# Test: Algebraic expressions II - Ambitious

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Question 1:   Simplify the expression  $2a+\frac{1}{3}b-5a+d$
$-3a+\frac{1}{3}b+d$
$3a+d$
$3a-d$
$3a+\frac{1}{3}b+d$
Question 2:   Expand  $\left(3a-1\right)\left(-3\right)$
$9a-3$
$9a+3$
$-6a$
$-9a+3$
Question 3:   Simplify the expression  $3\left(b-2\right)-\left(a+0.4\right)$
$-3b-a-6.4$
$3b-a+6.4$
$3b-a-6.4$
$3b+a+6.4$
Question 4:   Simplify  ${\left(\frac{2}{5}{a}^{2}{b}^{7}\right)}^{3}$
$\frac{8}{125}ab$
$\frac{8}{125}{a}^{6}{b}^{21}$
$\frac{8}{125}{a}^{2}{b}^{7}$
$\frac{2}{5}{a}^{6}{b}^{21}$
Question 5:   Simplify the expression  ${\left(a+2\right)}^{2}-{\left(a-2\right)}^{2}$
$8{a}^{2}$
$-8{a}^{2}$
$-8a$
$8a$
Question 6:   Reduce the fraction  $\frac{a-b}{{a}^{2}+{b}^{2}-4ab+2ab}$
$\frac{1}{a-b}$
$\frac{a}{a-b}$
$\frac{1}{b-a}$
$a-b$
Question 7:   Reduce the fraction  $\frac{x+\sqrt{x}}{\sqrt{x}+1}$
$x+1$
$\sqrt{x}+1$
$x$
$\sqrt{x}$
Question 8:   Get rid of irrationality in the denominator  $\frac{\sqrt{2}-a}{\sqrt{2}}$
$\frac{2+\sqrt{2}}{2}$
$\frac{2+a}{2}$
$\frac{2-a}{2}$
$\frac{2-\sqrt{2}a}{2}$
Question 9:   Using the formula  $s={s}_{0}+vt$ ,  rearrange it to find  $t$ 
$t=vs-{s}_{0}$
$t=\frac{s-{s}_{0}}{v}$
$t=\left(s-{s}_{0}\right)v$
$t=\frac{v}{s-{s}_{0}}$
Question 10:   One of the roots of equation  ${x}^{2}+3x+b$  is  $5$ .  Find  $b$  and the second root of the equation.
$\begin{array}{l}b=-40\\ {x}_{2}=-8\end{array}$

$\begin{array}{l}b=30\\ {x}_{2}=10\end{array}$

$\begin{array}{l}b=-30\\ {x}_{2}=-10\end{array}$

$\begin{array}{l}b=40\\ {x}_{2}=8\end{array}$