O-LevelMathematicsAlgebra and graphs4024/22 · May/June 2015 · Q912 Marks

(a) Factorise completely

(a)(i)4x³-10xy,[1]
(a)(ii)9a²-b².[1]
(b)Solve 7 / (3-2m) = 4.[2]
(c)A right-angled triangle has a base that is 7 cm longer than its height, h cm. The hypotenuse of the triangle is 23 cm. [Figure 9.1]
(c)(i)Show that h satisfies the equation h² +7h-240 = 0.[2]
(c)(ii)Write down an expression, in terms of h, for the area of the triangle.[1]
(c)(iii)Hence state the exact area of the triangle.[1]
(c)(iv)Solve h² + 7h - 240 = 0, giving your answers correct to 1 decimal place.[3]
(c)(v)Calculate the perimeter of the triangle.[1]

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Mark scheme

Marking points from the official mark scheme (May/June 2015). The mark or mark type is shown in brackets.

[1] 2x(2x² – 5y) final answer
[1] (3a + b)(3a – b) final answer
[2] M1 for 7 = 12-8m or 7/4 = 3-2m; m = 5/8, 0.625
[2] M1 for h² + (h + 7)² = 23²; h² + (h + 7)² = 23² leading to correct rearrangement
[1] h/2 (h + 7) oe isw
[1] 120 cao
[3] B2 for one correct solution, or for 12.38 to 12.40 and -19.38 to -19.40 Or if in form P±√q / r, B1 for p = -7 and r = 2 and B1 for q = 1009 or √q = 31.7 to 31.8; 12.4, -19.4
[1ft] 54.76 to 54.8

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