Work out how many people are in an office, given the ratio of females to males and what proportion wear glasses.

# Polygons

A polygon is a 2-dimensional many sided shape. If all the sides are the same length it is a regular polygon, if not it is an irregular polygon. A polygon is usually thought of as a convex shape (roughly circular), but they don't have to be, they can fold in on themselves and have intersecting... Continue Reading →

# Exam Question Technique

Here is question 18 from the AQA 3F June 2017 paper: The first thing to notice is this question is worth a whopping 5 marks and there is that tell-tale sentence 'You must show your working.', so it is going to require some thought and thorough working out. Before committing anything to paper have a... Continue Reading →

# What is the point of logarithms?

Lets say a scientist is studying the growth of a colony of bacteria. She has a hunch that the number of bacteria is given by the following: n = 10kt, where n is the number of bacteria in the colony, t is the time in minutes and k is a constant. She does an experiment... Continue Reading →

# Number bonds to 10

An important part of Key Stage 1 maths is fluency with addition and subtraction of single digit numbers. A significant step towards this is to play around with all the possible combinations of numbers which add up to 10, so called number bonds. Possibilities are: 0+10, 1+9, 2+8, 3+7, 4+6, 5+5, 6+4, 7+3, 8+2, 9+1,... Continue Reading →

# More on quadratics

Why does the general method Factorising quadratics, work? We are trying to factorise a general quadratic ax²+bx+c [1] into the form (dx+e)(fx+g). Multiplying this out gives: dx(fx+g)+e(fx+g) [2] dfx²+dgx+efx+eg [3] dfx²+(dg+ef)x+eg [4] If a = df, b = dg+ef and c = eg, then equation [1] is same as equation [4]. So ac can be... Continue Reading →

# Factorising quadratics

When factorising quadratics of the form x²+bx+c, the usual procedure is to write it like this: (x+..)(x+..) and then think of 2 numbers which multiply together to give c and add up to give b. So, for example: x²+x-12 factorises to (x+4)(x-3), because 4 * -3 = -12 and 4-3=1. Possible combinations which multiply together... Continue Reading →

# A trick for squaring numbers near 50

Did you know, there is a neat trick for working out the square of numbers near 50? Lets say, you want to find 53² Start with 2500 (the square of 50), add on 100 times the difference between your number and 50 (3x100 = 300 in this example), and finally add on the square of... Continue Reading →