Cheatography

# 9 Maths Exam Cheat Sheet by ceyre

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 termsab, 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 = 14pq6p 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.

### 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 = 0.65Percentage 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