2.12.1 Quadratic Functions, SPM Practice (Paper 1)

Question 1:
Solve the following quadratic equations by factorisation.

\begin{matrix} (a) x^{2} - 5 x - 10 = - 4 (b) 3 - x - 2 x^{2} = 0 (c) 11 a = 2 a^{2} + 12 (d) \frac{2 x + 7}{3 x - 2} = x \end{matrix}

$\begin{array}{l} (a) x^{2} - 5 x - 10 = - 4 \\ (b) 3 - x - 2 x^{2} = 0 \\ (c) 11 a = 2 a^{2} + 12 \\ (d) \frac{2 x + 7}{3 x - 2} = x \end{array}$

Solution:

Question 2:
Solve the following quadratic equations by completing the square.

\begin{matrix} (a) 5 x^{2} + 10 x - 3 = 0 (b) 2 x^{2} - 5 x - 6 = 0 \end{matrix}

$\begin{array}{l} (a) 5 x^{2} + 10 x - 3 = 0 \\ (b) 2 x^{2} - 5 x - 6 = 0 \end{array}$

Solution:

Question 3:
Solve the following quadratic equations by using quadratic formula. Give your answer in four significant figures.

\begin{matrix} (a) (x + 1) (x - 5) = 15 (b) \frac{x^{2} + 3 x - 2}{x^{2} - x - 1} = 3 \end{matrix}

$\begin{array}{l} (a) (x + 1) (x - 5) = 15 \\ (b) \frac{x^{2} + 3 x - 2}{x^{2} - x - 1} = 3 \end{array}$

Solution:

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