1. Define Factor and Index.
2. Multiply $\frac{2x}{3}-\frac{1}{2}$ by $\frac{x^2}{2}-\frac{x}{3}+\frac{1}{4}$.
3. Solve $ax-b=a+\frac{b^{2}x}{a}$.
4. What sum of money exceeds four-ninths of it by 4s., 9d?
5. Resolve into factors $2a^5-2a{b}^2$.
6. Find G. C. M. of $a^{3}b{c}^2{d}^4$, $a^5{c}^3{d}^2$, $a^4{b}^3{d}^3$. Also of $x^2-y^2+ax+ay$, and $x^2+y^2+ax-ay-2xy$.
7. Find L. C. M. of $x^{5}y$, $x^3{y}^4$, $a^2{y}^2$. Also of ${\left(x-1\right)}^2$, $x^2-1$, ${\left(x+1\right)}^3$, $x^3+1$.
8. Simplify $\frac{1}{x+\frac{1}{x-\frac{x}{x+1}}}$; and $\left\{\frac{1}{3}+\frac{2a}{3\left(1-a\right)}\right\}\times \left\{\frac{1}{4}-\frac{a}{2\left(1+a\right)}\right\}$.
9. Solve $3x+\frac{y}{2}=7x-y=13$.
10. A is twice as old as B, and 3 times as old as C. One year ago, B was twice as old as C. Find A’s age.
11. Find ${\left(\frac{1}{x^2}-\frac{3}{y^2}\right)}^3$; and the square root of $\frac{a^2}{b^4}+\frac{b^4}{a^2}-2$.
12. Simplify $\frac{x^{1-m}}{x^{1-n}}$; $\sqrt[3]{x^{9a^3}.a^3}$; and $\frac{x^{-1}}{y^0}$.