# Test: Algebra III - Challenging

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Question 1:   If $x=-\frac{2}{3}$ , solve: $\frac{x-1}{x+1}$
$\frac{2}{9}$
$1\frac{1}{2}$
$-1$
$-5$
Question 2:   Solve: $a-\frac{a-3}{3}=4+3a$
$a=-2\frac{1}{7}$
$a=-\frac{9}{11}$
$a=-1\frac{2}{7}$
$a=\frac{9}{11}$
Question 3:   Expand: $\left(2x\sqrt{2}-1\right)\left(3x-2\sqrt{2}\right)$
$6{x}^{2}\sqrt{2}-11x+2\sqrt{2}$
$-5x\sqrt{2}+2\sqrt{2}$
$5{x}^{2}\sqrt{2}-11x+2\sqrt{2}-1$
$6{x}^{2}\sqrt{2}-5x+\sqrt{2}$
Question 4:   Expand: $2\left(a-\sqrt{3}\right)\left(3\sqrt{3}+a\right)$
$2{a}^{2}-3a\sqrt{3}-3\sqrt{3}$
${a}^{2}-2a\sqrt{3}+9$
$4a\sqrt{3}-18$
$2{a}^{2}+4a\sqrt{3}-18$
Question 5:   Expand: $\frac{1}{3}{\left(3x+6\right)}^{2}$
$2{x}^{2}+12x+4$
$3{x}^{2}+12x+12$
$6{x}^{2}+18x+3$
$9{x}^{2}+36x+6$
Question 6:   Expand: $\left(x-5\right){\left(x+2\right)}^{2}$
$2{x}^{3}-16x-20$
${x}^{3}-{x}^{2}-16x-20$
${x}^{3}-2{x}^{2}-24x-20$
$16x+20$
Question 7:   Expand: ${\left(3a-2\right)}^{2}\left(a-2\right)$
$9{a}^{3}+6{a}^{2}+20a-8$
$9{a}^{3}+30{a}^{2}-14a-1$
$9{a}^{3}-6{a}^{2}+20a-8$
$9{a}^{3}-30{a}^{2}+28a-8$
Question 8:   Expand: $4{x}^{2}\left({x}^{2}-1\right)-\left({x}^{2}+3\right)\left({x}^{2}-2\right)$
$3{x}^{4}+5{x}^{2}-6$
$3{x}^{4}-5{x}^{2}+6$
$5{x}^{4}-3{x}^{2}+6$
$5{x}^{4}-3{x}^{2}-6$
Question 9:   Rearrange the formula to make $y$ the subject: $\frac{x}{y}=\frac{a-b}{c}$
$y=\frac{xc}{a-b}$
$y=\frac{a-b}{xc}$
$y=\frac{x\left(a-b\right)}{c}$
$y=cx\left(a-b\right)$
Question 10:   Formula for the volume of a cylinder is: $V=\pi {r}^{2}\cdot h$ Rearrange the formula to make $r$ the subject
$r=\sqrt{\frac{\pi h}{V}}$
$r=\sqrt{h\cdot \frac{V}{\pi }}$
$r=\sqrt{\frac{V}{\pi h}}$
$r=\sqrt[3]{\pi \cdot \frac{V}{h}}$