Equations and formulae: Age 14-16

This is part of our Secondary Curriculum collection of favourite rich tasks arranged by topic.

Scroll down to see the complete collection, or explore our subcollections on Perimeter and Area in two dimensions, and Surface Area and Volume in three dimensions.

problem

Arithmagons

Age

11 to 16

Challenge level

Can you find the values at the vertices when you know the values on the edges?

problem

Mega quadratic equations

Age

14 to 18

Challenge level

What do you get when you raise a quadratic to the power of a quadratic?

problem

How old am I?

Age

14 to 16

Challenge level

In 15 years' time my age will be the square of my age 15 years ago. Can you work out my age, and when I had other special birthdays?

problem

Symmetricality

Age

14 to 18

Challenge level

Five equations and five unknowns. Is there an easy way to find the unknown values?

problem

Warmsnug double glazing

Age

14 to 16

Challenge level

How have "Warmsnug" arrived at the prices shown on their windows? Which window has been given an incorrect price?

problem

Which is cheaper?

Age

14 to 16

Challenge level

When I park my car in Mathstown, there are two car parks to choose from. Can you help me to decide which one to use?

problem

Which is bigger?

Age

14 to 16

Challenge level

Which is bigger, n+10 or 2n+3? Can you find a good method of answering similar questions?

problem

Training schedule

Age

14 to 16

Challenge level

The heptathlon is an athletics competition consisting of 7 events. Can you make sense of the scoring system in order to advise a heptathlete on the best way to reach her target?

problem

Multiplication arithmagons

Age

14 to 16

Challenge level

Can you find the values at the vertices when you know the values on the edges of these multiplication arithmagons?

problem

Fair shares?

Age

14 to 16

Challenge level

A mother wants to share a sum of money by giving each of her children in turn a lump sum plus a fraction of the remainder. How can she do this in order to share the money out equally?

problem

Iff

Age

14 to 18

Challenge level

Take a triangular number, multiply it by 8 and add 1. What is special about your answer? Can you prove it?

problem

All CD Heaven stores were given the same number of a popular CD to sell for £24. In their two week sale each store reduces the price of the CD by 25% ... How many CDs did the store sell at each price?

problem

Terminology

Age

14 to 16

Challenge level

Given an equilateral triangle inside an isosceles triangle, can you find a relationship between the angles?

problem

Pick's theorem

Age

14 to 16

Challenge level

Polygons drawn on square dotty paper have dots on their perimeter (p) and often internal (i) ones as well. Find a relationship between p, i and the area of the polygons.

problem

Matchless

Age

14 to 16

Challenge level

There is a particular value of x, and a value of y to go with it, which make all five expressions equal in value, can you find that x, y pair ?

Equations and Formulae - Stage 4 STEM footer

You may also be interested in this collection of activities from the STEM Learning website, that complement the NRICH activities above.

Or search by topic

Number and algebra

Geometry and measure

Probability and statistics

Working mathematically

Advanced mathematics

For younger learners

Equations and formulae: Age 14-16

Arithmagons

Mega quadratic equations

How old am I?

Symmetricality

Warmsnug double glazing

Which is cheaper?

Which is bigger?

Training schedule

Multiplication arithmagons

Fair shares?

Iff

CD Heaven

Terminology

Pick's theorem

Matchless