Y10 cheat sheet for algebra
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Terms
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A term is separated by a + or - sign
E.g: 5x-3y+2 There are 3 terms in this equation: 5x, -3y and 2 |
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Coefficient
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The number in front.
E.g: In the term 5y, y's coefficient is 5 |
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Constant
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Constant is the single number which does not have any letters or numbers attached to it.
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Like terms
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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 |
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Unlike terms
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Terms which have different letters or combination of letters.
E.g: 3x and 3y are unlike terms |
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Rule
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Example
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Any numbers in the expression are multiplied.
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5 X 6x = 30x
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Numbers are placed in front of letters when multiplying.
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x X 3y = 3xy
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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 |
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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 |
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p4 means p multiplied by itself four times
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p4
= p X p X p X p |
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Simplify as powers and then multiply by
each other |
x X x X y X y
= x2y2 |
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When multiplying expressions with the
same base (letter), we add the powers. |
x2 X x5
= x2+5 =x7 |
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When dividing expressions with the
same base, we can subtract the powers. |
20x4 ÷ 10x
= 20x4-1 ÷ 10 =2x3 |
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When it is a "power of a power", multiply the powers
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(p4)2
= p4x2 = p8 |
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Power of 0 is always equal to 1
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p0=1, 40=1, 27680=1
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Multiply each term in the brackets by the outside term.
Then add together and simplify. |
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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 |
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1) Find the Highest Common Factor (number that divides in all terms equally) of all terms. Write this outside the brackets.
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2) Divide each term by the HCF, putting result in the brackets.
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Note: The HCF could be a number or a letter.
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