Algebra /Trigonometry Regents Exam 06 www.jmap.org 06a A market research firm needs to collect data on viewer preferences for local news programming in Buffalo. Which method of data collection is most appropriate? ) census survey ) observation ) controlled experiment What is the number of degrees in an angle whose radian measure is 8π 5? ) 576 88 ) 5 ) 5 The simplest form of ) x x + ) x ) x x x x 8 x 6 Which equation represents the graph below? is Which diagram represents a relation that is both one-to-one and onto? ) ) y = sinx y = sin x ) y = cos x ) y = cos x ) ) The sum of the first eight terms of the series + 8 9 +... is ),07,85 ) 9, ) 65,55 7 What is the graph of the solution set of x >5? ) ) )
Algebra /Trigonometry Regents Exam 06 www.jmap.org 8 What is the range of the function shown below? ) x 0 x 0 ) y 0 ) y 0 9 The expression sin(θ + 90) is equivalent to ) sin θ cos θ ) sin θ ) cos θ 0 The points (,),,, and (6,d) lie on the graph of a function. If y is inversely proportional to the square of x, what is the value of d? ) ) ) 7 In the right triangle shown below, what is the measure of angle S, to the nearest minute? ) 8 ' 8 ' ) 6 56' ) 6 9' Which ordered pair is in the solution set of the system of equations shown below? y x + = 0 ) (,6) (,) ) (, ) ) ( 6, y x = 0 Susie invests $500 in an account that is compounded continuously at an annual interest rate of 5%, according to the formula A = Pe rt, where A is the amount accrued, P is the principal, r is the rate of interest, and t is the time, in years. Approximately how many years will it take for Susie s money to double? ). 6.0 ).9 ).7 If n is a negative integer, then which statement is always true? ) 6n < n n > 6n ) 6n < n ) n > (6n) 5 The expression + (k x) is equal to ) 58 x 6 x ) 58 x ) 6 x 5 k = 6 Which value of r represents data with a strong positive linear correlation between two variables? ) 0.89 0. ).0 ) 0.0
Algebra /Trigonometry Regents Exam 06 www.jmap.org 7 Which problem involves evaluating 6 P? ) How many different four-digit ID numbers can be formed using,,,, 5, and 6 without repetition? How many different subcommittees of four can be chosen from a committee having six members? ) How many different outfits can be made using six shirts and four pairs of pants? ) How many different ways can one boy and one girl be selected from a group of four boys and six girls? 8 Which equation is represented by the graph below? 0 An angle, P, drawn in standard position, terminates in Quadrant II if ) cos P < 0 and csc P < 0 sin P > 0 and cos P > 0 ) csc P > 0 and cot P < 0 ) tanp < 0 and sec P > 0 The expression log m is equivalent to ) (log + logm) log + logm ) log + logm ) log6 + logm In PQR, p equals ) r sin P sin Q r sin P sin R ) r sin R sin P ) q sin R sin Q ) (x ) + (y + ) = 5 (x + ) + (y ) = 5 ) (x ) + (y + ) = ) (x + ) + (y ) = If tan Arccos ) ) ) k =, then k is 9 If x = i, y = i, and z = m + i, the expression xy z equals ) mi 6 6mi ) mi ) 6 6mi Which expression is equivalent to x y? y 5 ) ) ) y x y x x y x y
Algebra /Trigonometry Regents Exam 06 www.jmap.org 5 Expressed with a rational denominator and in x simplest form, x x is ) x + x x x x x ) x + x x ) x + x x 6 What is the common ratio of the sequence 6 a 5 b, a b, 9 6 ab5,...? ) b a 6b a ) a b ) 6a b 7 In KLM, KL = 0, LM =, and m K = 0. The measure of M? ) must be between 0 and 90 must equal 90 ) must be between 90 and 80 ) is ambiguous 8 Determine the sum and the product of the roots of the equation x + x 6 = 0. 9 Solve algebraically for x: log 7 (x ) = 0 Find the number of possible different 0-letter arrangements using the letters of the word STATISTICS. Express the product of cos 0 and sin 5 in simplest radical form. Find, algebraically, the measure of the obtuse angle, to the nearest degree, that satisfies the equation 5csc θ = 8. If g(x) = ax x, express g(0) in simplest form. cot x sin x Express as a single trigonometric sec x function, in simplest form, for all values of x for which it is defined. 5 On a multiple-choice test, Abby randomly guesses on all seven questions. Each question has four choices. Find the probability, to the nearest thousandth, that Abby gets exactly three questions correct. 6 Solve the equation below algebraically, and express the result in simplest radical form: x = 0 x 7 A ranch in the Australian Outback is shaped like triangle ACE, with m A =, m E = 0, and AC = 5 miles. Find the area of the ranch, to the nearest square mile. 8 Ten teams competed in a cheerleading competition at a local high school. Their scores were 9, 8, 9, 7, 5, 0,, 8, 7, and 8. How many scores are within one population standard deviation from the mean? For these data, what is the interquartile range? 9 Solve algebraically for all values of x: x + x + x = 6x
