Singapore GCE O-Level · Additional Mathematics

Quadratic functions and inequalities

30 practice questions, each with the answer and an explanation.

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Random questions from this topic, one at a time. You see the answer and the explanation straight after each one.

All 30 questions

Find the set of values of $k$ for which the equation $x^{2} + k x + 4 = 0$ has real roots.
Find the set of values of $k$ for which the equation $x^{2} + k x + 9 = 0$ has real roots.
Find the set of values of $k$ for which the equation $x^{2} + k x + 16 = 0$ has real roots.
Find the set of values of $k$ for which the equation $x^{2} + k x + 25 = 0$ has real roots.
Find the set of values of $k$ for which the equation $x^{2} + k x + 36 = 0$ has real roots.
Find the set of values of $k$ for which the equation $x^{2} + k x + 1 = 0$ has real roots.
Express $x^{2} + 6 x + 5$ in the form $(x + p)^{2} + q$ . What is the minimum value of the expression?
Express $x^{2} + 8 x + 3$ in the form $(x + p)^{2} + q$ . What is the minimum value of the expression?
Express $x^{2} + 4 x - 1$ in the form $(x + p)^{2} + q$ . What is the minimum value of the expression?
Express $x^{2} + 10 x + 20$ in the form $(x + p)^{2} + q$ . What is the minimum value of the expression?
Express $x^{2} - 6 x + 4$ in the form $(x + p)^{2} + q$ . What is the minimum value of the expression?
Express $x^{2} - 8 x + 7$ in the form $(x + p)^{2} + q$ . What is the minimum value of the expression?
Express $x^{2} + 12 x + 30$ in the form $(x + p)^{2} + q$ . What is the minimum value of the expression?
Express $x^{2} - 4 x + 9$ in the form $(x + p)^{2} + q$ . What is the minimum value of the expression?
Solve the inequality $x^{2} - 5 x + 4 < 0$ .
Solve the inequality $x^{2} - x - 6 < 0$ .
Solve the inequality $x^{2} - 9 x + 14 < 0$ .
Solve the inequality $x^{2} + 2 x - 3 < 0$ .
Solve the inequality $x^{2} - x - 20 < 0$ .
Solve the inequality $x^{2} + 6 x + 5 < 0$ .
The roots of $x^{2} - 5 x + 3 = 0$ are $α$ and $β$ . Find the value of $α^{2} + β^{2}$ .
The roots of $2 x^{2} + 3 x - 4 = 0$ are $α$ and $β$ . Find the value of $α^{2} + β^{2}$ .
The roots of $x^{2} + 4 x + 1 = 0$ are $α$ and $β$ . Find the value of $α^{2} + β^{2}$ .
The roots of $3 x^{2} - 6 x + 2 = 0$ are $α$ and $β$ . Find the value of $α^{2} + β^{2}$ .
The roots of $2 x^{2} - 7 x + 2 = 0$ are $α$ and $β$ . Find the value of $α^{2} + β^{2}$ .
The line $y = 2 x + k$ is a tangent to the curve $y = x^{2} + 4$ . Find the value of $k$ .
The line $y = 4 x + k$ is a tangent to the curve $y = x^{2} + 5$ . Find the value of $k$ .
The line $y = 6 x + k$ is a tangent to the curve $y = x^{2} + 10$ . Find the value of $k$ .
The line $y = - 2 x + k$ is a tangent to the curve $y = x^{2} + 6$ . Find the value of $k$ .
The line $y = 4 x + k$ is a tangent to the curve $y = x^{2} + 8$ . Find the value of $k$ .

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Quadratic functions and inequalities

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