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## Simplification of Linear Expressions

 1 $2x-5y+3x$ 2 $4x+2y-6x+3y$ 3 $-3x-2y-\left(-5x\right)+\left(-y\right)$ 4 $4x+\left(3x-2y\right)$ 5 $2x-5y+3x$ 6 $\left(8x+2\right)-\left(3x-5\right)$ 7 $\left(2x+3y+4\right)+\left(2y-3\right)$ 8 $\left(3x-4y-1\right)-\left(-4x+8y-7\right)$ 9 $4x+\left[2x-\left(3x+5\right)\right]$ 10 $7x-3y-\left[2x-\left(6x-5y\right)\right]$

## Simplification of Linear Expressions with Fractional Coefficients

 1 $\frac{1}{5}x+\frac{3}{5}x$ 2 $\frac{5}{6}x-\frac{2}{3}x$ 3 $\frac{1}{4}x+\frac{1}{3}y-\frac{1}{5}x$ 4 $2x-\frac{4}{9}y-\frac{4}{3}x-\frac{2}{3}y$ 5 $\frac{7x+3}{8}-\frac{3x}{8}$ 6 $\frac{5x}{8}+\frac{3x+1}{4}$ 7 $\frac{2x+y}{3}-\frac{x}{2}$ 8 $\frac{3x+5y}{4}+\frac{2x-y}{5}$ 9 $\frac{x-5}{3}+\frac{x+3}{5}+\frac{4x-7}{15}$ 10 $\frac{x+3y}{3}+\frac{2\left(3x-y\right)}{2}+2y$

## Addition and Subtraction of Algebraic Fractions

 1 $\frac{1}{x}+\frac{1}{4x}$ 2 $\frac{3}{5r}+\frac{7}{3r}$ 3 $\frac{1}{m}-\frac{1}{7m}$ 4 $\frac{7}{3s}-\frac{6}{5s}$ 5 $\frac{3h}{8k}-\frac{5}{2{k}^{2}}$ 6 $\frac{3h}{8k}-\frac{5}{2{k}^{2}}$ 7 $\frac{3}{2r+1}+\frac{4}{2r-3}$ 8 $\frac{7}{y+3}-\frac{2}{y}$ 9 $\frac{10}{m+2}-\frac{9}{m-2}$ 10 $\frac{8}{{y}^{2}-4}+\frac{3}{y+2}$

## Expansion of Linear Expressions

 1 $4\left(2x-5y\right)$ 2 $-2\left(3x-4y\right)$ 3 $3\left(2x-3y\right)+3x$ 4 $8x-3\left(x+3y\right)$ 5 $3\left(3x+5y\right)+3x-7y$ 6 $4\left(4x-1\right)-3\left(5x-6\right)$ 7 $4\left(4x-3y+2\right)+3\left(2x+5y-3\right)$ 8 $2\left(6x+5y-3\right)-3\left(2x-3y-4\right)$ 9 $4\left[5\left(3x+4y\right)+2\left(x-2y\right)\right]$ 10 $-2\left[5\left(2x-5y\right)-2\left(x-3y\right)\right]$

## Expansion of Algebraic Expressions

 1 $3x\left(4+y\right)$ 2 $-4y\left(2x+3\right)$ 3 $x\left(3x-y\right)$ 4 $-3y\left(2y-3x\right)$ 5 $2x\left(y+z\right)+3x\left(2y+z\right)$ 6 $2x\left(y+z\right)+3x\left(2y+z\right)$ 7 $\left(x+2y\right)\left(x+3y\right)$ 8 $\left(2x+5y\right)\left(3x-y\right)$ 9 $\left({x}^{2}+6\right)\left(2x+3\right)$ 10 $2\left(2x+1\right)\left(3x+2\right)$

## Expansion using Algebraic Identities

 1 ${\left(x+5\right)}^{2}$ 2 ${\left(3x+4\right)}^{2}$ 3 ${\left(3x+4\right)}^{2}$ 4 ${\left(5-2x\right)}^{2}$ 5 $\left(x+2\right)\left(x-2\right)$ 6 $\left(4x+3\right)\left(4x-3\right)$ 7 ${\left(x+3y\right)}^{2}$ 8 ${\left(x-7y\right)}^{2}$ 9 $\left(2x+y\right)\left(2x-y\right)$ 10 $\left(4x-5y\right)\left(4x+5y\right)$

