Search by Topic

Filter by: Content type:
Age range:
Challenge level:

There are 56 results

Broad Topics > Admin > CMEP

problem icon

Stretching an Integral

Age 16 to 18 Challenge Level:

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

problem icon

Trigsy Integrals

Age 16 to 18 Challenge Level:

What different ways can you find to calculate these integrals?

problem icon

Sine Stretching

Age 16 to 18 Challenge Level:

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

problem icon

Slippery Areas

Age 16 to 18 Challenge Level:

Can you find the definite integral of a transformed function?

problem icon

Can You Find... Asymptote Edition

Age 16 to 18 Challenge Level:

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

problem icon

Rotating Derivatives

Age 16 to 18 Challenge Level:

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

problem icon

Slices of Pi

Age 16 to 18 Challenge Level:

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

problem icon

Parabella

Age 14 to 18 Challenge Level:

Can you prove an algebraic statement using geometric reasoning?

problem icon

Worth 1000 Words

Age 16 to 18 Challenge Level:

Which of the sketches matches the function given?

problem icon

Muddled Trig

Age 16 to 18 Challenge Level:

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

problem icon

Translating or Not?

Age 16 to 18 Challenge Level:

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

problem icon

Function Builder 1

Age 16 to 18 Challenge Level:

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

problem icon

Trig Tables

Age 16 to 18 Challenge Level:

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

problem icon

Compose

Age 16 to 18 Challenge Level:

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

problem icon

Two-way Calculus

Age 16 to 18 Challenge Level:

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

problem icon

To Log or Not to Log?

Age 16 to 18 Challenge Level:

Which of these logarithmic challenges can you solve?

problem icon

Log Lattice

Age 16 to 18 Challenge Level:

Can you figure out how each log fits into the lattice?

problem icon

How Fast Does it Grow?

Age 16 to 18 Challenge Level:

Exponential functions grow pretty quickly...

problem icon

Reach for the Stars

Age 16 to 18 Challenge Level:

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

problem icon

$t$ for Tan

Age 16 to 18 Challenge Level:

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

problem icon

Proving Half-angle Formulae

Age 16 to 18 Challenge Level:

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

problem icon

Inspecting Identities

Age 16 to 18 Challenge Level:

Using trig identities to help sketch graphs of functions

problem icon

Trig Countdown

Age 16 to 18 Challenge Level:

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

problem icon

Paired Parabolas

Age 16 to 18 Challenge Level:

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

problem icon

Which Fraction Is Bigger?

Age 16 to 18 Challenge Level:

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

problem icon

Name That Graph

Age 16 to 18 Challenge Level:

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

problem icon

Between

Age 16 to 18 Challenge Level:

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

problem icon

Finding Your Feet

Age 16 to 18 Challenge Level:

Problems to help you get started with higher mathematics courses

problem icon

Designing a Polynomial

Age 16 to 18 Challenge Level:

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

problem icon

Curvy Cubics

Age 16 to 18 Challenge Level:

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

problem icon

Integral Chasing

Age 16 to 18 Challenge Level:

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

problem icon

Can You Find... Cubic Curves

Age 16 to 18 Challenge Level:

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

problem icon

Can You Find... Trigonometric Edition Part 2

Age 16 to 18 Challenge Level:

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

problem icon

Which Parabola?

Age 16 to 18 Challenge Level:

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

problem icon

Slippery Slopes

Age 16 to 18 Challenge Level:

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

problem icon

Name That Graph Again

Age 16 to 18 Challenge Level:

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

problem icon

Irrational Constructions

Age 16 to 18 Challenge Level:

What questions does the spiral construction prompt you to ask?

problem icon

Nested Surds

Age 16 to 18 Challenge Level:

Can you find values that make these surd statements true?

problem icon

Irrational Roots

Age 16 to 18 Challenge Level:

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

problem icon

Staircase Sequences

Age 16 to 18 Challenge Level:

Can you make sense of these unusual fraction sequences?

problem icon

Have a Sine

Age 16 to 18 Challenge Level:

There's much more to trigonometry than sin, cos and tan...

problem icon

Equation or Identity (2)

Age 16 to 18 Challenge Level:

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

problem icon

Equation or Identity (1)

Age 16 to 18 Challenge Level:

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

problem icon

Can You Find... Trigonometry Edition

Age 16 to 18 Challenge Level:

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

problem icon

The Circle of Apollonius... Coordinate Edition

Age 16 to 18 Challenge Level:

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

problem icon

Finding Circles

Age 16 to 18 Challenge Level:

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?

problem icon

Quadrature of the Lunes

Age 16 to 18 Challenge Level:

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

problem icon

The Quintessential Proof

Age 16 to 18 Challenge Level:

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

problem icon

Transformation ... or Not?

Age 16 to 18 Challenge Level:

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

problem icon

A Tangent Is ...

Age 16 to 18 Challenge Level:

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