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1.1 Number Operations Types of Numbers Natural Numbers (N): {1,2,3,…} Whole Numbers (W): {0,1,2,…} Integers: (Z): {…-2, -1, 0, 1, 2, …} Rational Numbers (Q): {a/b a and b are integers and b ≠ 0} Irrational Numbers (I) : {Any non repeating -non terminating number} Real Number (R): {The set of all rational and irrational numbers}

1.1 Number Operations Simplify 2 + 48 ÷ 6 5(8 - 6) + 2(4 -1) 3 - 4(2 - 7) 5 + [2 + (4 - 1) + 3(6 ÷ 2)] [24 - (2  8)] + 4(12 - 7)

1.1 Number Operations Write as decimals

1.1 Number Operations Write as percents

1.1 Number Operations Write as fractions

1.1 Number Operations Find the area 8 in 5 in 4 ft 2 ft

1.2 Variables in Algebra Definition of Algebraic Expression A collection of letters (called variables) and real numbers (called constants) combined using the operations of addition, subtraction, multiplication and division is called an algebraic expression. Term An expression separated by a plus or minus sign Variable A letter that represents a number Coefficient A number in front of a variable

Algebraic Expressions 1.2 Variables in Algebra Algebraic Expressions 5 + x 6  y 3  y – 4 + x 4x means 4 x and xy means x  y

1.2 Variables in Algebra Evaluate if a = 2, b = 3, and c = 4 3a - 2b 4ac - 3a 4(a + 2c)

1.3 Exponents and Powers Exponents If a is a real number and n is a natural number, then the nth power of a, or a raised to the nth power, written as an, is the product of n factors, each of which is a. exponent base an = a • a • a … • a

1.3 Exponents and Powers 72 is read as seven to the second power or 7 squared. 43 is read as 4 to the third power or 3 cubed.

1.3 Exponents and Powers Solve if x = 4 and y = 3 3x2 + 2y3 4(x + 3y)3

1.3 Exponents and Powers Formula Meaning A = lw Area of a rectangle A formula is an equation that describes a known relationship among measured quantities. Formula Meaning A = lw Area of a rectangle A = πr2 Area of a circle V = lwh Volume of a rectangular solid d =rt Motion equation

1.4 Order of Operation Order of Operation 1. Do all operations within grouping symbols such as parentheses or brackets. Evaluate any expressions with exponents. Multiply or divide in order from left to right. 4. Add or subtract in order from left to right.

1.4 Order of Operation 24 - 12 + 3 • 5 16 + 21 ÷ 3 - 6 4 • (3 + 7) - 2 • 4 3 + (2 + 3)2 - 7

1.4 Order of Operation Evaluate the expression if x = 2, y = 4, and z = 5 x + 2z - 5 x3 + 3x - 2 4 • (3x - y)2 + 5 • 4

1.5 Equations and Inequalities An equation is formed when an equal sign is placed between two expressions. Equations that contain variables are open sentences. Equations that do not contain variables are closed sentences.

1.5 Equations and Inequalities Check whether the numbers 3, 4, and 5 are solutions of the following equations. 3x - 5 = 7 4x2 - 31 = 5 3x + 7 = 2x + 12

1.5 Equations and Inequalities A solution of an inequality is a value of the variable that makes the inequality a true statement. The solution set of an inequality is the set of all solutions.

1.5 Equations and Inequalities Order on Real-Number Line a < b a is less than b a < b a is less than or equal to b a > b a is greater than b a > b a is greater than or equal to b a ≠b a is not equal to b

1.5 Equations and Inequalities Determine if x = 3 is a solution of each inequality 3x - 1 < 5 2x - 3 > 5x + 2 4x + 9 > 3(x + 4)

1.6 Models Addition Subtraction Multiplication Division Equals sum difference product quotient is plus minus times divided by gives added to subtracted multiply into yields more than less than twice per same increased decreased by of ratio total less double

1.6 Models Write each statement in mathematical terms Twice the sum of 3 and a number is 4. Three more than the square of a number is 6. 15 is 5 less than three times a number. The square of a number increased by 6 is -4.

1.7 Problem Solving 1. Read and understand the problem. General Strategies for Problem Solving 1. Read and understand the problem. Choose a variable 2. Translate the problem into an equation. 3. Solve the equation. 4. Interpret the results.(Check your answer)