## Factorisation by Common Factors

 1 $4x+12$ 2 $6x-9$ 3 $xy-xz$ 4 $xy-xz$ 5 $5x+5y-5z$ 6 $20x-18y+14z$ 7 $xy+xw+2xz$ 8 $x\left(x+2\right)+8\left(x+2\right)$ 9 $x\left(x-5\right)-3\left(x-5\right)$ 10 $8ab\left(x-5\right)-12b\left(x-5\right)$

## Factorisation by Grouping

 1 $xy+y+x+1$ 2 $ax-2x+a-2$ 3 $xy+3y+2x+6$ 4 $ab-6b-2a+12$ 5 $ax+bx+4a+4b$ 6 $15pr-10qr-6p+4q$ 7 $pqr+3r+pq+3$ 8 $pqr+3r+pq+3$ 9 $6xyz+9z+10xy+15$ 10 $6kmn-8n+21km-28$

## Factorisation using Algebraic Identities

 1 ${x}^{2}+2x+1$ 2 ${x}^{2}+2x+1$ 3 ${x}^{2}-9$ 4 $4{x}^{2}+12x+9$ 5 $25{x}^{2}-20x+4$ 6 $9{x}^{2}-16$ 7 $2{x}^{2}+12x+18$ 8 $2{x}^{2}-20x+50$ 9 $3{x}^{2}-48$ 10 $16-36{x}^{2}$

 1 ${x}^{2}+3x+2$ 2 ${x}^{2}+4x-12$ 3 ${x}^{2}-7x+10$ 4 ${x}^{2}-6x-16$ 5 $2{x}^{2}+14x+12$ 6 $3{x}^{2}-12x+9$ 7 $2{x}^{2}+5x+3$ 8 $3{x}^{2}+5x-2$ 9 $4{x}^{2}-13x+3$ 10 $4{x}^{2}-13x+3$

## Addition and Subtraction of Algebraic Fractions

 1 $\frac{1}{x}+\frac{1}{4x}$ 2 $\frac{3}{5r}+\frac{7}{3r}$ 3 $\frac{1}{m}-\frac{1}{7m}$ 4 $\frac{7}{3s}-\frac{6}{5s}$ 5 $\frac{3h}{8k}-\frac{5}{2{k}^{2}}$ 6 $\frac{4}{x+2}+\frac{3}{x}$ 7 $\frac{3}{2r+1}+\frac{4}{2r-3}$ 8 $\frac{7}{y+3}-\frac{2}{y}$ 9 $\frac{10}{m+2}-\frac{9}{m-2}$ 10 $\frac{8}{{y}^{2}-4}+\frac{3}{y+2}$

## Multiplication and Division of Algebraic Fractions

 1 $\frac{x}{6y}×\frac{2y}{5}$ 2 $\frac{4p}{3q}×\frac{5{q}^{2}}{2{p}^{2}}$ 3 $\frac{4s{t}^{3}}{3r}×\frac{5{r}^{2}}{8s{t}^{2}}$ 4 $\frac{2x}{3y}÷\frac{x}{5}$ 5 $\frac{3{m}^{3}}{4{n}^{2}}÷\frac{m}{8{n}^{2}}$ 6 $\frac{5{a}^{2}}{{b}^{3}}÷\frac{10{a}^{3}}{3{b}^{2}}$ 7 $\frac{x+y}{x-y}×\frac{2\left(x-y\right)}{3x+3y}$ 8 $\frac{{p}^{2}q+4q}{3p-2r}×\frac{6p-4r}{3{p}^{2}+12}$ 9 $\frac{6y-4z}{3y+6z}÷\frac{4y-2z}{9y+3z}$ 10 $\frac{3{k}^{2}+kn}{mn-4{m}^{2}}÷\frac{2n+6k}{4m-n}$

