O-LevelMathematicsAlgebra and graphs4024/22 · Oct/Nov 2016 · Q211 Marks

Simplify (3a² / 10bc) ÷ (9a / 5b²c) .

(a)Simplify (3a² / 10bc) ÷ (9a / 5b²c) .[2]
(b)Simplify (h-k) / (5h-5k) .[2]
(c)Factorise 9m² - 4n² .[1]
(d)Factorise q (p - 2) + 3(2 – p) .[2]
(e)(i)Find the two solutions of 5x-1=±9.[2]
(e)(ii)The solutions of 5x-1=±9 are also the solutions of 5x² + Bx + C = 0, where B and C are integers. Find B and C.[2]

Mark scheme

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

[2] ab/6 Final answer
[1] M1 for correct transition to multiplication soi
[2] 1/5 oe
[1] B1 for 5(h-k)
[1] (3m-2n)(3m + 2n) Final ans.
[2] (p-2)(q-3) oe
[1] B1 for -q(2-p) or -3(p-2) seen or
[1] M1 if brackets removed and rearranged and extraction of p or 2 or for a correct extraction of a common factor after a sign error.
[2] 2 and 8/5 oe
[1] B1 for one correct or
[1] B1 for either or
[2] -2 and -16 cao
[1] M1 for (5x−1)² = 9² or
[1] (x-2)(x+8/5) = 0 oe ft or
[1] Uses e(i) to form simultaneous equations or
[1] (1±9) / (5*2) (from -B±√(B²-4AC))/(2A) )

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