06a Answer Section ANS: PTS: REF: 060a STA: A.S. TOP: Analysis of Data ANS: 8π 5 80 π = 88 PTS: REF: 060a STA: A.M. TOP: Radian Measure KEY: degrees ANS: PTS: REF: 060a STA: A.A. TOP: Defining Functions ANS: S 8 = ( ( ) 8 ) ( ) = 96,605 5 = 9, PTS: REF: 060a STA: A.A.5 TOP: Summations KEY: geometric 5 ANS: x x x 8 x = x x x x 8 = x(x ) (x )(x + = x x + x PTS: REF: 0605a STA: A.A.7 TOP: Complex Fractions 6 ANS: PTS: REF: 0606a STA: A.A.7 TOP: Identifying the Equation of a Trigonometric Graph 7 ANS: x > 5. x < 5 x > 6 x > x > x < PTS: REF: 0607a STA: A.A. TOP: Absolute Value Inequalities KEY: graph 8 ANS: PTS: REF: 0608a STA: A.A.5 TOP: Domain and Range 9 ANS: sin(θ + 90) = sin θ cos 90 + cos θ sin 90 = sin θ (0) + cos θ () = cos θ PTS: REF: 0609a STA: A.A.76 TOP: Angle Sum and Difference Identities KEY: identities
0 ANS: = =. 6 d = 6d = d = PTS: REF: 060a STA: A.A.5 TOP: Inverse Variation ANS: sin S = 8 7 S = sin 8 7 S 8 ' PTS: REF: 06a STA: A.A.55 TOP: Trigonometric Ratios ANS: x = y. y (y) + = 0. x = ( = 6 y 9y = 8y = y = y = ± PTS: REF: 06a STA: A.A. TOP: Quadratic-Linear Systems KEY: equations ANS: 000 = 500e.05t = e.05t ln = ln e.05t ln.05.9 t =.05t ln e.05 PTS: REF: 06a STA: A.A.6 TOP: Exponential Growth
ANS: 6n < n. Flip sign when multiplying each side of the inequality by n, since a negative number. 6 n < n 6 > PTS: REF: 06a STA: A.N. TOP: Negative and Fractional Exponents 5 ANS: + ( x) + ( x) + ( x) + (5 x) + 6 x + 9 x + x + 5 x 6 x PTS: REF: 065a STA: A.N.0 TOP: Sigma Notation KEY: basic 6 ANS: PTS: REF: 066a STA: A.S.8 TOP: Correlation Coefficient 7 ANS: PTS: REF: 067a STA: A.S.9 TOP: Differentiating Permutations and Combinations 8 ANS: PTS: REF: 068a STA: A.A.9 TOP: Equations of Circles 9 ANS: (i)(i) (m + i) (i)(i )(m + i) (i)( )(m + i) ( i)(m + i) mi i mi + PTS: REF: 069a STA: A.N.9 TOP: Multiplication and Division of Complex Numbers 0 ANS: If csc P > 0, sin P > 0. If cot P < 0 and sin P > 0, cos P < 0 PTS: REF: 060a STA: A.A.60 TOP: Finding the Terminal Side of an Angle ANS: log m = log + log m = log + log m PTS: REF: 06a STA: A.A.9 TOP: Properties of Logarithms KEY: splitting logs ANS: PTS: REF: 06a STA: A.A.7 TOP: Law of Sines KEY: side, without calculator
ANS: tan0 =. Arc cos k = 0 k = cos 0 k = PTS: REF: 06a STA: A.A.6 TOP: Using Inverse Trigonometric Functions KEY: advanced ANS: PTS: REF: 06a STA: A.A.9 TOP: Negative Exponents 5 ANS: x x x x + x x + x = x + x x x x = x(x + x ) x(x ) = x + x x PTS: REF: 065a STA: A.A.5 TOP: Rationalizing Denominators KEY: index = 6 ANS: a b 6b = 6 a 5 b a PTS: REF: 066a STA: A.A. TOP: Sequences 7 ANS: sin 0 = 0. 8 + 0 < 80. (80 8) + 0 < 80 sin M M 8 PTS: REF: 067a STA: A.A.75 TOP: Law of Sines - The Ambiguous Case 8 ANS: Sum b a =. Product c a = PTS: REF: 068a STA: A.A.0 TOP: Roots of Quadratics
9 ANS: x = 7 x = 8 x = 8 x = PTS: REF: 069a STA: A.A.8 TOP: Logarithmic Equations KEY: advanced 0 ANS: P 0 0!!! =,68,800 = 50,00 7 PTS: REF: 060a STA: A.S.0 TOP: Permutations ANS: = 6 PTS: REF: 06a STA: A.A.56 TOP: Determining Trigonometric Functions KEY: degrees, common angles ANS: 5csc θ = 8 csc θ = 8 5 sin θ = 5 8 θ PTS: REF: 06a STA: A.A.68 TOP: Trigonometric Equations KEY: reciprocal functions ANS: g(0) = a(0) 0 = 00a ( 9) = 900a PTS: REF: 06a STA: A.A. TOP: Functional Notation ANS: cos x sin x sin x cot x sin x sec x = cos x = cos x PTS: REF: 06a STA: A.A.58 TOP: Reciprocal Trigonometric Relationships 5
5 ANS: C 7 = 5 8 6 56 = 85 68 0.7 PTS: REF: 065a STA: A.S.5 TOP: Binomial Probability KEY: exactly 6 ANS: x = 0 x = 0x x x 0x + = 0 0 ± 00 ()(). x = = () 0 ± 8 = 0 ± = 5 ± PTS: REF: 066a STA: A.A. TOP: Solving Rationals KEY: irrational and complex solutions 7 ANS: 5 sin 0 = a. (5)(0.) sin5 sin a 0. PTS: REF: 067a STA: A.A.7 TOP: Using Trigonometry to Find Area KEY: advanced 8 ANS: σ x 5.9 6 scores are within a population standard deviation of the mean. Q Q = 7 = x 8. PTS: REF: 068a STA: A.S. TOP: Dispersion KEY: advanced 9 ANS: x + x + x + 6x = 0 x(x + x + x + 6) = 0 x(x (x + ) + (x + )) = 0 x(x + )(x + ) = 0 x = 0,±i, PTS: 6 REF: 069a STA: A.A.6 TOP: Solving Polynomial Equations 6