## Manipulation of Algebraic Formulae

 1 Make $x$ the subject of $2y=3x+5$ 2 Make $m$ the subject of $4n=9m-3$ 3 Make $a$ the subject of $2a-13b=5b$ 4 Make $x$ the subject of $4x-y=x+5$ 5 Make $p$ the subject of $9p-4d=4p+5$ 6 Make $m$ the subject of $5m+2n=10m+9$ 7 Make $a$ the subject of $\frac{a}{2b}-3d=4x+5$ 8 Make $p$ the subject of $\sqrt{6p}=2q$ 9 Make $m$ the subject of $\sqrt{7m}=3n-4$ 10 Make $x$ the subject of $y=\frac{1-4x}{6+5x}$

## Solving Linear Equations

 1 $x+4=7$ 2 $x-2=1$ 3 $4x=12$ 4 $2x+3=7$ 5 $5x+8=3x$ 6 $4x-5=3x$ 7 $5x=3x+10$ 8 $4x+3=2x+9$ 9 $6x+3=4x-1$ 10 $7x-2=3x-10$

## Solving Linear Equations with Brackets

 1 $4\left(3x+5\right)=7x$ 2 $2\left(2x+3\right)=x+9$ 3 $3\left(4-3x\right)=2x+1$ 4 $4\left(2x-5\right)=5x-6$ 5 $2\left(5-2x\right)=3x-4$ 6 $4\left(6-2x\right)=-3x+4$ 7 $5\left(2x+1\right)=3\left(2x+3\right)$ 8 $3\left(3x-5\right)=2\left(2x-7\right)$ 9 $2\left(5x-7\right)=-3\left(3x+11\right)$ 10 $3\left(3x-5\right)=-4\left(2x-9\right)$

## Solving Linear Equations involving Fractional Coefficients

 1 $\frac{1}{5}x=\frac{6}{5}$ 2 $\frac{7x}{5}-\frac{2x}{5}=8$ 3 $\frac{5x}{6}+\frac{4x}{3}=7+x$ 4 $\frac{1}{3}x+5=10-\frac{1}{6}x$ 5 $\frac{x+3}{4}=6$ 6 $\frac{5x+6}{3}-7=0$ 7 $\frac{x+7}{5}-6=2$ 8 $\frac{4\left(2x-11\right)}{5}+2=5x$ 9 $\frac{6-x}{3}=\frac{x+2}{5}$ 10 $\frac{9-x}{3}-\frac{x+2}{6}=3$

## Solving Linear Equations involving Algebraic Fractions

 1 $\frac{6}{x}=3$ 2 $\frac{3}{x}=\frac{1}{4}$ 3 $\frac{4}{x+3}=-2$ 4 $\frac{2}{x+4}=\frac{1}{3}$ 5 $\frac{x}{x+5}=6$ 6 $\frac{x}{x+1}=\frac{3}{4}$ 7 $\frac{5}{2x}=10$ 8 $\frac{1}{3x-2}=-8$ 9 $\frac{3}{x+4}=\frac{1}{x+2}$ 10 $\frac{4}{x-2}-\frac{5}{x+4}=0$

## Solving Quadratic Equations (by Factorisation)

 1 $x\left(x+3\right)=0$ 2 $\left(x+1\right)\left(x-4\right)=0$ 3 ${x}^{2}+3x=0$ 4 $3{x}^{2}-6x=0$ 5 ${x}^{2}-2x-8=0$ 6 ${x}^{2}+5x+6=0$ 7 $2{x}^{2}+5x-12=0$ 8 ${x}^{2}+10x=-16$ 9 $\left(x-3\right)\left(x-5\right)=3$ 10 $\left(x+2\right)\left(x+4\right)=15$

## Solving Quadratic Equations (by Completing the Square)

 1 ${\left(x+3\right)}^{2}=16$ 2 ${\left(x-4\right)}^{2}=4$ 3 ${\left(3x+7\right)}^{2}=16$ 4 ${\left(2x-7\right)}^{2}=9$ 5 ${\left(x+6\right)}^{2}-49=0$ 6 ${\left(2x+3\right)}^{2}-25=0$ 7 ${\left(x+4\right)}^{2}+3=28$ 8 ${x}^{2}+12x=-20$ 9 ${x}^{2}+4x-21=0$ 10 ${x}^{2}+7x+8=2$

