Calculating the derivative of an exponential function of the form $ae^{bx}$, using a table of derivatives.

Find the derivative of a function of the form $y=a \tan(bx+c)$ using a table of derivatives.

Find the derivative of a function of the form $y=a \sin(bx+c)$ using a table of derivatives.

Find the derivative of a function of the form $y=a \cos(bx+c)$ using a table of derivatives.

Finding the stationary points of a cubic equation and determining their nature.

Calculating the definite integral $\int_{n_1}^{n_2}a_1x^{b_1}+a_2x^{b_2}+a_3x^{b_3} dx$.

Calculating the integral of a function of the form $a_1x^{b_1}+a_2x^{b_2}+a_3x^{b_3}$ using a table of integrals. 

Differentiate a polynomial expression involving coefficients and, negative and fractional indices. 

Calculating the derivative of a function of the form $a \ln(bx)$ using a table of derivatives.

Find the derivative of a function of the form $y=ax^b$ using a table of derivatives.

Solving $a\log(x)+\log(b)=\log(c)$ for $x$, where $a$, $b$ and $c$ are positive integers.

Finding $x$ from a logarithmic equation of the form $\log_ax = b$, where $a$ and $b$ are positive integers.

Finding composite functions of 2 linear functions.

Finding the inverse of a function of the form $f(x)=\frac{mx+c}{x+a},\,x\neq-a$.

Determining the range of a function of the form $f = m|x| + a$.

Evaluating a linear function for a given value of $x$.

Match the relevant graph (sin, cos, tan) with its equation. 

Multiple choice - select the quadratic graph.

Solving an equation of the form $a^x=b$ using logarithms to find $x$.

Calculating gradient and finding intercept from a geogebra graph.

Basic calculation from a sum given in Sigma notation.

Rewrite the expression $\frac{mx^2+nx+k}{(x+a)(x^2+bx+c)}$ as partial fractions in the form $\frac{A}{x+a}+\frac{Bx+C}{x^2+bx+c}$.

Simplifying first is essential in terms of managing expressions that might need factorising.

Manipulate fractions in order to add and subtract them. The difficulty escalates through the inclusion of a whole integer and a decimal, which both need to be converted into a fraction before the addition/subtraction can take place. 

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

Simplify the sum of two algebraic fractions where spotting factorising of both numerators and denominators can reduce the work massively.

Simplify (qx+a)/(rx+b) +/- (sx+c)/(tx+d)

x is a randomised variable. a,b,c,d,q,r,s,t are randomised integers. a,b,c,d run from -5 to 5, including 0. q,r,s,t run from -3 to 3, and can be 0 if the constant term is nonzero, but are mostly 1.

Factorising a quadratic expression of the form $a^2x^2-b^2$ to $(ax+b)(ax-b)$, using the difference of two squares formula.

Factorise a quadratic equation where the coefficient of the $x^2$ term is greater than 1 and then write down the roots of the equation

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