2.12.1 Quadratic Functions, SPM Practice (Paper 1 Question 1 – 5)

Question 1:
Solve the following quadratic equations by factorisation.
$\begin{array}{l}\text{(a) }{x}^2-5x-10=-4\\ \text{(b) }3-x-2x^2=0\\ \text{(c) }11a=2a^2+12\\ \text{(d) }\frac{2x+7}{3x-2}=x\end{array}$

Solution:

Question 2:
Solve the following quadratic equations by completing the square.
$\begin{array}{l}\text{(a) }5x^2+10x-3=0\\ \text{(b) }2x^2-5x-6=0\end{array}$

Solution:

Question 3:
Solve the following quadratic equations by using quadratic formula. Give your answer in four significant figures.
$\begin{array}{l}\text{(a) }(x+1)(x-5)=15\\ \text{(b) }\frac{x^2+3x-2}{x^2-x-1}=3\end{array}$

Solution:

Question 4:
If the roots of $2x^2+4x-1=0\text{ are }\alpha \text{ and }\beta \text{,}$ find the equations whose roots are
$\begin{array}{l}\text{(a) }{\alpha }^2,{\beta }^2\\ \text{(b) }\alpha -\beta ,\beta -\alpha \end{array}$

Solution:

Question 5:
Write and simplify the equation whose roots are double the roots of $3x^2-5x-1=0$ , without solving the given equation.

Solution: