Hints and Tips for Year 9 Maths Exam
A term is separated by a + or - sign
There are 3 terms in this equation:
5x, -3y and 2
The number in front.
E.g: In the term 5y, y's coefficient is 5
Constant is the single number which does not have any letters or numbers attached to it.
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
Terms which have different letters or combination of letters.
E.g: 3x and 3y are unlike terms
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
Numbers can be multiplied separately, then multiply letters.
2q X 7p = 14pq
6p X 3p
= 6 X 3 X p X p
Like terms can be grouped together and then added or
Remember, the + and - signs go with
the terms on their right.
2x + y - x + 8y
=(2x - x) + (y + 8y)
= x + 9y
p4 means p multiplied by itself four times
= p X p X p X p
Simplify as powers and then multiply by
x X x X y X y
When multiplying expressions with the
same base (letter), we add the powers.
x2 X x5
When dividing expressions with the
same base, we can subtract the powers.
20x4 ÷ 10x
= 20x4-1 ÷ 10
Multiply each term in the brackets by the outside term.
Then add together and simplify.
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
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.
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.
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.
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