# Test: Algebra I - Challenging

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Question 1:   If ${q}^{3}=27$ , solve $\frac{1}{2}{q}^{2}+2q$
$9$
$58\frac{1}{2}$
$6$
$10\frac{1}{2}$
Question 2:   If $s=-2$ , $t=\frac{1}{2}$ solve $-2{s}^{2}t+\frac{t}{s}$
$4$
$-3\frac{3}{4}$
$-4\frac{1}{4}$
$-2$
Question 3:   Simplify: $0.2x\left(-10{x}^{2}y+xy\right)$
$-2{x}^{3}y+0.2{x}^{2}y$
$2{x}^{2}{y}^{2}$
$-2.2{x}^{3}{y}^{2}$
$-1.8{x}^{3}y+0.2x{y}^{2}$
Question 4:   Simplify: $7\sqrt{3}\cdot {x}^{3}{y}^{2}\cdot \frac{\sqrt{13}}{21}$
${x}^{3}{y}^{2}\frac{\sqrt{13}}{3}$
${x}^{3}{y}^{2}\frac{\sqrt{39}}{3}$
$7{x}^{3}{y}^{2}$
$7{x}^{3}{y}^{2}\sqrt{13}$
Question 5:   Simplify: $3{x}^{2}y\sqrt{2}\cdot \left(-{y}^{4}\sqrt{6}\right)$
$-3{x}^{3}{y}^{5}\sqrt{6}$
$3{x}^{2}{y}^{5}\sqrt{12}$
$-6{x}^{2}{y}^{5}\sqrt{3}$
$-3{x}^{2}{y}^{5}\sqrt{8}$
Question 6:   Simplify: $\frac{2{p}^{2}\cdot 6{q}^{3}}{4p{q}^{2}}$
$2pq$
$p{q}^{2}$
$3pq$
${p}^{2}q$
Question 7:   Simplify: $\frac{{v}^{3}{u}^{2}\sqrt{3}}{u{v}^{2}}$
${v}^{2}u\sqrt{3}$
${u}^{2}v\sqrt{3}$
$\frac{{v}^{2}}{u}\sqrt{3}$
$vu\sqrt{3}$
Question 8:   Simplify: $\frac{5{x}^{3}\cdot 7{y}^{4}}{70{x}^{2}{y}^{2}}$
$x{y}^{2}$
$\frac{x{y}^{2}}{2}$
$\frac{{x}^{2}y}{2}$
$\frac{2xy}{5}$
Question 9:   Expand and simplify the expression: $2\left(x+y-z\right)-\left(2x-y+2z\right)$
$0$
$-4z$
$3y-4z$
$y$
Question 10:   Expand and simplify the expression: $-\frac{1}{2}\left({p}^{2}-2pq-r\right)-\left(-\frac{1}{2}{p}^{2}+2pq-\frac{1}{2}r\right)$
$-pq$
$-pq+r$
${p}^{2}-pq+r$
$pq-r$