Topics include: Sets of numbers Natural #’s: {1, 2, 3, ….} Whole {0, 1, #’s: 2, 3, ….} - 3, - 2, - 1, 0, 1, 2, 3, Integers: {… ….} Rational {n| n = a/b, where a and b are integers, b 0} #’s: Order of Operations 1. Parentheses/Grouping Symbols (including radicals, absolute value, etc.) 2. Exponents 3. Multiply & Divide 4. Add & Subtract Example a: Simplify Laws/Properties: Commutative Addition: a + b = b + a Multiplication: ab = ba Associative Addition: (a + b) + c = a + (b + c) Multiplication: (ab)c = a(bc) Distributive: a(b + c) = ab + ac Identity Addition: 0 + a = a additive identity is ______ Multiplication: 1 x a = a multiplicative identity is ______ Inverse Addition: a + (-a) = 0 additive inverse is _____ Multiplication: a x ( 1/a) = 1 multiplicative inverse is _____ Multiplication by 0: 0 x a = Multiplication by -1: -1 x a = -1(a) = Equivalent fractions both reduced forms will generally be accepted on tests Combining like terms; Ex b Simplify: (4x2 + x 5) 2(x2 7x 3) – – – – R. 2 Equations, Inequalities, and Problem-Solving Solving Equations - Isolate the Variable Use the Add. & Mult. Prop. of Equality to & multiplication “undo” addition Ex a Solve: 4(1 3x) = 9 7x – –
Topics include: Sets of numbers Natural #’s: {1, 2, 3, ….} Whole #’s: {0, 1, 2, 3, ….} Integers: {… - 3, - 2, - 1, 0, 1, 2, 3, ….} Rational #’s: {n| n = a/b, where a and b are integers, b 0} Order of Operations 1. Parentheses/Grouping Symbols (including radicals, absolute value, etc.) 2. Exponents 3. Multiply & Divide 4. Add & Subtract Example a: Simplify Laws/Properties: Commutative Addition: a + b = b + a Multiplication: ab = ba Associative Addition: (a + b) + c = a + (b + c) Multiplication: (ab)c = a(bc) Distributive: a(b + c) = ab + ac Identity Addition: 0 + a = a additive identity is ______ Multiplication: 1 x a = a multiplicative identity is ______ Inverse Addition: a + (-a) = 0 additive inverse is _____ Multiplication: a x ( 1/a) = 1 multiplicative inverse is _____ Multiplication by 0: 0 x a = Multiplication by -1: -1 x a = -1(a) = Equivalent fractions both reduced forms will generally be accepted on tests Combining like terms; Ex b Simplify: (4x2 + x – 5) – 2(x2 – 7x – 3) R. 2 Equations, Inequalities, and Problem-Solving Solving Equations - Isolate the Variable Use the Add. & Mult. Prop. of Equality to “undo” addition & multiplication Ex a Solve: 4(1 – 3x) = 9 – 7x