DSE - Algebra - 24ourMath™

1. Question

$(a-b)\left(a^{2}+a b-b^{2}\right)=$

$(a-b)^3$
$a^3 – b^3$
$a^3 – 2ab^2 + b^3$
$a^{3}-2 a^{2} b+2 a b^{2}+b^{3}$

2. Question

If $3 x-7 y=20=x+11 y \ ,$ then $\ y=$

-2
1
2
9

3. Question

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 only
II only
I and III only
II and III only

4. Question

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

${-4}$
$4$
$5$
$10$

5. Question

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

$0$
$2k$
$2k^3+2k$
$-2k^3+2k$

6. Question

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

${-3}$
${-2}$
$3$
$4$

7. Question

If $0.08957<x<0.08964$, which of the following is true?

$ x=0.089 \ $ (correct to 2 decimal places)
$ x=0.089 \ $ (correct to 2 significant figures)
$x=0.0896 \ $ (correct to 3 decimal places)
$x=0.0896 \ $ (correct to 3 significant figures)

8. Question

$ h =5-\dfrac{3}{k+4} $

$\dfrac{4 h-17}{5-h}$
$\dfrac{4 h-7}{5-h}$
$\dfrac{4 h-17}{5+h}$
$\dfrac{4 h-7}{5+h}$

9. Question

If $\alpha$ and $\beta$ are constants such that $(x-6)(x+\alpha)-3 \equiv(x-8)^{2}+\beta \ , \ $ then $\ \beta=$

${-26}$
${-10}$
${-7}$
${-6}$

10. Question

$\dfrac{\left(6 x^{7}\right)^{2}}{4 x^{5}}=$

$3x^4$
$9 x^{4}$
$3 x^{9}$
$9 x^{9}$

11. Question

The solution of $ \ {-7x} \gt 20 – 2x \ $ and $ \ 6x – 18 \lt 0 \ $ is

$ x \lt -4 \mbox{ or } x \gt 3. $
$ x \lt -4. $
$ x \lt 3. $
$ -4 \lt x \lt 3. $

DSE – Algebra

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