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Name ________________________________________ Date ________________ Algebra 1 Honors Quarterly #3 Review Packet Lessons 7.1 and 7.2 Multiplication & Division Properties of Exponents Simplify each expression. Your answer should only contain positive exponents. a.) (-3x2y)3(11x3y5)2 b.) 12 x8 y 7 4x 2 y 6 2 Lesson 7.3 Rational Exponents Write each expression in radical form a.) (5 x) 1 2 b.) 4m 1 2 c.) z 2 3 Lesson 7.4 Scientific Notation Evaluate. Express each answer in scientific notation & standard form. a.) 3.4 10 5 10 3 4 4.9 10 2.5 10 3 b.) 4 Lessons 7.5 & 7.6 Exponential Functions (Growth & Decay) a.) The owner of a 1953 Hudson Hornet convertible sold the car at an auction. The owner bought it in 1984 when its value was $11,000. The value of the car increased at a rate of 6.9% per year. Write a function that models the value of the car over time. The auction took place in 2004. What was the approximate value of the car at that time? b.) The number of acres of Ponderosa pine forests decreased in the western United States from 1963 to 2002 by 0.5% annually. In 1963, there were about 41 million acres of Ponderosa pine forests. Write a function that models the number of acres of Ponderosa pine forests in the western United States over time. To the nearest tenth, about how many millions of acres of Ponderosa pine forests were there in 2002? Lesson 7.7 Geometric Sequences as Exponential Functions. Write a rule for the nth term of each geometric sequence. Then find a7 . a.) 1, -5, 25, -125, ... b.) 13, 26, 52, 104, … Lesson 7.8 Recursive Formulas Write the first five terms of each sequence. a.) a1 5, an an1 5; n 2 b.) a1 1, an 2an1; n 2 Lesson 8.1 Adding & Subtracting Polynomials Find each sum or difference. a.) 4m 2 m 2 (3m 2 10m 7) b.) Lessons 8.2 & 8.3 Multiplying Polynomials Simplify each expression. a.) x 2 (7 x 5) (2 x 6)( x 1) b.) 6 z 2 z 1 9 z 5 Lesson 8.4 Special Products Find each product. 2 a.) 3 x 4 b.) 5 x 2 y 2 4d 6d 3 3d 2 9d 3 7d 2 c.) 2 x 1 2 x 1 Lesson 8.5 Using the Distributive Property Factor or solve. a.) 45r 3 15r 2 b.) 12a 2 3a 8a 2 c.) 9 x 2 x 0 Lesson 8.6 Solving x2 + bx + c = 0 Factor or solve. a.) x 2 9 x 14 b.) a 2 6a 16 c.) x 2 3x 18 Lesson 8.7 Solving ax2 + bx + c = 0 Factor or solve. a.) 2 x 2 7 x 3 b.) 3a 2 14a 5 c.) p (20 p 3) 2 d.) A baseball player hits a baseball into the air with an initial vertical velocity of 72 feet per second. The player hits the ball from a height of 3 feet. Write an equation that gives the baseball’s height as a function of the time (in seconds) after it is hit. After how many seconds is the baseball 84 feet above the ground? e.) A person throws a ball upward from a 506 foot tall building. The ball’s height h in feet after t seconds is given by the equation h = -16t2 + 48t + 506. The ball lands on a balcony that is 218 feet above the ground. How many seconds was it in the air? Lesson 8.8 Differences of Squares & 8.9 Perfect Squares Factor each polynomial completely. a.) 4 y 6 16 y 4 b.) h3 4h 2 25h 100 c.) 9 x 2 12 x 4 Lessons 9.1 Graphing Quadratic Functions & 9.2 Solving Quadratic Equations by Graphing Use the f(x) = x2 + 4x + 3 to answer the following questions. a.) Write an equation for the axis of symmetry. b.) Find the vertex & state whether it is a maximum or a minimum. c.) State the domain & range of the function. d.) Graph the function. x y e.) What are the roots/zeros/solutions of this equation? Lesson 9.3 Transformations of Quadratic Functions Describe how the graph of each function is related to the graph of f(x) = x2. a.) g(x) = (x – 5)2 + 4 b.) h(x) = -2x2 – 3 Lesson 9.4 Solving Quadratic Equations by Completing the Square Find the value of c that makes the expression a perfect square trinomial. a.) x2 + 6x + c b.) x2 + 12x + c Solve by completing the square. Round to the nearest hundredth if necessary. c.) x2 – 16x = -15 d.) 2x2 + 20x – 8 = 0