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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: 5x3y+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 =18p^{2} 
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
p^{4} means p multiplied by itself four times 
p^{4} = p X p X p X p 
Simplify as powers and then multiply by each other 
x X x X y X y = x^{2}y^{2} 
When multiplying expressions with the same base (letter), we add the powers. 
x^{2} X x^{5} = x^{2+5} =x^{7} 
When dividing expressions with the same base, we can subtract the powers. 
20x^{4} ÷ 10x = 20x^{41} ÷ 10 =2x^{3} 
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) =8x^{2}  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. 


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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