Equations and Formulae - Stage 4

Terminology

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

Triangle ABC is isosceles while triangle DEF is equilateral. Find one angle in terms of the other two.

Arithmagons

Stage: 3 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:1

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

Matchless

Stage: 3 and 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 ?

Golden Thoughts

Stage: 4 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Rectangle PQRS has X and Y on the edges. Triangles PQY, YRX and XSP have equal areas. Prove X and Y divide the sides of PQRS in the golden ratio.

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?

How Old Am I?

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

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?

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?

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?

Training Schedule

Stage: 4 Challenge Level: Challenge Level:1

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?

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?

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?

System Speak

Stage: 4 and 5 Challenge Level: Challenge Level:1

Solve the system of equations: ab = 1 bc = 2 cd = 3 de = 4 ea = 6

Equations and Formulae Stage 4 - Short Problems

Stage: 4 Challenge Level: Challenge Level:1

A collection of short Stage 4 problems on equations and formulae.