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Y10 cheat sheet for algebra
Algebra Vocabulary
Terms |
A term is separated by a + or - sign
E.g: 5x-3y+2
There are 3 terms in this equation:
5x, -3y and 2 |
Coefficient |
The number in front.
E.g: In the term 5y, y's coefficient is 5 |
Constant |
Constant is the single number which does not have any letters or numbers attached to it. |
Like terms |
Terms including exactly the same letter or combination of letters.
E.g: 6p, 8p and 5p are like terms
ab, 10ab and -2ab are like terms |
Unlike terms |
Terms which have different letters or combination of letters.
E.g: 3x and 3y are unlike terms |
Simplifying Expressions
Rule |
Example |
Any numbers in the expression are multiplied. |
5 X 6x = 30x |
Numbers are placed in front of letters when multiplying. |
x X 3y = 3xy |
If there is more than one letter they are written in
alphabetical order.
Numbers can be multiplied separately, then multiply letters. |
2q X 7p = 14pq
6p X 3p
= 6 X 3 X p X p
=18p2 |
Like terms can be grouped together and then added or
subtracted.
Remember, the + and - signs go with
the terms on their right. |
Simplify:
2x + y - x + 8y
=(2x - x) + (y + 8y)
= x + 9y |
Power Rules
p4 means p multiplied by itself four times |
p4
= p X p X p X p |
Simplify as powers and then multiply by
each other |
x X x X y X y
= x2y2 |
When multiplying expressions with the
same base (letter), we add the powers. |
x2 X x5
= x2+5
=x7 |
When dividing expressions with the
same base, we can subtract the powers. |
20x4 ÷ 10x
= 20x4-1 ÷ 10
=2x3 |
When it is a "power of a power", multiply the powers |
(p4)2
= p4x2
= p8 |
Power of 0 is always equal to 1 |
p0=1, 40=1, 27680=1 |
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Solving Equations
The goal of solving an equation is to get the letter term on the left of the = sign and the number/value on the right.
Remember if a number or term is moved across the equals, then you must use the opposite operation. |
Expanding
Multiply each term in the brackets by the outside term.
Then add together and simplify. |
Examples:
8(c + d - e)
= 8 X c + 8 X d - 8 X e
=8c + 8d - 8e |
4x(2x - 5)
=(4x X 2x) + (4x X -5)
=8x2 - 20x
|
Factorising
1) Find the Highest Common Factor (number that divides in all terms equally) of all terms. Write this outside the brackets. |
2) Divide each term by the HCF, putting result in the brackets. |
Note: The HCF could be a number or a letter. |
Factorising Quadratic Equations
Calculating Gradients of a Line
|
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