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Hints and Tips for Year 9 Maths Exam
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 |
Powers 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 |
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. |
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. |
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Converting Fractions, Decimals and Percentages
Percentages represent an amount out of 100 |
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) |
Decimals ↔ Percentages |
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% |
Fractions to decimals |
Divide the numerator by the denominator:
2/3 = 2 ÷ 3 = 0.33333 |
Decimals to fractions |
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 |
Calculating a Fraction or Percentage of an amount
If calculating a fraction or percentage of an amount, multiply the amount by the fraction or percentage.
For example:
25% of $250 = $250 X 25% = $62.50
1/3 of 300 = 300 X 1/3 = 100 |
Measurement - Converting Length Units
Measurement - Converting Mass/Weight Units
Measurement - Converting Capacity Units
Measurement - Converting Volume Units
Measurement - Converting Volume and Capacity
Statistics - Calculations
Statistics - Dot Plot/Box and Whisker
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