Equations and Formulae - Stage 4

System Speak

Stage: 5 Challenge Level: Challenge Level:1

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

How Old Am I?

Stage: 4 Challenge Level: Challenge Level:1

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?

Fair Shares?

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

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

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

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?

Terminology

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

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

Pick's Theorem

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

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.

Arithmagons

Stage: 4 Challenge Level: Challenge Level:1

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

Warmsnug Double Glazing

Stage: 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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

Matchless

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

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 ?

Which Is Cheaper?

Stage: 4 Challenge Level: Challenge Level:1

When I park my car in Mathstown, there are two car parks to choose from. Which car park should I use?

Which Is Bigger?

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

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

Training Schedule

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

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?

Multiplication Arithmagons

Stage: 4 Challenge Level: Challenge Level:1

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

Mega Quadratic Equations

Stage: 5 Challenge Level: Challenge Level:1

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

Table Total

Stage: 4 Short Challenge Level: Challenge Level:1

Can you find the sum of all of the numbers in the table?

Symmetric Reasoning

Stage: 4 Short Challenge Level: Challenge Level:1

Can you sum up the solutions to this equation?

Pure Algebra

Stage: 4 Short Challenge Level: Challenge Level:1

Can you work out the product of $a$ and $b$ from the information in the question?

Bat and Ball

Stage: 4 Short Challenge Level: Challenge Level:1

Can you work out how much this bat costs?

Square to a Rectangle

Stage: 4 Short Challenge Level: Challenge Level:1

Kevin has moved some tiles to change the shape of his patio from a square to a rectangle. What are the lengths of the sides of the rectangle?

Black and White Socks

Stage: 4 Short Challenge Level: Challenge Level:2 Challenge Level:2

There are 20 black socks and some white socks in a drawer. Can you work out how many of the socks are white?