Using indices rules to write powers as negative powers

Using indices rules to write expressions as negative powers.

Using indices rules to write fractions as negative powers.

Using rules for roots and powers to write expressions with only powers

Using indices rules to rewrite an expression from $a^\frac{m}{n}$ to $b$, for integers $a$, $b$, $m$ and $n$.

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Practice using the log rules to add and subtract logarithms

Practice using the log rules to add and subtract logarithms

Differentiation of  polynomials, cos, sin, exp, log functions. Product, quotient and chain rules.

rebelmaths

Solve a random oblique triangle for sides and angles.

Solving $a\log(x)+\log(b)=\log(c)$ for $x$, where $a$, $b$ and $c$ are positive integers.

Using indices rules to rewrite an expression from $a^\frac{m}{n}$ to $b$, for integers $a$, $b$, $m$ and $n$.

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Find $\displaystyle\int \frac{ax+b}{(x+c)(x+d)}\;dx,\;a\neq 0,\;c \neq d $.

Find the first 3 terms in the MacLaurin series for $f(x)=(a+bx)^{1/n}$ i.e. up to and including terms in $x^2$.

Rewriting fractional expressions involving $\sqrt[n]{x^m}$ using rules to combine and simplify indices. 

Recovering original function given some information such as derivative and value at some point.

Differentiate $\displaystyle e^{ax^{m} +bx^2+c}$

Differentiate $\displaystyle (ax^m+b)^{n}$.

Using indices rules to rewrite an expression from $\left(\frac{a^n}{b^n}\right)^{-1/n}$ to $\frac{b}{a}$.

Using indices rules to rewrite an expression from $a^\frac{m}{n}$ to $\frac{1}{b}$, for integers $a$, $b$, $m$ and $n$.

Fairly simple questions using differentiation "power rule" and "sum or difference rules" to differentiate single term functions and polynomials.

Some co-efficients and indices can be negative and/or fractional.

Find $\displaystyle \int \frac{2ax + b}{ax ^ 2 + bx + c}\;dx$

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Match the equivalence with the rule

Practice using the log rules to add and subtract logarithms

Differentiation of  polynomials, cos, sin, exp, log functions. Product, quotient and chain rules.

Missing: Application with bacteria, turning points, difficult chain rule