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

Inputting algebraic expressions into Numbas.

Inputting ratios of algebraic expressions.

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

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

Some practice collecting like terms of algebraic expressions, with detailed advice.

Adapted from 'Collecting like terms' by Ben Brawn.

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

Simplifying algebraic expressions

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

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

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

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

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

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

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.

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

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.

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

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

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

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

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

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

Inputting algebraic expressions into Numbas.

Inputting ratios of algebraic expressions.

Inputting algebraic expressions into Numbas.

Inputting algebraic expressions into Numbas.