# Equations and Formulae: Age 14-16

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

### Pick's Theorem

##### Age 14 to 16Challenge 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.

### Warmsnug Double Glazing

##### Age 14 to 16Challenge Level

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

### Which Is Cheaper?

##### Age 14 to 16Challenge 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?

### Arithmagons

##### Age 11 to 16Challenge Level

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

### Multiplication Arithmagons

##### Age 14 to 16Challenge Level

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

### How Old Am I?

##### Age 14 to 16Challenge 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?

### Matchless

##### Age 14 to 16Challenge 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 ?

### Fair Shares?

##### Age 14 to 16Challenge 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?

### CD Heaven

##### Age 14 to 16Challenge Level

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?

### Which Is Bigger?

##### Age 14 to 16Challenge Level

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

### Terminology

##### Age 14 to 16Challenge Level

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

### Training Schedule

##### Age 14 to 16Challenge 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?

### System Speak

##### Age 16 to 18Challenge Level

Five equations... five unknowns... can you solve the system?

##### Age 16 to 18Challenge Level

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