## Solving Quadratic Equations (by General Formula)

 1 ${x}^{2}-5x+2=0$ 2 $3{x}^{2}-6x+2$ 3 $-2{x}^{2}-7x+3=0$ 4 ${x}^{2}-5x=-1$ 5 $2{x}^{2}+9x=-3$ 6 ${x}^{2}+2=5x$ 7 $x\left(x+3\right)-2=0$ 8 $x\left(1-3x\right)+8=0$ 9 $x\left(x+3\right)+2x+5=0$ 10 $x\left(x+3\right)=6\left(x+2\right)$

## Solving Equations Reducible to Quadratic Equations (by Factorisation)

 1 $\frac{18}{x}=2x$ 2 $\frac{8}{x-2}=x$ 3 $\frac{4}{3x-5}=2x$ 4 $\frac{8}{x}=6-x$ 5 $\frac{12}{x+7}=6-x$ 6 $\frac{8}{x}=3x-2$ 7 $\frac{1}{x-2}=2x-3$ 8 $\frac{19}{4x+3}=2x-7$ 9 $4x+\frac{3}{2x}=5$ 10 $\frac{x-9}{x-4}=x+3$

## Solving Equations Reducible to Quadratic Equations (by General Formula)

 1 $\frac{3}{x}=x$ 2 $\frac{5}{x+2}=x$ 3 $\frac{8}{6-5x}=-2x$ 4 $\frac{4}{x-5}=x-4$ 5 $\frac{5}{x}=4x-10$ 6 $\frac{2}{x+4}=6-3x$ 7 $x+\frac{5}{x}=10$ 8 $\frac{x}{x-1}=x-1$ 9 $\frac{x+7}{7-x}=x$ 10 $\frac{x-5}{x+3}=2x+19$

## Solving Simple Linear Inequalities

 1 $x+3>7$ 2 $x-5<-6$ 3 $5x-8\ge 12$ 4 $4x+6\le -10$ 5 $5x+4<7x$ 6 $3x+14>10x$ 7 $6-x\le x-16$ 8 $15-x\ge x+7$ 9 $7x>4\left(3x-2\right)$ 10 $8x+3<3\left(7-2x\right)$

## Solving Linear Inequalities

 1 $2x>8$ 2 $5x<30$ 3 $4x\ge 10$ 4 $9x\le 6$ 5 $-7x<28$ 6 $-3x>-12$ 7 $-6x\ge -36$ 8 $-5x\le -40$ 9 $\frac{1}{2}x>5$ 10 $\frac{2}{3}x<6$

 1 $x\left(x+4\right)>0$ 2 $x\left(2x-7\right)\ge 0$ 3 $\left(x+2\right)\left(x-4\right)>0$ 4 $\left(3x-4\right)\left(x-5\right)<0$ 5 ${x}^{2}-6x<0$ 6 ${x}^{2}-25\le 0$ 7 ${x}^{2}+8>12$ 8 $16{x}^{2}+5<21$ 9 ${x}^{2}+3x-10\le 0$ 10 $3{x}^{2}+6x-24<0$

## Solving Equations involving Indices

 1 ${2}^{x}=16$ 2 ${3}^{-x}=243$ 3 ${5}^{x}=\frac{1}{125}$ 4 ${6}^{-x}=\frac{1}{216}$ 5 ${2}^{4x}=256$ 6 ${3}^{-4x}=81$ 7 ${3}^{-6x}=\frac{1}{243}$ 8 ${4}^{x}=32$ 9 ${25}^{-x}=125$ 10 ${2}^{5x+3}=256$

## Addition and Subtraction of Matrices

 1 $\left(\begin{array}{c}6\\ 1\end{array}\right)+\left(\begin{array}{c}2\\ -5\end{array}\right)$ 2 $\left(\begin{array}{c}7\\ -2\end{array}\right)-\left(\begin{array}{c}-2\\ 3\end{array}\right)$ 3 $\left(\begin{array}{cc}4& 7\end{array}\right)+\left(\begin{array}{cc}3& -6\end{array}\right)$ 4 $\left(\begin{array}{cc}5& 0\end{array}\right)-\left(\begin{array}{cc}1& -2\end{array}\right)$ 5 ${x}^{2}-2x-8=0$ 6 $\left(\begin{array}{c}-9\\ 7\\ -8\end{array}\right)-\left(\begin{array}{c}3\\ 3\\ -10\end{array}\right)$ 7 $\left(\begin{array}{ccc}3& 0& -2\end{array}\right)+\left(\begin{array}{ccc}-5& 9& 7\end{array}\right)$ 8 $\left(\begin{array}{ccc}0& 4& -3\end{array}\right)-\left(\begin{array}{ccc}2& 2& 9\end{array}\right)$ 9 $\left(\begin{array}{cc}-4& 2\\ 4& 9\end{array}\right)+\left(\begin{array}{cc}-3& 8\\ 2& -2\end{array}\right)$ 10 $\left(\begin{array}{cc}-4& -4\\ 3& 5\end{array}\right)-\left(\begin{array}{cc}-6& 6\\ 1& -9\end{array}\right)$

