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A cheerful learner practising Mathematics beside a tablet showing the algebra steps 2x plus 3 equals 11, 2x equals 8, and x equals 4

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Simplification

Simplify linear expressions and work confidently with fractional coefficients.

3 worksheets
30 questions

Simplification of Linear Expressions

$2 x - 5 y + 3 x$
$4 x + 2 y - 6 x + 3 y$
$- 3 x - 2 y - (- 5 x) + (- y)$
$4 x + (3 x - 2 y)$
$2 x - 5 y + 3 x$
$(8 x + 2) - (3 x - 5)$
$(2 x + 3 y + 4) + (2 y - 3)$
$(3 x - 4 y - 1) - (- 4 x + 8 y - 7)$
$4 x + [2 x - (3 x + 5)]$
$7 x - 3 y - [2 x - (6 x - 5 y)]$

Simplification of Linear Expressions with Fractional Coefficients

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

Addition and Subtraction of Algebraic Fractions

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

Develop structure

Expansion

Expand expressions and apply algebraic identities accurately.

3 worksheets
30 questions

Expansion of Linear Expressions

$4 (2 x - 5 y)$
$- 2 (3 x - 4 y)$
$3 (2 x - 3 y) + 3 x$
$8 x - 3 (x + 3 y)$
$3 (3 x + 5 y) + 3 x - 7 y$
$4 (4 x - 1) - 3 (5 x - 6)$
$4 (4 x - 3 y + 2) + 3 (2 x + 5 y - 3)$
$2 (6 x + 5 y - 3) - 3 (2 x - 3 y - 4)$
$4 [5 (3 x + 4 y) + 2 (x - 2 y)]$
$- 2 [5 (2 x - 5 y) - 2 (x - 3 y)]$

Expansion of Algebraic Expressions

$3 x (4 + y)$
$- 4 y (2 x + 3)$
$x (3 x - y)$
$- 3 y (2 y - 3 x)$
$2 x (y + z) + 3 x (2 y + z)$
$2 x (y + z) + 3 x (2 y + z)$
$(x + 2 y) (x + 3 y)$
$(2 x + 5 y) (3 x - y)$
$(x^{2} + 6) (2 x + 3)$
$2 (2 x + 1) (3 x + 2)$

Expansion using Algebraic Identities

${(x + 5)}^{2}$
${(3 x + 4)}^{2}$
${(3 x + 4)}^{2}$
${(5 - 2 x)}^{2}$
$(x + 2) (x - 2)$
$(4 x + 3) (4 x - 3)$
${(x + 3 y)}^{2}$
${(x - 7 y)}^{2}$
$(2 x + y) (2 x - y)$
$(4 x - 5 y) (4 x + 5 y)$

Recognise patterns

Factorisation

Factorise expressions using common factors, grouping and identities.

4 worksheets
40 questions

Factorisation by Common Factors

$4 x + 12$
$6 x - 9$
$x y - x z$
$x y - x z$
$5 x + 5 y - 5 z$
$20 x - 18 y + 14 z$
$x y + x w + 2 x z$
$x (x + 2) + 8 (x + 2)$
$x (x - 5) - 3 (x - 5)$
$8 a b (x - 5) - 12 b (x - 5)$

Factorisation by Grouping

$x y + y + x + 1$
$a x - 2 x + a - 2$
$x y + 3 y + 2 x + 6$
$a b - 6 b - 2 a + 12$
$a x + b x + 4 a + 4 b$
$15 p r - 10 q r - 6 p + 4 q$
$p q r + 3 r + p q + 3$
$p q r + 3 r + p q + 3$
$6 x y z + 9 z + 10 x y + 15$
$6 k m n - 8 n + 21 k m - 28$

Factorisation using Algebraic Identities

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

Factorisation of Quadratic Expressions

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

Connect operations

Algebraic Fractions

Work with algebraic fractions and rearrange algebraic formulae.

