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9 Maths Exam Cheat Sheet by

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

Examples - Simpli­fying

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.

Factor­ising Example

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.

Solving Examples

 

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 - Example

Statistics - Dot Plot/Box and Whisker

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