## Multiplication of a Matrix by a Real Number

 1 $3\left(\begin{array}{c}3\\ -6\end{array}\right)$ 2 $3\left(\begin{array}{c}-4\\ -2\end{array}\right)+\left(\begin{array}{c}4\\ 1\end{array}\right)$ 3 $2\left(\begin{array}{c}6\\ 3\end{array}\right)-\left(\begin{array}{c}-7\\ 5\end{array}\right)$ 4 $5\left(\begin{array}{cc}1& -1\end{array}\right)+\left(\begin{array}{cc}9& -3\end{array}\right)$ 5 $4\left(\begin{array}{cc}2& -5\end{array}\right)-\left(\begin{array}{cc}-2& -9\end{array}\right)$ 6 $3\left(\begin{array}{cc}4& 6\\ 6& 2\end{array}\right)+\left(\begin{array}{cc}-7& -10\\ -6& 5\end{array}\right)$ 7 $2\left(\begin{array}{cc}3& -9\\ 3& -5\end{array}\right)-\left(\begin{array}{cc}10& 0\\ 6& 5\end{array}\right)$ 8 $3\left(\begin{array}{cc}5& -7\\ 3& -3\\ 6& -2\end{array}\right)+2\left(\begin{array}{cc}-1& 6\\ -7& 4\\ -3& 0\end{array}\right)$ 9 $4\left(\begin{array}{cc}1& -1\\ 4& -1\\ 2& -3\end{array}\right)-\left(\begin{array}{cc}1& 3\\ 5& -3\\ 0& 2\end{array}\right)$ 10 $3\left(\begin{array}{ccc}5& -1& 1\\ 0& -4& 7\end{array}\right)+4\left(\begin{array}{ccc}-3& -4& 2\\ 1& 4& -5\end{array}\right)$

## Multiplication of Matrices

 1 $\left(\begin{array}{cc}3& 1\end{array}\right)\left(\begin{array}{c}2\\ 4\end{array}\right)$ 2 $\left(\begin{array}{cc}-3& 0\end{array}\right)\left(\begin{array}{cc}1& -2\\ 5& -5\end{array}\right)$ 3 $\left(\begin{array}{cc}-3& 2\end{array}\right)\left(\begin{array}{ccc}-1& 5& -2\\ 3& 5& -4\end{array}\right)$ 4 $\left(\begin{array}{ccc}2& -1& -3\end{array}\right)\left(\begin{array}{c}-3\\ 5\\ -1\end{array}\right)$ 5 $\left(\begin{array}{ccc}-3& -2& 5\end{array}\right)\left(\begin{array}{cc}-1& 7\\ 3& -5\\ 0& 4\end{array}\right)$ 6 $\left(\begin{array}{c}1\\ -4\end{array}\right)\left(\begin{array}{cc}-2& 3\end{array}\right)$ 7 $\left(\begin{array}{cc}-2& 4\\ 3& -3\end{array}\right)\left(\begin{array}{c}-5\\ 2\end{array}\right)$ 8 $\left(\begin{array}{cc}-1& 3\\ 4& -1\end{array}\right)\left(\begin{array}{cc}-5& -2\\ 4& 3\end{array}\right)$ 9 $\left(\begin{array}{cc}3& 5\\ 3& 4\end{array}\right)\left(\begin{array}{ccc}1& -5& -2\\ -4& 0& 5\end{array}\right)$ 10 $\left(\begin{array}{ccc}1& -2& 3\\ 7& -4& -2\end{array}\right)\left(\begin{array}{c}-1\\ -1\\ 4\end{array}\right)$

