Solve the following equation for x

\(3(2x +1) − 2(3 − x)=13\).

Factorize the expression \(x^2 + 2x − 3\).

Find the positive solution of the equation

\(x^2 + 2x − 6 = 0\).

\(6x+ 3 - 6 + 2x = 13\)     (M1)

\(8x = 16\)

\(x = 2\)     (A1)     (C2)

[2 marks]

\((x + 3) (x - 1)\)     (A1)(A1)     (C2)

[2 marks]

\(x = 1.64575...\)

\(x = 1.65\)     (A2)

If formula is used award (M1)(A1) for correct solution. If graph is sketched award (M1)(A1) for correct solution.     (C2)

[2 marks]

(a) Many candidates forgot that a minus times a minus gives a plus and so did not solve the equation correctly.

(b) A good attempt was made at factorising the function although \(x(x + 2)  – 3\) was seen frequently too.

(a) Many candidates forgot that a minus times a minus gives a plus and so did not solve the equation correctly.

(b) A good attempt was made at factorising the function although \(x(x + 2) – 3\) was seen frequently too.

(c) Few candidates realised that they had to use their GDC to find this answer and hence there were few correct answers. Some did not read the question correctly and solved part (b) to find the positive solution of the expression they had factorised.