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End of Course Algebra I Study Guide: November, 2011 End-of-Course Exam Items Es

End of Course Algebra I Study Guide: November, 2011 End-of-Course Exam Items Estimated Number of Questions (37 questions) Numbers & Operations 6-8 Function Characteristics 11-13 Linear Functions & Inequalities 11-13 Data Analysis 6-8 Format of exam questions: 29 multiple choice, 5 completion items and 3 short answer questions. A graphing calculator can be used for all questions and will be cleared at the start of the exam. A formula sheet and graph paper will be provided in the test booklet. Study Guide Organization: On the next page is the Review Topic Index. These items are key “green” standards that will be assessed for graduation. The number of test questions for each topic heading is shown to help guide your study priorities. Following the Index are Sample Questions for each topic. After each set of questions, there are STUDY NOTES that explain the answers. 1 Review Topic Index: (A2, A7) Numbers & Operations 6-8 questions Compare & Order Real Numbers Evaluate expressions with variables Exponents, roots, use properties to evaluate Evaluate Exponential Functions Arithmetic & Geometric Sequences Solving equations with several variables: ex. (A = prt) (A3) Function Characteristics 11-13 questions Relations and Functions Domain, range, finding roots Functions defined piecewise Independent, dependent variables Multiple representations: symbolic, graph, table, words Connections between representations Evaluate f(x) at a, solving f(x) (A4) Linear Functions & Inequalities 11-13 questions Write & Solve Linear Equations Graph Linear Equations Point slope forms, translate between Interpret Slope and intercepts Parallel & perpendicular lines Write & Solve systems of two linear equations Absolute value in equations Graphing Absolute value (A6) Data Analysis 6-8 questions Summary Statistics Valid Inferences Univariate Data Linear T ransformations Effect on Center & Spread Fit an equation to a line Best fit lines Predicting from data Correlation of data in Scatterplots (A2A) Numbers & Operations Compare & Order Real Numbers 2 Sample Question A2A1: Order the following from greatest to least. , 3 , 8.9, 8, , 9.3 o A. 8, 8.9, , 9.3 , 3 o B. , 3 , 8, 8.9, , 9.3 o C. 9.3 , 3 , , , 8.9, 8 o D. 3 , 9.3 , , , 8.9, 8 Answer: D Sample Question A2A2: A star’s color gives an indication of temperature and age. The chart shows four types of stars and the lowest temperature of each type. List the temperatures in order from lowest to highest. Type Lowest Temperature Color A 1.35 Blue- White B 2.08 Blue G 9.0 Yellow P 4.5 Blue o A. 1.35 , 2.08 , 4.5 , 9.0 o B. 1.35 , 4.5 2.08 , 9.0 o C. 9.0 , 1.35 , 2.08 , 4.5 o D. 9.0 , 4.5 1.35 , 2.08 , Answer: C STUDY NOTES: When ordering numbers, always be sure which order, greatest to least or least to greatest. 3 Real numbers include scientific notation, fractions, decimals, exponents and radicals. (Subsets of real numbers are natural, whole, counting, integers, rational and irrational numbers... ) Not included: imaginary numbers 4i. When comparing or ordering numbers, the fastest way is to use your calculator and convert all numbers to decimal approximations, then order. Scientific notation is a way to write very large or very small numbers. The base number is always written as one place followed by a decimal: 1.2343 , not as 123.43 to convert from to standard, move the decimal 3 places to the right, From 5.2 to 5200 to convert from to standard, move the decimal 3 places to the left, From 5.2 to 0.0052 Radicals: : to approximate, use your calculator. It is the opposite of exponents, it undoes an exponent. T o convert from a fraction to a decimal, divide the top by the bottom Sample item for Performance Expectation A1.2.A/M1.6.A Wh i c h n u mb e r s a r e b o t h l e s s t h a n 5 6  ? O A . - 2 . 