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 $n$.

Differentiate the function $f(x)=(a + b x)^m  e ^ {n x}$ using the product rule. Find $g(x)$ such that $f^{\prime}(x)= (a + b x)^{m-1}  e ^ {n x}g(x)$.

Use the product rule (number of ways of doing A and B = (no. for A)*(no. for B)) to count the number of ways of doing two independent tasks.

Simple application of "Power Rule" to differentiate single term functions.

All co-efficients and powers are integer (though some may be negative.

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.

Calculating the missing side-length of a triangle using the cosine rule.

Given two angles and a side-length of a triangle, use the sine rule to calculate an unknown side-length.

Calculate probability using P(A) = 1-P(not A)

A function $f(x) = cln(ax^2+bx) -x$ is sketched and tangent is also drawn. The equation of the tangent line is asked for and $x$-coordinate for horizontal tangent is asked for. Calculator.

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

Students are given a diagram with 2 triangles. They are given 2 randomised lengths, and a randomised angle of depression.

They need to compute an angle by subtracting the angle of depression from 90°. Then they need to use the sine rule to calculate a second angle. Then they need to use the alternate angles on parallel lines theorem to work out a third angle. They use these to calculate a third angle, which they use in the right-angle triangle with the sine ratio to compute the third side. They then use the cos ratio to compute the length of the third side.

Student is given a triangle with the value of 2 sides and 1 or 2 angles and asked to find the value of the third side using the cosine rule. Triangle can be acute or obtuse.

Side and angle lengths are randomised. Units are randomised.

Student is given a triangle with the value of 3 sides and asked to find the value of an angle. Triangle can be acute or obtuse.

Side and angle lengths are randomised. Units are randomised.