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There are 64 NRICH Mathematical resources connected to CMEP, you may find related items under Admin.
Broad Topics > Admin > CMEPCan 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?
Given a sketch of a curve with asymptotes, can you find an appropriate function?
Can you find cubic functions which satisfy each condition?
Have you ever tried to work out the largest number that your calculator can cope with? What about your computer? Perhaps you tried using powers to make really large numbers. In this problem you will think about how much you can do to understand such numbers when your calculator is less than helpful!
Here you have an expression containing logs and factorials! What can you do with it?
Here you have an opportunity to explore the proofs of the laws of logarithms.
This problem is a nice introduction that will give you a feeling for how logs work and what that button on your calculator might be doing.
This gives you an opportunity to explore roots and asymptotes of functions, both by identifying properties that functions have in common and also by trying to find functions that have particular properties. You may like to use the list of functions in the Hint, which includes enough functions to complete the table plus some extras.You might like to work on this problem in a pair or small group, or to compare your table to someone else's to see where you have used the same functions and where not.
Can you describe what an asymptote is? This resource includes a list of statements about asymptotes and a collection of graphs, some of which have asymptotes. Use the graphs to help you decide whether you agree with the statements about asymptotes.
How does the temperature of a cup of tea behave over time? What is the radius of a spherical balloon as it is inflated? What is the distance fallen by a parachutist after jumping out of a plane? After sketching graphs for these and other real-world processes, you are offered a selection of equations to match to these graphs and processes.
What can you say about this graph? A number of questions have been suggested to help you look at the graph in different ways. Use these to help you make sense of this and similar graphs.
In this activity you will need to work in a group to connect different representations of quadratics.
This will encourage you to think about whether all quadratics can be factorised and to develop a better understanding of the effect that changing the coefficients has on the factorised form.
You're invited to decide whether statements about the number of solutions of a quadratic equation are always, sometimes or never true.
This comes in two parts, with the first being less fiendish than the second. It’s great for practising both quadratics and laws of indices, and you can get a lot from making sure that you find all the solutions. For a real challenge (requiring a bit more knowledge), you could consider finding the complex solutions.