Singapore GCE O-Level · Additional Mathematics

Algebra, Quadratic Inequalities and Polynomials

6 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 6 questions

Find the range of values of $k$ for which the quadratic equation $x^{2} + (k - 2) x + (k + 1) = 0$ has real and distinct roots.
The polynomial $P (x) = 2 x^{3} - 5 x^{2} + a x + b$ leaves a remainder of $4$ when divided by $(x - 1)$ , and a remainder of $- 26$ when divided by $(x + 2)$ . Find the values of $a$ and $b$ .
Solve the logarithmic equation: $lo g_{3} (x + 2) + lo g_{3} (x - 4) = 3$ .
In the binomial expansion of $(2 x - \frac{1}{x ^{2}})^{9}$ , find the term independent of $x$ .
Solve the simultaneous equations: $2^{x + y} = 32$ and $3^{2 x - y} = 3$ .
The roots of the quadratic equation $2 x^{2} - 6 x + 1 = 0$ are $α$ and $β$ . Find the exact value of $α^{3} + β^{3}$ .

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