Hints and Tips for Year 9 Maths Exam
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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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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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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. |
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Percentages represent an amount out of 100
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To convert, write the percentage as a fraction out of 100.
E.g: 65% = 65/100 This can then be simplified by dividing both numbers by their HCF. 65/100 = 13/20 (HCF of 65 and 100 is 5) |
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Decimals ↔ Percentages
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Decimal to Percentage:
Divide % by 100 (or move decimal point to the left by two places) 65% = 65 ÷ 100 = 0.65 Percentage to Decimal: Multiply the decimal by 100 (or move decimal point to the right by two places) 0.74 = 0.74 * 100 = 74% |
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Fractions to decimals
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Divide the numerator by the denominator:
2/3 = 2 ÷ 3 = 0.33333 |
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Decimals to fractions
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Take the decimal as an amount out of 10, 100, 100 etc depending on how many decimal places:
0.65 = 65/100 (2dp) 0.625 = 625/1000 (3dp) From here you may be able to simplify further using HCF |
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