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Page 1

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ALGEBRA
COLLECTING LIKE TERMS
4a + 2a = 6a

3a2 + 6a2 = 9a2


If there are no like terms it cannot be simplified

WRITING FORMULA
Example: Frances buys x books at £2.50 each. She pays with a £20 note. If she receives c pounds
change write down as a…

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Page 3

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FORMULAS MUST HAVE AN `=' SIGN
Example Andrew hires a van. There is a standing charge of £8 and it costs £3 per hour. How much does it
cost for a 6 hours drive?

8 + (3×6) = £26


SOLVING LINEAR EQUATIONS ( ax + b = c )


2x…

Page 4

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Make sure the quadratic equation = 0. Then factorise the Quadratic equation.
a) x2 - 5x = 0
`x' is a common factor
x(x - 5) = 0

x = 0 or x - 5 = 0

x = 5


b) x2 - 3x = 10
x2 - 3x -…

Page 5

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(x + 2)(x + 1)


STEP 4: Expand to get ­ x2 + 3x + 2 = 0

MULTIPLYING OUT BRACKETS
Helps to simplify algebraic expressions.
The number outside the bracket multiplies with the terms inside the brackets.
Example:
a) 3(2x + 5) = 6x + 15

b) 2(x -…

Page 6

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We have already seen how to factorise a quadratic equations of the form x2 + bx + c = 0 there are other
methods for solving Quadratic equations.

METHOD 1: FACTORISATION
METHOD 2: QUADRATIC FORMULA
x = (- bb 2
2
-4ac
a )


The formula can be used to…

Page 7

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b =- 4

c=1

d = The co-efficient of b divided by 2 = ( b
2 ) therefore d =- 2


(x - 2)2 - (- 2)2 + 1 = 0

(x - 2)2 - 4 + 1 = 0

(x - 2)2 - 3 = 0

Now we…

Page 8

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x<4

The solution of the inequality may be represented on a number line




Use when the end point is included and when the end point is not included.

b) - 5 < 3x + 113
Subtract 1 from each side
- 6 < 3x12

Divide by 3
- 2 <…

Page 9

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2(n - 1)(n - 2)C (LEARN
a + (n - 1)d + 1 FORMULA)
1. ` a ' is the first term of the sequence.
2. ` d
' is the first difference between first 2 numbers.
3. C ' is the change between one difference and the next (2nd…

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