9709. P3. Algebra. Past Exam Questions

9709/31/M/J/25q1 – Mark Scheme

(a) Sketch the graph of $y = \vert 2x-3 \vert$ . [1 mark]

(b) Solve the inequality $3x - 1 < \vert 2x-3 \vert$ [2 marks]

9709/31/M/J/25q5 – Mark Scheme

The polynomial 3x³ + pax² + 7a²x + qa³ is denoted by f(x), where p, q and a are constants and $a \leq 0$ .

When f(x) is divided by (x+2a) the remainder is -22a³. When f(x) is divided by (3x-a) the remainder is -a³.

Find the values of p and q. [5 marks]

9709/33/M/J/25q1 – Mark Scheme

(a) Sketch the graph of $y = \vert 3x - 2a \vert$ , where a is a positive constant. [1 mark]

(b) Hence or otherwise solve the inequality $\vert 3x - 2a \vert < x + 5a$ . [3 marks]