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

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

Two quadratic graphs are sketched with some area beneath them shaded. Question is to determine the area of shaded regions using integration. The first graph's area is all above the $x$-axis. The second graph has some area above and some below the $x$-axis.

Definite Intgerals

Definite Integrals

Recovering original function given some information such as derivative and value at some point.

Find $\displaystyle \int ae ^ {bx}+ c\sin(dx) + px ^ {q} + k/x \;dx$.

SUVAT equation questions, for mechanics page in wiki. Uses $v=u+at$ and $s=((u+v)/2)t$.

Introduction to using the product rule

Differentiate $\displaystyle \ln((ax+b)^{m})$

Differentiate $\displaystyle e^{ax^{m} +bx^2+c}$

Differentiate $\displaystyle (ax^m+b)^{n}$.

Finding the coordinates and determining the nature of the stationary points on a polynomial function

A graph (of a cubic) is given. The question is to determine the number of roots and number of stationary points the graph has. Non-calculator. Advice is given.

Calculating gradients - polynomials

Differentiating exponentials and Logs

More work on differentiation with trigonometric functions

Simple derivatives

Rate of change problem involving velocity & acceleration

$x$ is given and (sin(x),cos(x)) is plotted on a unit circle.  Then the student is asked to determine sin(y) and cos(y), where y is closely related to x (e.g. y=-x, y=180+x, etc.) Also find values and sign of cos/tan/sin(x).

Solve a logarithmic equation

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

Finding the coordinates and determining the nature of the stationary points on a polynomial function

Calculate the centroidal moment of intertia of a rectangle with a excentric rectangular hole.

Find the centroidal moment of inertia of a sideways T shape. This requires first locating the centroid, then applying the parallel axis theorem.

Find moment of inertia of a shape which requires the use of the parallel axis theorem for a semicircle.

Find moment of inertia of a composite shape consisting of a rectangle and two triangles with respect to the x-axis. Shapes rest on the x-axis so the parallel axis theorem is not required.

Calculate the moment of inertia of a composite shape consiting of two rectangles about the x or y-axis.  Parallel axis theorem is often required.

Find the moment of inertia of semi and quarter circles using the parallel axis theorem.

Use the parallel axis theorem to find the area moment of inertia of a triangle and a rectangle about various axes.