QSM – Algebra – Maths with Mr. Lai

Welcome to your DSE Algebra

1.

Let $ k $ be a constant such that $ 2 x^{4}+k x^{3}-4 x-20\, $ is divisible by $2 x+k .$ Find $k $.

$ -4 $

$ 4 $

$ 10 $

$ 5 $

2.

Which of the following statements about the graph of $ y=(3-x)(x+2)+6 $ is/are true? \[ \begin{array}{ll} \text{I. } \text{ The graph opens downwards.} \\\text{II. } \text{ The graph passes through the point (1, 10). } \\\text{III.} \text{ The } x \text{-intercepts of the graph are } {-3} \text{ and } 4 . \end{array} \]

I and III only

II and III only

I only

II only

3.

Let $k$ be a constant. If $f(x)=x^{3}+ kx^{2}+k,$ then $f(k)+f(-k)=$

0

$ -2k^3 + 2k $

$2k $

$ 2k^3+2k$

4.

The least integer satisfying the compound inequality $\dfrac{3 x-5}{4} > 1$ or $ -2(x-5)+5 < 21 $ is

${-2}$

${-3}$

$3$

$4$