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Algebra 2 – Semester 1 Review Topics: Below are the objectives for each chapter, each followed by a few problems related to the objective. You should work through these problems and check your answers with the answer sheet on a separate document. Chapter 1: • Plug an x-value into a function to determine the value of f(x) • Plug f(x) into a function to determine what x value(s) is/are needed to generate that output • Draw a complete graph for an equation • Identify domain and range of a graph and write them in mathematical language • Solve for x • Determine x- and y-intercepts of a linear or quadratic equation • Find slope and distance between two points • Relate table, graph, context, and equation for a given equation • Recognize linear behavior in graphs, tables, and contexts • Determine the equation of a line given 2 points Chapter 2: • Recognize algebraic and geometric sequences if given a list of numbers • Write the equation for an arithmetic sequence that does not start at term 0 • Write multipliers involving percents • Write the equation for a geometric sequence that does not start at term 0 • Generate equivalent expressions for a given expression by simplifying, distributing, rewriting, or factoring • Simplify exponential expressions • Solve for x • Solve a system of linear equations • Factor 15, 18, 36, 66 22, ch 3 #44 21, 60, 86, 90 21, 35, 60, Ch.2 #26 41, 49. 53, 107 86, 89 50 93 128 125 Ch 3 #46 46, 73, 111, 112, 153 86, Ch. 3 # 18 81, 112 122, 135 10, 29, 88 50, 56, 144(a,b,c,e) 25, 91 28, 90, 155 Chapter 3: • Describe what values of the multiplier give exponential increase and decrease • Solve for x when it is in the exponent 15 31, 57, 79, 110 • Determine an exponential equation given table, graph, or context 26, 39, 46, 64 • Use an exponential equation to calculate money when interest is compounded annually • Determine an exponential equation given either a and a point, b and a point, or 2 points • Simplify expressions involving roots and powers – use radical and exponent notation • Simplify fractional and negative exponents 41 • Simplify exponents 55, 139 • Solve a system of equations 43, 81, Ch 2 #101 • Factor 29, 60, 111 95, 96, 101, 109 134, 135 59, 133 Chapter 4: • Describe how a, h, and k change a parent graph • Graph a parabola from an equation in vertex form Graph: y = -0.5(x – 3)2 + 3 y = 2(x + 1)2 - 4 • Given a quadratic equation in standard form, rewrite it in vertex form, using any method 93 • Determine the value of a given h, k, x, and y 51, • Make an accurate graph of an exponential, hyperbola, cubic, and square root equation without a graphing calculator Graph: a) y = -2|x – 4| + 3 b) y = 1/(x + 3) c) y = 0.5(x + 1)3 – 5 d) y = 3√(x – 2) + 1 • Write the equation for parabolic, exponential, hyperbola, cubic, and square root graphs 78, 91 • Solve for x 39 Chapter 5: • Solve for x when squares, square roots, absolute value, and fractions are involved • Check your answer by plugging it back into the original equation • Solve for x by graphing and finding the x-values of the points of intersection or by putting all terms on one side of the equation and determining the x-intercepts • Solve a system of equations algebraically • Solve a linear inequality by determining the boundary points, testing regions, and shading appropriately • Solve a two-variable inequality by graphing the equation, testing a point, and shading appropriately • Solve a system of linear inequalities by graphing both equations, testing regions, and shading appropriately 4 40, 71, 135 4 6, 19, 25 37, 79 62, 69 83, 106 90 – graph only, 106