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.

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.

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.

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

Substitution in maths means swopping the letters for the right numbers so you can work out the value of an expression. Don’t forget that ab means a multiplied by b and c/d means c divided by d. Have a go at this interactive worksheet to get the idea.

http://www.mathswithgraham.org.uk/potatoes/numeracy/substitution.htm

#### Simple equations

Can you solve the simple equations Test your knowledge on this science quiz to see how you do and compare your score to others. Quiz by mathswithgraham

I have just discovered the quiz site Sporcle. Here is a multiplication game to get us started! You have to be really quick at typing as well as arithmetic!