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

Express $\log_a(x^{c}y^{d})$ in terms of $\log_a(x)$ and $\log_a(y)$. Find $q(x)$ such that $\frac{f}{g}\log_a(x)+\log_a(rx+s)-\log_a(x^{1/t})=\log_a(q(x))$.

There is a video included explaining the rules of logarithms by going through simplification of logs of numbers rather than algebraic expressions.

Simplify $(ax+b)(cx+d)-(ax+d)(cx+b)$. Answer is a multiple of $x$.

Simplify $(ax+by)(cx+dy)-(ax+dy)(cx+by)$. Answer is a multiple of $xy$.

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

Evaluate $\int_0^{\,m}e^{ax}\;dx$, $\int_0^{p}\frac{1}{bx+d}\;dx,\;\int_0^{\pi/2} \sin(qx) \;dx$. 

A basic introduction to differentiation

Multiple response question (4 correct out of 8) covering properties of convergent and divergent series and including questions on power series. Selection of questions from a pool.

Four questions on finding least upper bounds and greatest lower bounds of various sets.

Eight questions on finding least upper bounds and greatest lower bounds of various sets.

One question on determining whether statements are propositions.

Four questions on find truth tables for various logical expressions.

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

Inputting algebraic expressions into Numbas.

Inputting ratios of algebraic expressions.

Integrating by parts.

Find $ \int ax\sin(bx+c)\;dx$ or $\int ax e^{bx+c}\;dx$ 

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

Eight questions on finding least upper bounds and greatest lower bounds of various sets.

Express $\log_a(x^{c}y^{d})$ in terms of $\log_a(x)$ and $\log_a(y)$. Find $q(x)$ such that $\frac{f}{g}\log_a(x)+\log_a(rx+s)-\log_a(x^{1/t})=\log_a(q(x))$

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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.

Use the BODMAS rule to determine the order in which to evaluate some arithmetic expressions. 

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

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 $a(x+b)^2+c$.

Apply the factor and remainder theorems to manipulate polynomial expressions