3 worksheets
30 questions

Addition and Subtraction of Algebraic Fractions

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

Multiplication and Division of Algebraic Fractions

$\frac{x}{6 y} \times \frac{2 y}{5}$
$\frac{4 p}{3 q} \times \frac{5 q^{2}}{2 p^{2}}$
$\frac{4 s t^{3}}{3 r} \times \frac{5 r^{2}}{8 s t^{2}}$
$\frac{2 x}{3 y} \div \frac{x}{5}$
$\frac{3 m^{3}}{4 n^{2}} \div \frac{m}{8 n^{2}}$
$\frac{5 a^{2}}{b^{3}} \div \frac{10 a^{3}}{3 b^{2}}$
$\frac{x + y}{x - y} \times \frac{2 (x - y)}{3 x + 3 y}$
$\frac{p^{2} q + 4 q}{3 p - 2 r} \times \frac{6 p - 4 r}{3 p^{2} + 12}$
$\frac{6 y - 4 z}{3 y + 6 z} \div \frac{4 y - 2 z}{9 y + 3 z}$
$\frac{3 k^{2} + k n}{m n - 4 m^{2}} \div \frac{2 n + 6 k}{4 m - n}$

Manipulation of Algebraic Formulae

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

Solve step by step

Solving Equations

Practise linear, quadratic, inequality and index equations.

13 worksheets
130 questions

Solving Linear Equations

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

Solving Linear Equations with Brackets

$4 (3 x + 5) = 7 x$
$2 (2 x + 3) = x + 9$
$3 (4 - 3 x) = 2 x + 1$
$4 (2 x - 5) = 5 x - 6$
$2 (5 - 2 x) = 3 x - 4$
$4 (6 - 2 x) = - 3 x + 4$
$5 (2 x + 1) = 3 (2 x + 3)$
$3 (3 x - 5) = 2 (2 x - 7)$
$2 (5 x - 7) = - 3 (3 x + 11)$
$3 (3 x - 5) = - 4 (2 x - 9)$

Solving Linear Equations involving Fractional Coefficients

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

Solving Linear Equations involving Algebraic Fractions

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

Solving Quadratic Equations (by Factorisation)

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

Solving Quadratic Equations (by Completing the Square)

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

Solving Quadratic Equations (by General Formula)

$x^{2} - 5 x + 2 = 0$
$3 x^{2} - 6 x + 2$
$- 2 x^{2} - 7 x + 3 = 0$
$x^{2} - 5 x = - 1$
$2 x^{2} + 9 x = - 3$
$x^{2} + 2 = 5 x$
$x (x + 3) - 2 = 0$
$x (1 - 3 x) + 8 = 0$
$x (x + 3) + 2 x + 5 = 0$
$x (x + 3) = 6 (x + 2)$

Solving Equations Reducible to Quadratic Equations (by Factorisation)

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

Solving Equations Reducible to Quadratic Equations (by General Formula)

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

Solving Simple Linear Inequalities

$x + 3 > 7$
$x - 5 < - 6$
$5 x - 8 \geq 12$
$4 x + 6 \leq - 10$
$5 x + 4 < 7 x$
$3 x + 14 > 10 x$
$6 - x \leq x - 16$
$15 - x \geq x + 7$
$7 x > 4 (3 x - 2)$
$8 x + 3 < 3 (7 - 2 x)$

Solving Linear Inequalities

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

Solving Quadratic Inequalities

$x (x + 4) > 0$
$x (2 x - 7) \geq 0$
$(x + 2) (x - 4) > 0$
$(3 x - 4) (x - 5) < 0$
$x^{2} - 6 x < 0$
$x^{2} - 25 \leq 0$
$x^{2} + 8 > 12$
$16 x^{2} + 5 < 21$
$x^{2} + 3 x - 10 \leq 0$
$3 x^{2} + 6 x - 24 < 0$

Solving Equations involving Indices

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

Organise relationships

Matrices

Build confidence with matrix operations, inverses and simultaneous equations.

