O-LevelMathematicsAlgebra and graphs4024/22 · Oct/Nov 2015 · Q613 Marks

Solve the equation (x + 7/2) = ± √5/2 . Give both answers correct to 2 decimal places.

(a)(i)Solve the equation (x + 7/2) = ± √5/2 . Give both answers correct to 2 decimal places.[2]
(a)(ii)The solutions of (x + 7/2)² = ± √5/2 are also the solutions of x² + Bx + C = 0, where B and C are integers. Find B and C.[3]
(b)Solve the inequality 7 – 3x > 13.[2]
(c)Factorise 6x – 3yt + 18y – xt .[2]
(d)Solve these simultaneous equations. 3a + 4b = -13, 5a + 6b = -11.[4]

Mark scheme

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

[2] B1 for one value SC1 for both -4.6 and -2.4
-4.62 -2.38 final answer
[3] M1 for (x+7/2)² = 5/4 and B1 for one correct value
(B =) 7 (C=) 11
[2] M1 for isolating 3x and – 6 soi
x < -2
[2] M1 for the correct extraction of a common factor at any stage
(x + 3y)(6-t) oe
[4] M1 for equalising one set of coefficients or substitution and a further M1 for eliminating one variable or simplifying an equation in one variable and A1 for 17 and A1 for - 16 After A0, SC1 for correct substitution into one of the original equations to find the other variable
(a = ) 17 (b =) – 16

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