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

Use laws for addition and subtraction of logarithms to simplify a given logarithmic expression to an arbitrary base.

Simplify logarithmic expressions using rules on logarithms.

Inputting ratios of algebraic expressions.

Use laws for addition and subtraction of logarithms to simplify a given logarithmic expression to an arbitrary base.

Use laws for addition and subtraction of logarithms to simplify a given logarithmic expression to an arbitrary base.

Use laws for addition and subtraction of logarithms to simplify a given logarithmic expression to an arbitrary base.

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.

Create a truth table for a logical expression of the form $(a \operatorname{op1} b) \operatorname{op2}(c \operatorname{op3} d)$ where $a, \;b,\;c,\;d$ can be the Boolean variables $p,\;q,\;\neg p,\;\neg q$ and each of $\operatorname{op1},\;\operatorname{op2},\;\operatorname{op3}$ one of $\lor,\;\land,\;\to$.

For example: $(p \lor \neg q) \land(q \to \neg p)$.

Create a truth table for a logical expression of the form $a \operatorname{op} b$ where $a, \;b$ can be the Boolean variables $p,\;q,\;\neg p,\;\neg q$ and $\operatorname{op}$ one of $\lor,\;\land,\;\to$.

For example $\neg q \to \neg p$.

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

Some questions demonstrating new features in Numbas v4.0: pattern-matching, inference of variable types in mathematical expression parts, and marking equations.

English sentences which are propositions are given and the appropriate logical expression chosen for the negation of the sentence.

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

Use laws for addition and subtraction of logarithms to simplify a given logarithmic expression to an arbitrary base.

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.

Given a description in words of the costs of some items in terms of an unknown cost, write down an expression for the total cost of a selection of items. Then simplify the expression, and finally evaluate it at a given point.

The word problem is about the costs of sweets in a sweet shop.

Multiplication and addition of complex numbers. Four parts.

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

Given a description in words of the costs of some items in terms of an unknown cost, write down an expression for the total cost of a selection of items. Then simplify the expression, and finally evaluate it at a given point.

The word problem is about the costs of sweets in a sweet shop.

Use laws for addition and subtraction of logarithms to simplify a given logarithmic expression to an arbitrary base.

Testing whether students know how to use multiple log laws.

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

Factorise a quadratic expression of the form $x^2+akx+bk^2$ for $x$, in terms of $k$. $a$ and $b$ are constants.