What happens to areas under the graph of $\frac{1}{x}$ when they are stretched?

What different ways can you find to calculate these integrals?

Can you find the gradient function of $\sin 3x$. How did you convince yourself?

Can you find the definite integral of a transformed function?

Can you work out the equation of the function from its graph?

By considering a point on a unit circle, can you use geometry to find the derivatives of $\sin x$ and $\cos x$?

How are $\sin x$, $\cos x$ and $\tan x$ related to each other? Can you make sense of the the 'slices'?

Can you prove an algebraic statement using geometric reasoning?

Can you match all the different trig functions to their graphs?

Can you sketch the graphs of these two reciprocal functions? What are the links between them?

What happens when you combine functions? Can you sketch the results?

Can you fill in all the missing values and trig functions to make the tables complete?

Can you compose four functions to create the set of functions given?

Can you find functions with the desired properties to fill in the table?

Which of these logarithmic challenges can you solve?

Some graphs grow so quickly you can reach dizzy heights...

Can you find a geometric proof for some $\tan\theta$ trig identities?

Can you find a geometric proof of these half-angle trig identities?

Using trig identities to help sketch graphs of functions

A game for one or more players in which you make a target value by building a trig expression

Some parabolas are related to others. How are their equations and graphs connected?

Given two algebraic fractions, how can you decide when each is bigger?

How can you work out the equation of a parabola just by looking at key features of its graph?

If you know some points on a line, can you work out other points in between?

Problems to help you get started with higher mathematics courses

Can you find a polynomial function whose first derivative is equal to the function?

Use some calculus clues to pin down an equation of a cubic graph.

Can you find the missing constants from these not-quite-so-obvious definite integrals?

Can you find equations for cubic curves that have specific features?

Can you find trig graphs to satisfy a variety of conditions?

Can you work out the equations of all these mixed up parabolas?

When you transform a function, what can you work out about the gradient?

If you know some information about a parabola, can you work out its equation?

What questions does the spiral construction prompt you to ask?

You're used to working with quadratics with integer roots, but what about when the roots are irrational?

Can you make sense of these unusual fraction sequences?

Here are some more triangle equations. Which are always true?

Which of these equations concerning the angles of triangles are always true?

What graphs can you make by transforming sine, cosine and tangent graphs?

Can you sketch and then find an equation for the locus of a point based on its distance from two fixed points?

Can you find the centre and equation of a circle given a number of points on the circle? When is it possible and when is it not?

A lune is the area left when part of a circle is cut off by another circle. Can you work out the area?

In this resource, the aim is to understand a fundamental proof of Pythagoras's Theorem.

This graph looks like a transformation of a familiar function...

What do we REALLY mean when we talk about a tangent to a curve?