# Test: Algebraic expressions I - Challenging

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Question 1:   Simplify the expression ${x}^{2}+\left({x}^{2}+3\right)+x\left(2-0.5x\right)$
$1.5{x}^{2}+2x+3$
$0.5{x}^{2}+3$
$1.5{x}^{2}-2x+3$
$1.5{x}^{2}-2x-3$
Question 2:   Simplify: ${\left(-4{a}^{5}{b}^{3}\right)}^{2}\left(-\frac{1}{2}ab\right)$
$8{a}^{11}{b}^{7}$
$-4{a}^{8}{b}^{6}$
$4{a}^{8}{b}^{6}$
$-8{a}^{11}{b}^{7}$
Question 3:   Find $24%$ of $\left(2\frac{1}{7}+\frac{3}{14}\right):\left(4\frac{5}{7}\right)$
$12$
$0.12$
$120$
$1.2$
Question 4:   The difference in the squares of two numbers is 25, the sum of these numbers is also 25. Find these numbers.
Question 5:   Simplify: ${\left(1+{c}^{2}\right)}^{{}^{2}}-2{c}^{2}$
$1-c$
$1+c$
$1-{c}^{2}$
$1+{c}^{4}$
Question 6:   Simplify: ${\left(2{x}^{2}y\right)}^{3}{\left(-x{y}^{3}\right)}^{2}$
$-2xy$
$2{x}^{7}{y}^{8}$
$8{x}^{8}{y}^{9}$
$-8{x}^{8}{y}^{9}$
Question 7:   Factorise: $27{a}^{2}-{a}^{5}$
${a}^{2}\left(3-a\right)\left(9+3a+{a}^{2}\right)$
${a}^{2}\left(3+a\right)\left(9+3a+{a}^{2}\right)$
$\left(3-a\right)\left(9+3a+{a}^{2}\right)$
$\left(3-a\right)\left(3+a\right)$
Question 8:   Reduce: $\frac{a+9-6\sqrt{a}}{a-9}$
$\frac{\sqrt{a}-3}{\sqrt{a}+3}$
$\frac{\sqrt{a}+3}{\sqrt{a}-3}$
$6\sqrt{a}$
$\frac{a+3}{a-3}$
Question 9:   Remove irrationals from the denominator: $\frac{\sqrt{2}-a}{\sqrt{2}+a}$
$\frac{{\left(\sqrt{2}-a\right)}^{2}}{2-{a}^{2}}$
$\frac{\sqrt{2}}{2}$
$\frac{{\left(\sqrt{2}+a\right)}^{2}}{2+a}$
$\frac{\sqrt{2}+a}{2}$
Question 10:   Determine value of $m$ for which equations have the same root: $2x-3=7$ and $m-2x=1$
$-11$
$11$
$12$
$-12$