Factorise the expression \({x^2} - 3x - 10\).

A function is defined as \(f(x) = 1 + {x^3}\) for \(x \in \mathbb{Z}{\text{, }} {- 3} \leqslant x \leqslant 3\).

(i)     List the elements of the domain of \(f(x)\).

(ii)    Write down the range of \(f(x)\).

\((x - 5)(x + 2)\)     (A1)(A1)     (C2)

Note: Award (A1) for \((x + 5)(x - 2)\), (A0) otherwise. If equation is equated to zero and solved by factorizing award (A1) for both correct factors, followed by (A0).

[2 marks]

(i)     \( - 3\), \( - 2\), \( - 1\), \(0\), \(1\), \(2\), \(3\)     (A1)(A1)     (C2)

Note: Award (A2) for all correct answers seen and no others. Award (A1) for 3 correct answers seen.

(ii)    \( - 26\), \( - 7\), 0,1, 2, 9, 28     (A1)(A1)     (C2)

Note: Award (A2) for all correct answers seen and no others. Award (A1) for 3 correct answers seen. If domain and range are interchanged award (A0) for (b)(i) and (A1)(ft)(A1)(ft) for (b)(ii).

[4 marks]

It was surprising how many candidates could not factorise this expression. Of those that could some went on to find the zeros of a quadratic equation which was not what the question was asking. Some confused domain and range and many did not write down all the values when they did know domain and range.

It was surprising how many candidates could not factorise this expression. Of those that could some went on to find the zeros of a quadratic equation which was not what the question was asking. Some confused domain and range and many did not write down all the values when they did know domain and range.