0816a2. Algebra 2/Trigonometry Regents Exam 0816

Transcription

1 Algebra /Trigonometry Regents Exam a If the roots of the quadratic equation ax + bx + c = 0 are real, irrational, and unequal, then the value of the discriminant is ) equal to zero ) less than zero ) greater than zero and a perfect square 4) greater than zero and not a perfect square 5 What is the product of the roots of the quadratic equation x x = 4? ) ) ) 4) 4 Factored completely, the expression 6tanθ tan θ is equivalent to ) tanθ(4 tanθ) ) tanθ(tanθ 4) ) tanθ(4 tanθ)(4 + tanθ) 4) tanθ(tanθ + 4)(tanθ 4) 6 In which method of data collection does the researcher intentionally intervene to arrange for a comparison of results? ) taking a survey ) making observations ) filling out a questionnaire 4) conducting a controlled experiment High school officials wanted to assess the need for a new diving board. They created a survey and distributed it to a large, diverse crowd at the State Swim Meet held at their school. Which characteristic of the survey is most likely to create a bias? ) the number of participants ) the height of the participants ) the way the set of data from the survey was analyzed 4) the way the participants were selected to take the survey 7 Which equation could be represented by the graph below? 4 Which expression is equivalent to cos Pcos 50 sin P sin 50? ) cos(p 50) ) sin(p 50) ) cos(p + 50) 4) sin(p + 50) ) y = sin x ) y = cos x ) y = sinx 4) y = cos x

2 Algebra /Trigonometry Regents Exam The first four terms of the sequence with a = 40 and a n = 4 a n are ) 0,,7, ) 40,0,,6 7 8 ) 40,0,,7 4) 0,,6 7, 8 0 For all values for which the function is defined, the expression a is equivalent to ) a ) a ) a 4) a 9 Which diagram represents an angle of 7 4 π radians in standard position? ) The expression x ) ) ) y 4 x x y 4 x y 4 4) x y 4 y 6 is equivalent to ) ) The value of i x, where i is the imaginary unit, is ) ) - ) i 4) -i 8 x = 4 4)

3 Algebra /Trigonometry Regents Exam Which expression has a value of ) cot 60 ) tan60 ) csc 0 4) sec 0? 8 If log a = x and log b = y, then log(ab ) equals ) (x + y) ) x + y ) x + y 4) x + y 4 The solution set of x 9 = is ) { } ) {0} ) {,0} 4) {,0} 5 Which relation is not a function? ) y = x + ) y = 5(.) x ) x + y = 0 4) 4x + y = 9 6 The expression sin x is equivalent to cos x ) ) ) cos x 4) sinx 9 For a member of a certain species of bird, the probability of surviving to adulthood is 4 7. In a nest of five eggs, what is the probability, to the nearest hundredth, that at least four eggs will survive to adulthood? ) 0. ) 0.9 ) 0.6 4) In XYZ, m X = 7, x = 6, and z =. How many distinct triangles can be created with these parameters? ) ) ) 4) 0 7 Which relation is one-to-one? ) x = ) y = x x ) y = logx 4) y = x

4 Algebra /Trigonometry Regents Exam Which expression could be used to determine the value of y in the equation log x 8 = y? ) log 8 x ) log 8 log x ) 8 log x 4) log x log 8 An electron travels along a circular path with a radius of 4.6 miles. What is the number of miles the electron traveled during an interval when the central angle formed by the electron s path was 0? ).84 ) 8.8 ) ) 0 Which statement about the function f(x) = x x + is true? ) Its domain does not include. ) Its domain does not include. ) Its range does not include. 4) Its range does not include. 5 The fourth term of the expansion of (x ) 5 is ) 080x ) 540x ) 70x 4) 80x 6 What are the center and radius of the circle whose equation is x + y + 4x = 5? ) (,0) and ) (,0) and ) (,0) and 4) (,0) and 7 The product of 4m and 0m expressed in simplest radical form is ) 40m ) 5m ) m 40 4) m 5 8 Jamal has forgotten his password for the school computers. He knows that it must be 4 characters long (only lowercase letters or digits). He also knows that his password begins with one of 6 letters and ends with a digit. Determine how many different 4-character passwords are possible for Jamal if no letter or digit may be repeated. 4 Which value of a correlation coefficient represents the strongest relationship between the two variables in a given linear regression model? ) ) 0 ) 0.5 4) 0.9 4

