Questions on rearranging expressions, expanding brackets and collecting like terms.

Use the rule $\log_a(n^b) = b\log_a(n)$ to rearrange some expressions.

Instructions on inputting ratios of algebraic expressions.

One question on determining whether statements are propositions.

Four questions about truth tables for various logical expressions.

A basic introduction to differentiation

A basic introduction to differentiation

Collecting like terms, expanding a bracket (distributive law), substitution of values, finding factors, simplifying algebraic fractions.

Using $\cos^2\theta+\sin^2\theta=1$ to evaluate expressions.

Rearrange some expressions involving logarithms by applying the relation $\log_b(a) = c \iff a = b^c$.

Simplifying expressions such as $b^{\log_b(x)}$ and $b^{\log_b(x)}$.

Rearrange some expressions involving logarithms by applying the relation $\log_b(a) = c \iff a = b^c$.

Use the rule $\log_a(n^b) = b\log_a(n)$ to rearrange some expressions.

Simplify logarithmic expressions using rules on logarithms.

Inputting ratios of algebraic expressions.

Testing whether students know how to use multiple log laws.

Find $\displaystyle \frac{d}{dx}\left(\frac{m\sin(ax)+n\cos(ax)}{b\sin(ax)+c\cos(ax)}\right)$. Three part question.

A question to practice simplifying fractions with the use of factorisation (for binomial and quadratic expressions).

Use the rule $\log_a(n^b) = b\log_a(n)$ to rearrange some expressions.

Evaluate $\int_1^{\,m}(ax ^ 2 + b x + c)^2\;dx$, $\int_0^{p}\frac{1}{x+d}\;dx,\;\int_0^\pi x \sin(qx) \;dx$, $\int_0^{r}x ^ {2}e^{t x}\;dx$

Questions involving various techniques for rearranging and solving quadratic expressions and equations

Write expressions for the moment of inertia of simple shapes about various axes.

Rearrange some expressions involving logarithms by applying the relation $\log_b(a) = c \iff a = b^c$.

Eight expressions, of increasing complexity. The student must simplify them by expanding brackets and collecting like terms.

Rearrange expressions in the form $ax^2+bx+c$ to $a(x+b)^2+c$.

Testing whether students know how to use multiple log laws.

Rearrange expressions in the form $ax^2+bx+c$ to $a(x+b)^2+c$.

Rearrange some expressions involving logarithms by applying the relation $\log_b(a) = c \iff a = b^c$.

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The derivative of $\displaystyle \frac{a+be^{cx}}{b+ae^{cx}}$ is $\displaystyle \frac{pe^{cx}} {(b+ae^{cx})^2}$. Find $p$.

The derivative of $\displaystyle \frac{a+be^{cx}}{b+ae^{cx}}$ is $\displaystyle \frac{pe^{cx}} {(b+ae^{cx})^2}$. Find $p$.