# Past Secondary Features

### Symmetry, Substitutions and Surprises

##### Age 14 to 18

In this feature you will be challenged to derive elegant and efficient solutions to problems which, at first sight, might seem very difficult.

### Amazing Algebra

##### Age 11 to 16

We hope that these problems will help you appreciate that algebra can be a versatile tool for solving a range of problems.

### To Iff or Not to Iff?

##### Age 14 to 18

This feature will introduce the symbols $\implies$ and $\iff$ and challenge you to reason logically and create true statements using these symbols.

### Are You Sure?

##### Age 11 to 16

In this feature you are invited to explore a variety of problems, and are then asked to construct convincing arguments to explain what you have discovered.

### The Art of Deduction

##### Age 14 to 18

The problems in this feature offer you the chance to explore geometrical properties, and then challenge you to create clear, rigorous proofs.

### Geometrical Reasoning

##### Age 11 to 16

The problems in this feature offer you the chance to explore geometrical properties, make conjectures and create proofs to show that these are always true.

### Sums, Squares and Substantiation

##### Age 14 to 18

The problems in this feature challenge you to create convincing arguments or "proofs", and to identify where the logic breaks down in some "dodgy proofs".

### Can You Prove It?

##### Age 11 to 16

The problems in this feature offer you the chance to identify number patterns, make conjectures and create convincing mathematical proofs.

### Do You Know Your Carbon Footprint?

##### Age 11 to 16

The problems in this feature will encourage you to explore the impact that your lifestyle choices have on the environment.

### Maths and Climate Change

##### Age 14 to 18

The problems in this feature will allow you to explore the impact of lifestyle choices and help you gain a better understanding of the contributors to global emissions.

### Networks

##### Age 11 to 16

The resources in this feature introduce you to the world of networks and graph theory.

### Graph Theory and Networks

##### Age 14 to 18

The resources in this feature have been designed to give you an introduction to the world of graph theory and networks, and to their applications.

##### Age 16 to 18Challenge Level

This collection of activities offers you a variety of playful contexts in which you will be challenged to plan ahead and analyse the outcomes.

### Can You Plan Strategically?

##### Age 11 to 18

This collection of activities offers you a variety of playful contexts in which you will be challenged to plan ahead and analyse the outcomes.

### Around and Around

##### Age 11 to 16

The problems in this feature will give you the chance to investigate the properties of numbers in a variety of contexts.

### Modular Arithmetic

##### Age 16 to 18

Enter the world of modular arithmetic and discover the secrets of public key cryptography.

##### Age 11 to 16

This feature introduces you to number theory, a rich source of interesting problems which can lead to surprising results.

### Some Problems in Number Theory

##### Age 14 to 18

Number theory is a rich source of interesting problems which can lead to surprising results.

### Uphill and Downhill

##### Age 11 to 16

A chance to consider the equations of straight line graphs before moving on to consider the properties of quadratics and cubics.

### Curve Sketching Feature

##### Age 16 to 18

Curve sketching can be a very useful tool when you are solving equations or inequalities.

### Can You Think Flexibly?

##### Age 11 to 16Challenge Level

The problems in this feature challenge you to explore different ways of arriving at a solution

### Maths at Home

##### Age 11 to 18Challenge Level

Maths problems to try at home

### Comparing and Matching

##### Age 11 to 16Challenge Level

A chance to compare numbers expressed in different ways, and to use these different representations in calculations.

### Picturing with Rods

##### Age 11 to 16Challenge Level

Use Cuisenaire rods to help you visualise patterns and relationships with numbers

### Explore and Explain

##### Age 11 to 18

Explore these problems and explain the mathematical ideas you discover!

### Mathematical Wizardry

##### Age 11 to 18

Can you explain the mathematics behind the trickery?

### Is There a Better Way?

##### Age 11 to 18Challenge Level

Can you find the best strategy?

### Many Ways to See

##### Age 11 to 18Challenge Level

These problems can be represented in many different ways!

### Dynamic Explorations

##### Age 11 to 18

Explore using interactive tools.

### Journeys of Discovery

##### Age 11 to 18

Journey into new and exciting territory!

### Look Again

##### Age 11 to 18

Think you know what's going on? Look again!

### Tales of the Unexpected

##### Age 11 to 18Challenge Level

Problems to astonish and amaze

### Stick at It!

##### Age 14 to 18Challenge Level

When you get stuck, stick at it!

### Get Stuck...in

##### Age 11 to 16Challenge Level

Challenging problems to get stuck into!

##### Age 14 to 18Challenge Level

Find out about Complex Numbers and their applications.

### What If...?

##### Age 11 to 16Challenge Level

These problems will make you say "I wonder what happens if...?"

### Inverse Problems

##### Age 14 to 18Challenge Level

If you know the output, how can you work out the input?

### Cracking Codes

##### Age 11 to 16

Learn about the maths you need to become a codebreaker!

### Root to Success

##### Age 16 to 18Challenge Level

Surds are surprising!

##### Age 11 to 16Challenge Level

Practice makes perfect.

### Imagine This!

What if we could find the square root of negative numbers?

### Playful Puzzling

##### Age 11 to 16Challenge Level

We hope you enjoy being mathematically playful with these puzzling problems.