## The Inverse Matrix

 1 $\left(\begin{array}{cc}-4& -2\\ 3& 3\end{array}\right)$ 2 $\left(\begin{array}{cc}4& -6\\ -5& 5\end{array}\right)$ 3 $\left(\begin{array}{cc}6& 5\\ -3& -5\end{array}\right)$ 4 $\left(\begin{array}{cc}-6& 9\\ -5& 5\end{array}\right)$ 5 $\left(\begin{array}{cc}8& 2\\ -10& -5\end{array}\right)$ 6 $\left(\begin{array}{cc}8& -6\\ -10& 5\end{array}\right)$ 7 $\left(\begin{array}{cc}-8& 9\\ -4& 3\end{array}\right)$ 8 $\left(\begin{array}{cc}-8& -10\\ -6& -9\end{array}\right)$ 9 $\left(\begin{array}{cc}9& -2\\ -3& 2\end{array}\right)$ 10 $\left(\begin{array}{cc}9& -8\\ -6& 4\end{array}\right)$

## Using Matrices to Solve Simultaneous Equations

 1 $\left(\begin{array}{cc}4& -2\\ 3& -3\end{array}\right)\left(\begin{array}{c}x\\ y\end{array}\right)=\left(\begin{array}{c}-12\\ 6\end{array}\right)$ 2 $\left(\begin{array}{cc}-4& -3\\ 2& 3\end{array}\right)\left(\begin{array}{c}x\\ y\end{array}\right)=\left(\begin{array}{c}19\\ 1\end{array}\right)$ 3 $\left(\begin{array}{cc}4& -5\\ 2& -5\end{array}\right)\left(\begin{array}{c}x\\ y\end{array}\right)=\left(\begin{array}{c}17\\ 1\end{array}\right)$ 4 $\left(\begin{array}{cc}-6& -4\\ -5& -5\end{array}\right)\left(\begin{array}{c}x\\ y\end{array}\right)=\left(\begin{array}{c}16\\ 5\end{array}\right)$ 5 $\left(\begin{array}{cc}8& 2\\ -6& -3\end{array}\right)\left(\begin{array}{c}x\\ y\end{array}\right)=\left(\begin{array}{c}20\\ -6\end{array}\right)$ 6 $\left(\begin{array}{cc}-8& -6\\ -5& -5\end{array}\right)\left(\begin{array}{c}x\\ y\end{array}\right)=\left(\begin{array}{c}8\\ -5\end{array}\right)$ 7 $\left(\begin{array}{cc}8& 9\\ 4& 6\end{array}\right)\left(\begin{array}{c}x\\ y\end{array}\right)=\left(\begin{array}{c}4\\ -4\end{array}\right)$ 8 $\left(\begin{array}{cc}9& 6\\ -4& -4\end{array}\right)\left(\begin{array}{c}x\\ y\end{array}\right)=\left(\begin{array}{c}-3\\ -4\end{array}\right)$ 9 $\left(\begin{array}{cc}-9& 8\\ -6& 4\end{array}\right)\left(\begin{array}{c}x\\ y\end{array}\right)=\left(\begin{array}{c}6\\ 12\end{array}\right)$ 10 $\left(\begin{array}{cc}10& 8\\ -4& -2\end{array}\right)\left(\begin{array}{c}x\\ y\end{array}\right)=\left(\begin{array}{c}-18\\ 12\end{array}\right)$

## Differentiation (Power Rule)

 1 $\frac{d}{dx}\left(3{x}^{2}\right)$ 2 $\frac{d}{dx}\left(-2{x}^{5}\right)$ 3 $\frac{d}{dx}\left(\frac{5}{{x}^{2}}\right)$ 4 $\frac{d}{dx}\left(6{x}^{\frac{2}{3}}\right)$ 5 $\frac{d}{dx}\left(7x+5\right)$ 6 $\frac{d}{dx}\left(2{x}^{3}+4x-3\right)$ 7 $\frac{d}{dx}\left(\frac{3}{{x}^{2}}+\frac{1}{x}-4\right)$ 8 $\frac{d}{dx}\left(4{x}^{2}-5\sqrt{x}\right)$ 9 $\frac{d}{dx}\left(\frac{{x}^{2}+4x}{2}\right)$ 10 $\frac{d}{dx}\left(\frac{6{x}^{3}-5{x}^{2}-8}{2{x}^{2}}\right)$