1 a n d 6 5  O B . 2 3  a n d 3 4  O C . - 0 . 6 5 a n d - 1 . 2 O D . 2 3  a n d - 0 . 8 4 Answer: A 5 (A2B) Numbers & Operations Evaluate expressions with variables Sample Question A2B1: For what values of a is an integer? o A. a = 1, 0 o B. a ≤ 1 o C. a = 1, a ≠ 0 o D. a > 1 Answer: C Sample Question A2B2: Evaluate 2w + 6y2 for w = 4 and y = 3. o A. 330 o B. 62 o C. 60 o D. 44 Answer: B STUDY NOTES: Evaluate means to find the value of an algebraic expression by substituting a number for each variable and simplifying by using order of operations. PEMDAS. Do (P)arenthesis first, then any (E)xponents, (M)ultiply and (D)ivide from left to right, then (A)ddition and (S)ubtraction left to right. is undefined. = 5 distributive property: ex. 2(c + 4) = 2c + 8 ex. 3f(f – g3) = 3f2 – 3fg3 T est hint: rewrite the expression with the substitution, then use your calculator for each step. Verify order of operations one step at a time. Do not just use your calculator left to right. -a2 does not equal (-a)2 6 = 3, = 3, Absolute value is the distance from 0 to the expression inside the brackets. (A2C) Numbers & Operations Exponents, roots, use properties to evaluate Sample Question A2C1: Simplify: 2 -2 3 2 5 223-352 o A. 3 5 52 o B. 24325 o C. 3 5 245 o D. 3 2 245 Answer: C Sample Question A2C2: Simplify: o A. o B. 4 o C. (correct) o D. Sample Question A2C3: Simplify the expression using positive exponents. o A. x3 o B x5 o C. x20 o D. x4 Answer: C STUDY NOTES: 7 24 = 2×2×2×2 = 16 When simplifying exponents, change negative exponents to fraction form as shown below. 1 23 T o simplify square or cube roots, look for factors that are perfect squares: = = 2 Or perfect cube roots: (A7AB) Numbers & Operations Evaluate Exponential Functions, approximate solutions using graphs or tables. Sample Question A7A1: You won a door prize and are given a choice between two options. A: $150 invested for 10 years at 4% compounded annually, or B: $200 invested for 10 years at 3% compounded annually. Which plan is best and what is the final amount of the investment? Investment = P(1+r)t o A. A; $242 o B. B; $222 o C. A; $4,338 o D. B; $268 Answer: D Sample Question A7B1: Select the set of ordered pairs that represents an exponential function. o A. (0,0) (-2,2) (1,1) (2,2) o B. (4,6) (2,3) (6,8) (10,12) o C. (1,1) (3,9) (2,4) (0,0) o D. (0,0) (-1, 2) (-2, 3) (2,3) Answer: C STUDY NOTES: An exponential function has the form f(x) =abx where initial amount a , and the base ratio b≠ 0, b > 0 8 T ypical examples are compound interest and growth rates. The graph of an exponential functions is not linear, it increases at a progressively faster rate. (Exponentially) For example: population growth of crickets: f(x) =2(4)x models the growth in weeks (x) of 4 initial crickets, with a base growth rate of 2 In 8 weeks, we will have f(8) =4(2)8 = 1,024 crickets. An example of an exponential graph of these Points (1,1) (1,2) (2,4) Items may be presented as graphs, in tables or coordinates. Functions can be increasing, decreasing, be positive or negative, (A7D) Numbers & Operations Solving equations in several variables: ex. (A = prt) Sample Question A7D1: Solve A = p + prt for p o A. o B. o C. o D. Answer: A Sample Question A7D2: Solve for r o A. o B. o C. 9 o D. Answer: A (A3) Function Characteristics Relations and Functions Sample Question A3A1: Which of the following equations listed below determine y as a function of x? A. x = 3; y = 2x + 1 B. y = x2 + 1; x = 0 C. x2 + y2 = 1; x = y D. 3x – 2y = 7; y = 2x Answer: D Sample item for Performance Expectation A1.3.A/M1.2.A T h e e q u a t i o n o f a f u n c t i o n i s s h o w n . ( ) 1 f x x   Wh a t i s t h e d o ma i n o f f ( x ) ? O A . A l l r e a l n u mb e r s O B . A l l r e a l n u mb e r s e x c e p t - 1 O C . A l l r e a uploads/Finance/ algebra-study-guide.pdf