# Test: Algebraic expressions II - Challenging

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Question 1:   Multiply  $4\frac{1}{3}a×2{b}^{2}$
$4\frac{1}{6}a{b}^{2}$
$8\frac{2}{3}a{b}^{2}$
$4\frac{2}{3}a{b}^{2}$
$8\frac{1}{3}a{b}^{2}$
Question 2:   Calculate  $3.85×5\frac{1}{7}-69.25:27.7$
$173$
$1.73$
$0.173$
$17.3$
Question 3:   Multiply fractions  $\frac{3}{{x}^{2}-{y}^{2}}×\frac{{\left(x+y\right)}^{2}}{3}$
$\frac{x-y}{x}$
$\frac{x+y}{x-y}$
$\frac{x+y}{x}$
$\frac{x-y}{x+y}$
Question 4:   Divide:  $\left(x-y\right):\left(\sqrt{x}-\sqrt{y}\right)$
$\sqrt{x}+\sqrt{y}$
$x+y$
$\sqrt{x}-\sqrt{y}$
$x-y$
Question 5:   Simplify:  $\frac{{a}^{7}{\left({a}^{2}\right)}^{-3}}{{a}^{6}}$
${a}^{-5}$
${a}^{5}$
$a$
${a}^{4}$
Question 6:   Factorise the expression:  ${a}^{2}+{b}^{2}-25+2ab$
$5\left(a-b\right)$
$\left(a+b+5\right)\left(a+b+5\right)$
$\left(a+b\right)\left(a-5\right)$
$\left(a+b+5\right)\left(a+b-5\right)$
Question 7:   Simplify:  ${\left(4x-5y\right)}^{2}-4x\left(4x-10y\right)$
$-25{y}^{2}$
$-25{x}^{2}$
$25{x}^{2}$
$25{y}^{2}$
Question 8:   Solve  $\frac{a-6-b}{12}$ ,  if  $a=11+b$
$\frac{7}{12}$
$-\frac{7}{12}$
$-\frac{5}{12}$
$\frac{5}{12}$
Question 9:   How will the volume of the cube change if each edge is increased by  $20%$ ?
Volume increases $1.728$ times
Volume decreases by $1.728$ times
Volume decreases by $1.2$ times
Volume increases $1.2$ times
Question 10:   Simplify the expression  $\sqrt{9-24x+16{x}^{2}}$ ,  if  $x>\frac{3}{4}$
$4x+3$
$3+4x$
$3-4x$
$4x-3$