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Date	November 2018	Marks available	2	Reference code	18N.1.AHL.TZ0.H_4
Level	Additional Higher Level	Paper	Paper 1	Time zone	Time zone 0
Command term	Find	Question number	H_4	Adapted from	N/A

Question

Consider the following system of equations where $a \in \mathbb{R}$ .

$2x + 4y - z = 10$

$x + 2y + az = 5$

$5x + 12y = 2a$ .

Find the value of $a$ for which the system of equations does not have a unique solution.

[2]

Find the solution of the system of equations when $a = 2$ .

[5]

Markscheme

* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.

an attempt at a valid method eg by inspection or row reduction (M1)

$2 \times {R_2} = {R_1} \Rightarrow 2a = - 1$

$\Rightarrow a = - \frac{1}{2}$ A1

[2 marks]

using elimination or row reduction to eliminate one variable (M1)

correct pair of equations in 2 variables, such as

$\left. {\begin{array}{*{20}{c}} {5x + 10y = 25} \\ {5x + 12y = 4} \end{array}} \right\}$ A1

Note: Award A1 for $z$ = 0 and one other equation in two variables.

attempting to solve for these two variables (M1)

$x = 26$ , $y = - 10.5$ , $z = 0$ A1A1

Note: Award A1A0 for only two correct values, and A0A0 for only one.

Note: Award marks in part (b) for equivalent steps seen in part (a).

[5 marks]

Examiners report

[N/A]

Syllabus sections

Topic 1—Number and algebra » SL 1.8—Use of technology to solve systems of linear equations and polynomial equations

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Topic 1—Number and algebra

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