4024/21 · May/June 2024 · Q1016 Marks

r = (4p+3t)/2 Find the value of p when r = 10 and t = −2. p=

(a)r = (4p+3t)/2 Find the value of p when r = 10 and t = −2. p=[3]
(b)The diagram shows a quadrilateral. Form an equation in w and solve it to find the size of the largest angle in the quadrilateral. Largest angle =[4]
(c)Simplify (2k²-5k-3)/(k²-9).[3]
(d)Solve 2/(x+3) + 5/(x-2) = 1. Show all your working and give your answers correct to 2 decimal places. x = or x =[6]

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Mark scheme

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

[3] 6.5 oe
[3] M2 for 10×2 - 3×(-2) = 4p oe
[3] or p = (2r-3t)/4 oe
[3] or M1 for 10 = (4p+3(-2))/2 oe
[3] or 2r = 4p+3t
[3] or r - (3t/2) = 2p or better
[4] w + 2w + w + 10 + w - 15 = 360 oe
[4] M1 e.g. 5w - 5 = 360
[4] 146
[4] B3 B2 for [w =] 73
[4] OR
[4] M1 for correctly rearranging their initial equation to kw = c
[4] M1 for largest angle = 2 × their 73
[3] (2k+1)/(k+3) final answer
[3] B1 for (2k+1)(k-3) seen
[3] B1 for (k+3)(k-3) seen
[6] x² - 6x – 17 [= 0]
[6] or equivalent 3-term quadratic all terms on one side
[6] B4 M2 for 2(x-2) + 5(x+3) = (x+3)(x-2) or (2(x-2) + 5(x+3))/((x+3)(x-2)) = 1
[6] or M1 for 2(x-2)+5(x+3) seen
[6] M1 for x²+3x-2x-6 soi
[6] B1 FT their quadratic
[6] -(-6) ± √((-6)²-4×1×(-17))/(2×1) oe
[6] oe e.g. (6±√(6²+17))/2
[6] 8.10, -2.10
[6] B1

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