### Areas and Integrals

##### Age 14 to 18Challenge Level

This feature explores problems connected with area and integration

### Area Intrigue

##### Age 11 to 16Challenge Level

These problems invite you to think about area in unusual ways.

### Factorise This!

##### Age 11 to 16Challenge Level

Explore quadratics and the power of factorisation

### Inequality Extravaganza

##### Age 16 to 18Challenge Level

A selection of challenges about inequalities

### Short Problem Showcase

##### Age 11 to 16Challenge Level

Test yourself with these short challenges

### Hidden Treasures

##### Age 11 to 16Challenge Level

Try these treasures to celebrate NRICH's birthday!

### Making Connections

##### Age 16 to 18Challenge Level

Can you connect different areas of maths?

### Exploring Our Number System

##### Age 11 to 16Challenge Level

Simple starting points in Number Theory

### Get Functioning

##### Age 16 to 18Challenge Level

Transpose and compose functions

### Maths for Champions

##### Age 11 to 16Challenge Level

Can you win the Maths Olympics?

### Seeing Is Believing

##### Age 11 to 16Challenge Level

Some mathematical results can be proved beautifully with just a simple diagram...

### Underground Mathematics

##### Age 16 to 18Challenge Level

Check out the new Underground Maths website

### Number Patterns and Infinity

##### Age 11 to 16

Can you reach for the stars and make sense of infinity?

### Powerful Logs

##### Age 16 to 18Challenge Level

Explore exponentials and logarithms

### Probability and Evidence

##### Age 11 to 16Challenge Level

These resources explore probability in medicine and the law.

### Should I Risk It?

##### Age 11 to 16Challenge Level

Explore how to use statistics and probability to make informed decisions

### Identifying Trigonometry

##### Age 16 to 18Challenge Level

These CMEP resources explore the use of trigonometric identities and other trig features

### Number Teasers

##### Age 11 to 16Challenge Level

Some tricky number teasers for you to puzzle over

### Angles and Polygons

##### Age 11 to 16Challenge Level

Discover some angle relationships

### Graphs and Networks

##### Age 14 to 18Challenge Level

Be playful with graphs and networks, and see what theorems you can discover!

### Playing with Polygons

##### Age 11 to 16Challenge Level

Be playful with polygons. What patterns can you find?

### Curvy Calculus

##### Age 16 to 18Challenge Level

These resources from CMEP explore some aspects of differentiation and integration

### Transforming Ideas

##### Age 16 to 18

In this feature, explore what happens to functions when you transform their graphs

### Sequence Surprises

##### Age 11 to 16Challenge Level

Be surprised by some familiar sequences.

### Time to Be Irrational!

##### Age 16 to 18Challenge Level

There's nothing irrational about these problems!

### Tricky Trigonometry

##### Age 11 to 16

How well do you really understand mean, median and mode?

### Circular Arguments

##### Age 16 to 18Challenge Level

This CMEP feature explores the properties of circles and triangles

### Surprised by Shapes

##### Age 11 to 16Challenge Level

Explore some shape problems and make some discoveries!

### Logs by the Fire

##### Age 16 to 18Challenge Level

Try some of our CMEP resources around the theme of logarithms.

### Curves, Tangents and Asymptotes

##### Age 16 to 18Challenge Level

Explore and sketch curves with different properties.

### Thinking Functionally

##### Age 11 to 16Challenge Level

Who would have thought that addition could be so intriguing?

##### Age 16 to 18Challenge Level

Try some of our CMEP resources around the theme of quadratics.

### Making Decisions

##### Age 16 to 18Challenge Level

This feature introduces some topics from Decision Mathematics

### Plotting Graphs

##### Age 16 to 18Challenge Level

You can get a great feel for functions by sketching their graphs or using graph plotting software...

### Freedom and Constraints

##### Age 11 to 16

There's more room to manoeuvre than you might think!

### Exploring Dotty Grids at Upper Secondary

##### Age 14 to 18Challenge Level

What advanced mathematics can you do on a dotty grid?

### Exploring Mathematics on Dotty Grids

##### Age 11 to 16

I wonder what maths we can do on dotty paper...

### Making Sense of Data

##### Age 14 to 18

What stories do complicated data sets tell us? How can we present the information clearly?

### How Numbers Behave

##### Age 11 to 14

By exploring these problems you'll gain a greater appreciation of the importance of place value.

### How Powers Behave

##### Age 16 to 18

When numbers are raised to different powers, there are lots of properties you can explore.

### Working with Vectors

##### Age 14 to 18Challenge Level

Learn about vectors and how to use them to solve problems

### Positives and Negatives

##### Age 11 to 14Challenge Level

Learn all about positive and negative numbers!

### Visualising and Representing Complex Numbers

##### Age 16 to 18Challenge Level

What are complex numbers, and how can we represent them?

### Seeing Mathematically

##### Age 11 to 14Challenge Level

Creating mental images is a powerful way to solve maths problems.

### All about Area and Perimeter

##### Age 11 to 14Challenge Level

Working on these problems will offer you insights into how areas and perimeters are related.

### Integration as Area

##### Age 16 to 18Challenge Level

These problems invite you to explore integration as area, and use area integrals to solve problems.