5 worksheets
50 questions

Addition and Subtraction of Matrices

$(\begin{matrix} 6 \\ 1 \end{matrix}) + (\begin{matrix} 2 \\ - 5 \end{matrix})$
$(\begin{matrix} 7 \\ - 2 \end{matrix}) - (\begin{matrix} - 2 \\ 3 \end{matrix})$
$(\begin{matrix} 4 & 7 \end{matrix}) + (\begin{matrix} 3 & - 6 \end{matrix})$
$(\begin{matrix} 5 & 0 \end{matrix}) - (\begin{matrix} 1 & - 2 \end{matrix})$
$x^{2} - 2 x - 8 = 0$
$(\begin{matrix} - 9 \\ 7 \\ - 8 \end{matrix}) - (\begin{matrix} 3 \\ 3 \\ - 10 \end{matrix})$
$(\begin{matrix} 3 & 0 & - 2 \end{matrix}) + (\begin{matrix} - 5 & 9 & 7 \end{matrix})$
$(\begin{matrix} 0 & 4 & - 3 \end{matrix}) - (\begin{matrix} 2 & 2 & 9 \end{matrix})$
$(\begin{matrix} - 4 & 2 \\ 4 & 9 \end{matrix}) + (\begin{matrix} - 3 & 8 \\ 2 & - 2 \end{matrix})$
$(\begin{matrix} - 4 & - 4 \\ 3 & 5 \end{matrix}) - (\begin{matrix} - 6 & 6 \\ 1 & - 9 \end{matrix})$

Multiplication of a Matrix by a Real Number

$3 (\begin{matrix} 3 \\ - 6 \end{matrix})$
$3 (\begin{matrix} - 4 \\ - 2 \end{matrix}) + (\begin{matrix} 4 \\ 1 \end{matrix})$
$2 (\begin{matrix} 6 \\ 3 \end{matrix}) - (\begin{matrix} - 7 \\ 5 \end{matrix})$
$5 (\begin{matrix} 1 & - 1 \end{matrix}) + (\begin{matrix} 9 & - 3 \end{matrix})$
$4 (\begin{matrix} 2 & - 5 \end{matrix}) - (\begin{matrix} - 2 & - 9 \end{matrix})$
$3 (\begin{matrix} 4 & 6 \\ 6 & 2 \end{matrix}) + (\begin{matrix} - 7 & - 10 \\ - 6 & 5 \end{matrix})$
$2 (\begin{matrix} 3 & - 9 \\ 3 & - 5 \end{matrix}) - (\begin{matrix} 10 & 0 \\ 6 & 5 \end{matrix})$
$3 (\begin{matrix} 5 & - 7 \\ 3 & - 3 \\ 6 & - 2 \end{matrix}) + 2 (\begin{matrix} - 1 & 6 \\ - 7 & 4 \\ - 3 & 0 \end{matrix})$
$4 (\begin{matrix} 1 & - 1 \\ 4 & - 1 \\ 2 & - 3 \end{matrix}) - (\begin{matrix} 1 & 3 \\ 5 & - 3 \\ 0 & 2 \end{matrix})$
$3 (\begin{matrix} 5 & - 1 & 1 \\ 0 & - 4 & 7 \end{matrix}) + 4 (\begin{matrix} - 3 & - 4 & 2 \\ 1 & 4 & - 5 \end{matrix})$

