Algebra /Trigonometry Regents Exam 06 www.jmap.org 06a A doctor wants to test the effectiveness of a new drug on her patients. She separates her sample of patients into two groups and administers the drug to only one of these groups. She then compares the results. Which type of study best describes this situation? ) census ) survey ) observation ) controlled experiment If fx = ) ) ) 8 ) 8 x, what is the value of f( 0)? x 6 6 What is the value of x in the equation log x =? ).6 ) 0 ) 6 ),0 7 The expression 6x y 7 is equivalent to 7 y ) x ) x 8 y 8 7 y ) x ) x 8 y 8 8 Which equation is represented by the graph below? An auditorium has rows of seats. The first row has 8 seats, and each succeeding row has two more seats than the previous row. How many seats are in the auditorium? ) 0 ) 67 ) 760 ) 798 Expressed as a function of a positive acute angle, cos( 0 ) is equal to ) cos ) cos ) sin ) sin The value of x in the equation x + = 8 x is ) ) ) ) 0 ) y = x ) y = 0. x ) y = x ) y = 0. x 9 What is the fifteenth term of the geometric sequence, 0,,...? ) 8 ) 8 0 ) 68 ) 68 0
Algebra /Trigonometry Regents Exam 06 www.jmap.org 0 In ABC, a =, b =, and c =, as shown in the diagram below. What is the m C, to the nearest degree? Which graph represents a relation that is not a function? ) ) ) 9 ) 67 ) 7 What is the period of the function f(θ) = cos θ? ) π ) π ) π ) π ) ) What is the range of f(x) = (x + ) + 7? ) y ) y ) y = 7 ) y 7 Ms. Bell's mathematics class consists of sophomores, 0 juniors, and seniors. How many different ways can Ms. Bell create a four-member committee of juniors if each junior has an equal chance of being selected? ) 0 ),876 ),00 ) 9,0 ) The value of tan6 to the nearest ten-thousandth is ).07 ).08 ).8 ).9
Algebra /Trigonometry Regents Exam 06 www.jmap.org 6 The expression ) ) ) ) ( ) 8 + ( + ) 8 is equivalent to 9 Which graph shows y = cos x? ) 7 Akeem invests $,000 in an account that pays.7% annual interest compounded continuously. Using the formula A = Pe rt, where A = the amount in the account after t years, P = principal invested, and r = the annual interest rate, how many years, to the nearest tenth, will it take for Akeem s investment to triple? ) 0.0 ).6 ). ).0 8 The value of the expression ( r + r) is ) 8 ) ) 6 ) 6 r = ) ) )
Algebra /Trigonometry Regents Exam 06 www.jmap.org 0 If r = A B, then log r can be represented by C ) 6 log A + log B log C ) (loga + log B log C) ) log(a + B) C ) log A + log B log C The solution set of x + 6 = x + is ) {,} ) {,} ) {} ) { } Brian correctly used a method of completing the square to solve the equation x + 7x = 0. Brian s first step was to rewrite the equation as x + 7x =. He then added a number to both sides of the equation. Which number did he add? 7 ) 9 ) 9 ) ) 9 The expression sin θ + cos θ is equivalent to sin θ ) cos θ ) sin θ ) sec θ ) csc θ The number of minutes students took to complete a quiz is summarized in the table below. If the mean number of minutes was 7, which equation could be used to calculate the value of x? ) 7 = 9 + x x 9 + 6x ) 7 = x ) 7 = 6 + x 6 + x 6 + 6x ) 7 = 6 + x What is the radian measure of the smaller angle formed by the hands of a clock at 7 o clock? ) π ) π ) π 6 ) 7π 6 6 What is the coefficient of the fourth term in the expansion of (a b) 9? ),76 ) 6 ) 6 ),76
Algebra /Trigonometry Regents Exam 06 www.jmap.org 7 Samantha constructs the scatter plot below from a set of data. x y Simplify the expression and write the (x y 7 ) answer using only positive exponents. If f(x) = x 6 and g(x) = x, determine the value of (g f)( ). 6 Express as a single fraction the exact value of sin 7. 7 Solve the inequality 6 x < for x. Graph the solution on the line below. Based on her scatter plot, which regression model would be most appropriate? ) exponential ) linear ) logarithmic ) power 8 Express the product of y y and y + as a trinomial. 9 In a study of 8 video game players, the researchers found that the ages of these players were normally distributed, with a mean age of 7 years and a standard deviation of years. Determine if there were video game players in this study over the age of 0. Justify your answer. 8 The probability that a professional baseball player will get a hit is. Calculate the exact probability that he will get at least hits in attempts. 9 Solve the following systems of equations algebraically: = y x x = 7x + y + 0 Write a quadratic equation such that the sum of its roots is 6 and the product of its roots is 7. Evaluate e xlny when x = and y =. If f(x) = x 6, find f (x). Factor the expression t 8 7t completely.
