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

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

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

$x$ 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).

Finding the lengths and angles within a right-angled triangle using: pythagoras theorem, SOHCAHTOA and principle of angles adding up to 180 degrees.

A set of questions practicing finding equivalent fractions with an emphasis on simplifying.

Finding equivalent fractions, and expressing fractions in their simplest form.

Finding equivalent fractions, and expressing fractions in other equivalent forms.

Find  $\displaystyle \int\cosh(ax+b)\;dx,\;\;\int x\sinh(cx+d)\;dx$

Practice finding factors, HCF and LCM.

Find the HCF of two numbers using prime factor decomposition.

Find the common factors of two numbers

A question to practice equation line and finding gradients

Find moment of inertia and radius of gyration for a built-up beam made of two channels and two plates.

Find centroidal moments of inertia and radius of gyration for a beam composed of  two angle sections forming a box beam.

Find the centroid and the centroidal moments of inertia for a beam composed of a flat plate and two angle sections.

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.

Prime factor decomposition starting steps.

Multiples, factors, lowest common multiples and highest common factors.

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

Draws a triangle based on 3 side lengths and randomises asking for hypotenuse or not.

Find moment of inertia wrt the x- and y- axes for a shape made up of two rectangles.

Use a table of properties to find the Area Moment of inertia for simple shapes: rectangle, triangle, circle, semicircle, and quarter circle.

 The parallel axis theorem is not required for any of these shapes.  One situation requires subtracting a triangle from a rectangle however.

Distinguish between centroidal and non-centroidal moments of inertia.

Use two points on a line graph to calculate the gradient and $y$-intercept and hence the equation of the straight line running through both points.

The answer box for the third part plots the function which allows the student to check their answer against the graph before submitting.

This particular example has a positive gradient.

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

A quadratic equation (equivalent to $(x+a)^2-b$) is given and sketched. Three equations are given that can be solved using the graph. There is a chance there will only be one solution.

Finding X-Y intercepts for quadratic and cubic equations.

Students are supposed to use Excel (or similar) to find the answers (e.g., enter coordinates of two points then plot and add trendline).

Uses an embedded Geogebra graph of a line $y=mx+c$ with random coefficients set by NUMBAS.

Find the force required to produce a given moment, or vice-versa.