Multiplication of Matrices

$(\begin{matrix} 3 & 1 \end{matrix}) (\begin{matrix} 2 \\ 4 \end{matrix})$
$(\begin{matrix} - 3 & 0 \end{matrix}) (\begin{matrix} 1 & - 2 \\ 5 & - 5 \end{matrix})$
$(\begin{matrix} - 3 & 2 \end{matrix}) (\begin{matrix} - 1 & 5 & - 2 \\ 3 & 5 & - 4 \end{matrix})$
$(\begin{matrix} 2 & - 1 & - 3 \end{matrix}) (\begin{matrix} - 3 \\ 5 \\ - 1 \end{matrix})$
$(\begin{matrix} - 3 & - 2 & 5 \end{matrix}) (\begin{matrix} - 1 & 7 \\ 3 & - 5 \\ 0 & 4 \end{matrix})$
$(\begin{matrix} 1 \\ - 4 \end{matrix}) (\begin{matrix} - 2 & 3 \end{matrix})$
$(\begin{matrix} - 2 & 4 \\ 3 & - 3 \end{matrix}) (\begin{matrix} - 5 \\ 2 \end{matrix})$
$(\begin{matrix} - 1 & 3 \\ 4 & - 1 \end{matrix}) (\begin{matrix} - 5 & - 2 \\ 4 & 3 \end{matrix})$
$(\begin{matrix} 3 & 5 \\ 3 & 4 \end{matrix}) (\begin{matrix} 1 & - 5 & - 2 \\ - 4 & 0 & 5 \end{matrix})$
$(\begin{matrix} 1 & - 2 & 3 \\ 7 & - 4 & - 2 \end{matrix}) (\begin{matrix} - 1 \\ - 1 \\ 4 \end{matrix})$

The Inverse Matrix

$(\begin{matrix} - 4 & - 2 \\ 3 & 3 \end{matrix})$
$(\begin{matrix} 4 & - 6 \\ - 5 & 5 \end{matrix})$
$(\begin{matrix} 6 & 5 \\ - 3 & - 5 \end{matrix})$
$(\begin{matrix} - 6 & 9 \\ - 5 & 5 \end{matrix})$
$(\begin{matrix} 8 & 2 \\ - 10 & - 5 \end{matrix})$
$(\begin{matrix} 8 & - 6 \\ - 10 & 5 \end{matrix})$
$(\begin{matrix} - 8 & 9 \\ - 4 & 3 \end{matrix})$
$(\begin{matrix} - 8 & - 10 \\ - 6 & - 9 \end{matrix})$
$(\begin{matrix} 9 & - 2 \\ - 3 & 2 \end{matrix})$
$(\begin{matrix} 9 & - 8 \\ - 6 & 4 \end{matrix})$

Using Matrices to Solve Simultaneous Equations

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

Explore change

Calculus

Practise core differentiation and integration techniques.

5 worksheets
50 questions

Differentiation (Power Rule)

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

Differentiation (Chain Rule)

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

Differentiation (Product Rule)

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

Differentiation (Quotient Rule)

$\frac{d}{d x} (\frac{4}{x - 3})$
$\frac{d}{d x} (\frac{3 x}{2 x - 1})$
$\frac{d}{d x} (\frac{x + 3}{4 x + 1})$
$\frac{d}{d x} (\frac{x^{2} + 4}{7 x + 2})$
$\frac{d}{d x} (\frac{3 x}{x^{2} + 4})$
$\frac{d}{d x} (\frac{7 x - 3}{4 x^{2} - 11})$
$\frac{d}{d x} (\frac{x^{2}}{5 - 2 x^{2}})$
$\frac{d}{d x} (\frac{\sqrt{x}}{x^{2} - 2})$
$\frac{d}{d x} (\frac{x}{\sqrt{x - 4}})$
$\frac{d}{d x} (\frac{5 x - 2}{\sqrt{3 x - 5}})$

Integration involving Functions with Linear Factors

$\int {(x + 5)}^{2} d x$
$\int {(6 x - 1)}^{2} d x$
$\int \frac{1}{{(4 x - 3)}^{3}} d x$
$\int 3 {(x + 9)}^{2} d x$
$\int - 2 {(2 x + 3)}^{3} d x$
$\int \frac{4}{{(2 x + 3)}^{2}} d x$
$\int \sqrt{x + 3} d x$
$\int \frac{1}{\sqrt[3]{3 - x}} d x$
$\int \sqrt{{(x + 2)}^{5}} d x$
$\int \frac{3}{\sqrt{{(x - 4)}^{5}}} d x$

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