06a Answer Section ANS: PTS: REF: 060a STA: A.S. TOP: Analysis of Data ANS: f0 = 0 ( 0) 6 = 0 8 = PTS: REF: 060a STA: A.A. TOP: Functional Notation ANS: S n = n [a + (n )d] = [(8) + ( )] = 798 PTS: REF: 060a STA: A.A. TOP: Series KEY: arithmetic ANS: cos( 0 +60 ) = cos( ) PTS: REF: 060a STA: A.A.7 TOP: Reference Angles ANS: x + = 8 x. x + = x + 0 = 9x x + 0 = 9x 0 = x = x x PTS: REF: 060a STA: A.A.7 TOP: Exponential Equations KEY: common base not shown 6 ANS: x = = 6 PTS: REF: 0606a STA: A.A.8 TOP: Logarithmic Equations KEY: basic 7 ANS: 6x y 7 = 6 7 x y = x 7 y PTS: REF: 0607a STA: A.A. TOP: Radicals as Fractional Exponents 8 ANS: PTS: REF: 0608a STA: A.A. TOP: Identifying the Equation of a Graph
9 ANS: a n = ( ) n a = ( ) = ( ) = 7 = 8 PTS: REF: 0609a STA: A.A. TOP: Sequences 0 ANS: = + ()() cos C 69 = 0cos C = 0cos C 0 = cos C C PTS: REF: 060a STA: A.A.7 TOP: Law of Cosines KEY: find angle ANS: π b = π PTS: REF: 06a STA: A.A.69 TOP: Properties of Graphs of Trigonometric Functions KEY: period ANS: PTS: REF: 06a STA: A.A.9 TOP: Domain and Range KEY: real domain ANS: C = 0 0 PTS: REF: 06a STA: A.S. TOP: Combinations ANS: PTS: REF: 06a STA: A.A.8 TOP: Defining Functions KEY: graphs ANS: PTS: REF: 06a STA: A.A.66 TOP: Determining Trigonometric Functions 6 ANS: + + = ( + ) = + PTS: REF: 066a STA: A.N. TOP: Rationalizing Denominators
7 ANS: 7000 = 000e.07t = e.07t ln = ln e.07t ln.07t ln e =.07.07. t PTS: REF: 067a STA: A.A.6 TOP: Exponential Growth 8 ANS: n Σ r + r + = 6 + = + = 0 8 PTS: REF: 068a STA: A.N.0 TOP: Sigma Notation KEY: basic 9 ANS: PTS: REF: 069a STA: A.A.6 TOP: Graphing Trigonometric Functions 0 ANS: PTS: REF: 060a STA: A.A.9 TOP: Properties of Logarithms KEY: splitting logs ANS: x + 6 = (x + ). is an extraneous solution. x + 6 = x + x + 0 = x + x 0 = (x + )(x ) x = x = PTS: REF: 06a STA: A.A. TOP: Solving Radicals KEY: extraneous solutions ANS: PTS: REF: 06a STA: A.A. TOP: Completing the Square ANS: sin θ + cos θ sin θ = cos θ = sec θ PTS: REF: 06a STA: A.A.8 TOP: Reciprocal Trigonometric Relationships ANS: PTS: REF: 06a STA: A.S. TOP: Average Known with Missing Data
ANS: π = 0π = π 6 PTS: REF: 06a STA: A.M. TOP: Radian Measure 6 ANS: C a 6 9 ( b) = 76a 6 b PTS: REF: 066a STA: A.A.6 TOP: Binomial Expansions 7 ANS: PTS: REF: 067a STA: A.S.6 TOP: Regression 8 ANS: 6y 7 0 y y. y y = 6y + 0 y y y = 6y 7 0 y y PTS: REF: 068a STA: A.N. TOP: Operations with Polynomials 9 ANS: no. over 0 is more than standard deviation above the mean. 0.9 8.08 PTS: REF: 069a STA: A.S. TOP: Normal Distributions KEY: predict 0 ANS: x 6x 7 = 0, b a = 6. c = 7. If a = then b = 6 and c = 7 a PTS: REF: 060a STA: A.A. TOP: Roots of Quadratics KEY: basic ANS: e ln = e ln = e ln 8 = 8 PTS: REF: 06a STA: A.A. TOP: Evaluating Exponential Expressions ANS: y = x 6. f (x) is not a function. x = y 6 x + 6 = y ± x + 6 = y PTS: REF: 06a STA: A.A. TOP: Inverse of Functions KEY: equations ANS: t 8 7t = t (t ) = t (t + )(t ) PTS: REF: 06a STA: A.A.7 TOP: Factoring the Difference of Perfect Squares KEY: binomial
ANS: x y 9. x y (x y 7 ) = y (x y 7 ) = y (x 6 y ) = x 6 y 9 = x x x x y 9 PTS: REF: 06a STA: A.A.9 TOP: Negative Exponents ANS: 7. f( ) = ( ) 6 =. g(x) = = 7. PTS: REF: 06a STA: A.A. TOP: Compositions of Functions KEY: numbers 6 ANS: sin( + 0) = sincos 0 + cos sin0 = + = 6 + = 6 + PTS: REF: 066a STA: A.A.76 TOP: Angle Sum and Difference Identities KEY: evaluating 7 ANS: 6 x < 6 x > 6 x > or 6 x < > x or < x. PTS: REF: 067a STA: A.A. TOP: Absolute Value Inequalities KEY: graph 8 ANS:. C C C 0 = 0 = 0 = PTS: REF: 068a STA: A.S. TOP: Binomial Probability KEY: at least or at most
9 ANS: 9, and,. y = x +. x + 7x = x + y = x + 7x x + 6x 9 = 0 (x + 9)(x ) = 0 x = 9 and x = y = 9 + = and y = + = PTS: 6 REF: 069a STA: A.A. TOP: Quadratic-Linear Systems KEY: equations 6