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Draw graphs on your computer!

 Blog, GCSE Higher, GCSE Maths, Graphs  No Responses »
Feb 232014
 

If you are studying GCSE you need to be able to draw and recognise graphs of simple functions, both straight lines and curves.  If you are at college your computer might have software on it such as Omnigraph. If you are at home you can download free open source software that does the same job, called “Graph”. You can read more about Graph and download it here. When you have downloaded it experiment with different functions and see what happens to the graph. To enter x² you have to use x^2.

Here are some ideas of functions to try.

y=x,  y=2x,  y=3x,  y=4x etc

y=x+1, y=x+2,  y=x+3 etc

y=-x,  y=-2x,  y=-3x etc

y=x-1,  y=x-2, y=x-3 etc

y=x^2,  y=x^2+1,  y=x^2+2 etc

y=x^2+x,  y=x^2 +2x,  y=x^2 +3x etc

y=x^3,  y=x^3 +1,  y=x^3 +2 etc

 

Statistics Crossword

 Averages, Collecting Data, Data Handling, GCSE Higher, GCSE Maths, Graphs and Charts, Hot Potato, Range, Uncategorized, Vocabulary  No Responses »
Feb 162014
 

Here is a crossword to help you with some of the important vocabulary you need for statistics at GCSE level. You can do the interactive version or print off a paper copy and check you answers later on the interactive version. There are a few non-mathematical clues!

Formula, expression, identity, equation?

 algebra, equations, formula, GCSE, GCSE Higher, GCSE Maths, Hot Potato, Uncategorized  2 Responses »
Feb 022014
 

Do you understand the difference between a formula, expression, identity and equation?

A formula is a rule written using symbols that describe a relationship between different quantities. Typical maths formulae include

A = πr² (area of a circle)

C=πd (circumference of a circle)

An expression is a group of mathematical symbols representing a number or quantity. Expressions never have equality or inequality signs like =, >, <, ≠ ,≥ ,≤. Some examples

3a

3xy + 4x

t² + t³

An identity is an equation that is always true, no matter what values are chosen.

Examples

3a + 2a =  5a

x²+x² = 2x²

5 x 10 = 10 x 5

An equation is a mathematical statement that shows that two expressions are equal. It always includes an equals sign.

Examples

x² =100

3x(x+5)= 42

(x+3)(x-2)=0


Use this exercise to make sure you understand the difference.

Mobile Phone apps

 Blog, GCSE, GCSE Higher, GCSE Maths  No Responses »
Feb 022014
 

I am becoming increasingly concerned by students who seem to have developed a complete addiction to their mobile phone! Many struggle to concentrate for a minute without having to check their device. So, mobile phone addicts, here is my solution to get you engaged in maths again! Download these great apps, and prepare for your GCSE. They both have limited free versions so you can try them out, but the price for the full version is very reasonable and much less than a revision book.

https://play.google.com/store/apps/details?id=com.webrich.gcsemathslite

 

Equations of straight lines. y=mx+c

 GCSE, GCSE Higher, GCSE Maths, Graphs and Charts, Hot Potato, Uncategorized, y=mx+c  No Responses »
Jan 262014
 

GCSE students need to be able to work out the equation of a graph from what it looks like.
If it’s a straight line graph you just need to look for two things.
1. The Intercept. This is where the line crosses the y axis.
2. The gradient. This is the steepness of the line. If the line goes up from left to right it will be positive. If the line goes down from left to right it will be negative. The larger the number the steeper the line.

This example shows the line y=2x-4. The line goes up two units for each unit it goes across. The gradient is 2÷1=2. It crosses the y axis at -4, so the intercept is -4.

Mathematicians use y=mx+c as the general formula for any straight line. The gradient is m and the intercept is c.

Try this exercise to see if you can match the graphs with their equations.

Try this exercise to see if you can match the equations with the correct gradient and intercept.

Try this jigsaw.

Can you match the following nth terms with their sequences?

 GCSE, GCSE Maths, Hot Potato, sequences, Uncategorized  No Responses »
Jan 152014
 

Each number in a sequence is called a “term”. In the sequence 3, 6, 9, 12, 15 the first term is 3 and the 5th term is 15.

You could call this sequence “the three times table”. In algebra we describe it as 3n.In other words the first term is 3×1, the second term is 3×2 etc.

3n+ 4 describes the sequence 7, 10, 13, 16, 19… because the first term is 3×1+4=7, the second term is 3×2+4=10 and the third term is 3×3+4=13. Notice that because n is multiplied by 3 the sequence goes up in 3’s.

Have a go at matching these nth terms with the right sequence.

Solve quadratic equations by factorisation

 equations, factorisation, GCSE, GCSE Higher, GCSE Maths, Hot Potato, quadratic equations, Uncategorized  No Responses »
Jan 122014
 

In the last exercise you learnt how to factorise quadratic expressions. We will now use this in order to solve simple quadratic equations.

Suppose x²+9x +20 = 0

If we factorise we get (x+4) (x+5) = 0

In other words, two numbers multiply together to make 0. This means one of those numbers must be 0!

So we know EITHER x+4 = 0 OR x+5 = 0

If x +4 = 0 x = -4

If x+5 =0 then x=-5

So the solution is x = -4 or -5

Remember quadratic equations will nearly always have 2 solutions.

Try this- you will probably need pencil and paper to factorise the equations first.

Factorise Quadratics

 factorisation, GCSE Higher, GCSE Maths, quadratic equations, Uncategorized  1 Response »
Jan 122014
 

To solve simple quadratic equations you need to be able to factorise quadratic expressions, like x²+9x +20

To do this look for a pair of numbers that add up to 9 and muliply together to make 20.

If you can’t find the right pair, write down all the pairs of factors of 20.

1 x 20

2 x 10

4 x 5

Now we can see the correct pair is 4 and 5.

So x²+9x +20=(x+4)(x+5)

Check this by multiplying out the brackets.

Lets try one involving negative numbers.

x² -x -12

The pairs of factors of -12 are

-12 x 1

-6 x 2

-4 x 3

-3 x 4

-2 x 6

-1 x 12

The pair that add up to -1 (because there is -x in the expression) are -4 and 3

So x² -x -12=(x-4)(x+3)

Now you try

Circle theorems from My Maths

 Circle, GCSE, GCSE Higher, GCSE Maths  No Responses »
Dec 122013
 

My Higher GCSE students really enjoyed using this tool to discover Circle Theorems this week. Highly recommended!

my maths circle theorems

Controversy over UK students performance in maths

 Blog, Data Handling, Functional Maths, GCSE Maths, Level 1, Level 2, Number, Shape, Space and Measure, Website  No Responses »
Dec 032013
 

The news today is concentrating on UK students performance in maths, and how the students in countries like China, Korea and Japan seem to be doing much better.

Why not have a go at some of the test questions and see how you can do?

http://www.oecd.org/pisa/test/

This is what the Guardian has to say about it.  The OECD believe their results show that boys are better at maths than girls. Do you think this is true? Over the many years I have taught maths I have not found a great difference between the sexes, but I do acknowledge that the boys generally find shape and space activities such as working with nets of three dimensional shapes easier.

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