## Differentiation (Chain Rule)

 1 $\frac{d}{dx}{\left(2x+1\right)}^{3}$ 2 $\frac{d}{dx}\left(\frac{1}{5x-6}\right)$ 3 $\frac{d}{dx}{\left(8x-3\right)}^{\frac{1}{4}}$ 4 $\frac{d}{dx}{\left(2{x}^{2}+3\right)}^{4}$ 5 $\frac{d}{dx}\left(\sqrt[3]{4{x}^{2}-5}\right)$ 6 $\frac{d}{dx}{\left(5{x}^{2}+4\right)}^{\frac{3}{5}}$ 7 $\frac{d}{dx}{\left({x}^{2}-4x+6\right)}^{3}$ 8 $\frac{d}{dx}\left(\sqrt{5x-{x}^{2}+3}\right)$ 9 $\frac{d}{dx}{\left(2{x}^{4}-1\right)}^{6}$ 10 $\frac{d}{dx}{\left(\frac{1}{2}x-\frac{3}{7}\right)}^{4}$

## Differentiation (Product Rule)

 1 $\frac{d}{dx}\left(x{\left(x+5\right)}^{3}\right)$ 2 $\frac{d}{dx}\left(2x{\left(5x-1\right)}^{4}\right)$ 3 $\frac{d}{dx}\left({x}^{2}{\left(6x+1\right)}^{3}\right)$ 4 $\frac{d}{dx}\left(3{x}^{2}{\left(3{x}^{2}-8\right)}^{6}\right)$ 5 $\frac{d}{dx}\left(\left(2x-1\right){\left(4x-5\right)}^{5}\right)$ 6 $\frac{d}{dx}\left(\left({x}^{2}+7\right){\left(9{x}^{2}+4\right)}^{5}\right)$ 7 $\frac{d}{dx}\left(\left({x}^{2}+2x-4\right){\left(x-1\right)}^{3}\right)$ 8 $\frac{d}{dx}\left({\left(x+3\right)}^{5}{\left(x-4\right)}^{4}\right)$ 9 $\frac{d}{dx}\left(\left(x-4\right)\sqrt{x+7}\right)$ 10 $\frac{d}{dx}\left(\left({x}^{2}+8\right)\sqrt{{x}^{2}-8}\right)$

## Differentiation (Quotient Rule)

 1 $\frac{d}{dx}\left(\frac{4}{x-3}\right)$ 2 $\frac{d}{dx}\left(\frac{3x}{2x-1}\right)$ 3 $\frac{d}{dx}\left(\frac{x+3}{4x+1}\right)$ 4 $\frac{d}{dx}\left(\frac{{x}^{2}+4}{7x+2}\right)$ 5 $\frac{d}{dx}\left(\frac{3x}{{x}^{2}+4}\right)$ 6 $\frac{d}{dx}\left(\frac{7x-3}{4{x}^{2}-11}\right)$ 7 $\frac{d}{dx}\left(\frac{{x}^{2}}{5-2{x}^{2}}\right)$ 8 $\frac{d}{dx}\left(\frac{\sqrt{x}}{{x}^{2}-2}\right)$ 9 $\frac{d}{dx}\left(\frac{x}{\sqrt{x-4}}\right)$ 10 $\frac{d}{dx}\left(\frac{5x-2}{\sqrt{3x-5}}\right)$

## Integration involving Functions with Linear Factors

 1 $\int {\left(x+5\right)}^{2}dx$ 2 $\int {\left(6x-1\right)}^{2}dx$ 3 $\int \frac{1}{{\left(4x-3\right)}^{3}}dx$ 4 $\int 3{\left(x+9\right)}^{2}dx$ 5 $\int -2{\left(2x+3\right)}^{3}dx$ 6 $\int \frac{4}{{\left(2x+3\right)}^{2}}dx$ 7 $\int \sqrt{x+3}dx$ 8 $\int \frac{1}{\sqrt[3]{3-x}}dx$ 9 $\int \sqrt{{\left(x+2\right)}^{5}}dx$ 10 $\int \frac{3}{\sqrt{{\left(x-4\right)}^{5}}}dx$

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