# ALGEBRA -

basics of algebra

expanding and simplying brakets

equations, collecting like terms

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• Created by: Rayman08
• Created on: 09-05-12 19:37

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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 formula.
c = 20 - 2.50x
For example if Frances bought 2 books:
x = 2, so substitute x as 2.
SUBSTITUTION
Replacing a letter with a number is called substitution.
Example if w = 5.6, t =- 7.1, u = 2
5
And equation is w+t
u
Using brackets substitute numbers in:
= 5.6-7.1
2
5
1.5
=- 0.4
= - 3.75

## Other pages in this set

### 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.…read more

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### Page 5

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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 - 3) + x(x + 4)
= 2x - 6 + x2 + 4x
= x2 + 6x - 6
MULTIPLICATION OF TWO BRACKETS
Each term in first bracket is multiplied with the terms in the second brackets.…read more

### 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
METHOD 1: FACTORISATION
x = (- bb 2
2
-4ac
a )
The formula can be used to solve any quadratic equation which cannot be factorised.…read more

### Page 7

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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 need to solve the equation:
(x - 2)2 - 3 = 0
(x - 2)2 = 3
(x - 2) = ±3
x = ±3 + 2
x = 3.73 or 0.…read more

### Page 8

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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 < x4
The integer values which satisfy the above inequality are
-1, 0, 1, 2, 3, 4
NUMBER PATTERNS AND SEQUENCES
A Sequence is a list of numbers. There is usually a relationship between the numbers.…read more

### Page 9

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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 difference).…read more