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

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

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.

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 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.

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

Write expressions for the moment of inertia of simple shapes about various axes.

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.

Pythagoras' Theorem and naming sides of right angled triangle

rebelmaths

Homework set.  Find 2-D moments or balance moments using Verignon's theorem:  $ M = \pm F_x d_y \pm F_y d_x$

Calculate the moment of a force about three points using Verignon' theorem.  All forces and points are in the same plane.

Find the tension in a rope necessary to prevent a bracket from rotating by applying $\Sigma M = 0$.

Homework set.  Application of Parallel Axis Theorem to find area Moment of Inertia

No description given

Find the diagonal or one side of a rectangle using Pythagoras' theorem.

Use Pythagoras' Theorem to find the length of a side on a right-angled triangle.

Solving a system of simultaneous congruences using the Chinese Remainder Theorem.

An explore mode question which allows you to write a solution straight away, or break it down into steps.

After solving a system of three congruences, you can ask for a new problem with more congruences.

Quotient and remainder, polynomial division.

Quotient and remainder, polynomial division.

Use Pythagoras' Theorem to find the length of a side on a right-angled triangle.

Apply the factor and remainder theorems to manipulate polynomial expressions

No description given

Apply the factor theorem to check which of a list of linear polynomials are factors of another polynomial.

No description given

Given a factor of a cubic polynomial, factorise it fully by first dividing by the given factor, then factorising the remaining quadratic.

Using Pythagoras' Theorem to find a missing side. Illustrated using simple Eukleides diagram

rebelmaths

Questions using Pythagoras' theorem involving integers and surds. 

Find modulus and argument of two complex numbers. Then use De Moivre's Theorem to find positive powers of the complex numbers.

Find modulus and argument of the complex number $z_1$ and find the $n$th roots of $z_1$ where $n=5,\;6$ or $7$.