5 Algebra /Trigonometry Regents Exam Emma s parents deposited $5000 into a bank account during her freshman year. The account pays 5% interest compounded continuously using the formula A = Pe rt, where A is the total amount accrued, P is the principal, r is the annual interest rate, and t is time, in years. Determine, to the nearest dollar, the amount in the account 4 years later. 4 Determine the exact value of csc P if P is an angle in standard position and its terminal side passes through the point (5, 8). 5 Determine the number of degrees in 8π 9 radians. 0 Find the common difference in the arithmetic sequence, a n, in which a = 6 and a 9 = 6. 6 Solve for x: 8 x + = x Solve the equation below algebraically for all values of θ in the interval 0 θ < 60. cos θ = cos θ 7 Determine algebraically the solution to 4x 5x 6(5 4x). Bacteria are being grown in a Petri dish in a biology lab. The number of bacteria in the culture after a given number of hours is shown in the table below. 8 The table below shows the number of hurricanes in the North Atlantic Ocean from 990 to 00. Determine the interquartile range for this set of data. Determine the population variance for this set of data, to the nearest tenth. Assuming this exponential trend continues, is it reasonable to expect at least 500 bacteria at hour 7? Justify your answer. Express in simplest form: a b b a b a a b 9 The Bermuda Triangle on a map is a section of the Atlantic Ocean bordered by line segments stretching from Miami to Bermuda to Puerto Rico and back to Miami. The distance from Miami to Bermuda is 04 miles; the distance from Bermuda to Puerto Rico is 057 miles; and the distance from Puerto Rico to Miami is 7 miles. Find the area contained within the Bermuda Triangle, to the nearest square mile. 5

6 ID: A 086a Answer Section ANS: 4 PTS: REF: 0860a STA: A.A. TOP: Using the Discriminant ANS: 6tanθ tan θ = tanθ(6 tan θ) = tanθ(4 tanθ)(4 + tanθ) PTS: REF: 0860a STA: A.A.7 TOP: Factoring the Difference of Perfect Squares KEY: binomial ANS: 4 The crowd includes people who are not connected with the high school. PTS: REF: 0860a STA: A.S. TOP: Analysis of Data KEY: bias 4 ANS: PTS: REF: 08604a STA: A.A.76 TOP: Angle Sum and Difference Identities KEY: simplifying 5 ANS: x x 4 = 0 c a = 4 = PTS: REF: 08605a STA: A.A.0 TOP: Roots of Quadratics 6 ANS: 4 PTS: REF: 08606a STA: A.S. TOP: Analysis of Data KEY: type 7 ANS: PTS: REF: 08607a STA: A.A.7 TOP: Identifying the Equation of a Trigonometric Graph 8 ANS: 4 (40) = 0; 4 (0) =.5; (.5) = PTS: REF: 08608a STA: A.A. TOP: Sequences KEY: term 9 ANS: PTS: REF: 08609a STA: A.A.56 TOP: Determining Trigonometric Functions KEY: graphs 0 ANS: 4 a = a PTS: REF: 0860a STA: A.A.5 TOP: Rationalizing Denominators KEY: index =

7 ID: A ANS: x y 6 = x y 4 = y 4 x PTS: REF: 086a STA: A.A.9 TOP: Negative and Fractional Exponents ANS: i 4 + i 5 + i 6 + i 7 + i 8 = + i + + i + = PTS: REF: 086a STA: A.N.0 TOP: Sigma Notation KEY: advanced ANS: PTS: REF: 086a STA: A.A.59 TOP: Reciprocal Trigonometric Relationships 4 ANS: 4 x 9 = x 9 = x 9 = x = 0 x = 0 x = x = PTS: REF: 0864a STA: A.A. TOP: Absolute Value Equations 5 ANS: 4 4x + y = 9 is an ellipse. PTS: REF: 0865a STA: A.A.8 TOP: Defining Functions 6 ANS: sin x cos x = cos x cos x = PTS: REF: 0866a STA: A.A.67 TOP: Simplifying Trigonometric Expressions 7 ANS: y = log x passes the horizontal line test. PTS: REF: 0867a STA: A.A.4 TOP: Defining Functions 8 ANS: log(ab ) = log a + log b = log a + log b = x + y PTS: REF: 0868a STA: A.A.9 TOP: Properties of Logarithms KEY: expressing logs algebraically 9 ANS: C C PTS: REF: 0869a STA: A.S.5 TOP: Binomial Probability KEY: at least or at most

8 ID: A 0 ANS: 6 sin 7 = < 80 sin Z > 80 Z 8.4 PTS: REF: 0860a STA: A.A.75 TOP: Law of Sines - The Ambiguous Case ANS: log x 8 = y x y = 8 log x y = log 8 y log x = log 8 y = log 8 log x PTS: REF: 086a STA: A.A.8 TOP: Logarithmic Equations KEY: advanced ANS: s = θ r = 0 π PTS: REF: 086a TOP: Arc Length KEY: arc length ANS: = x x + x + = x 0 5 PTS: REF: 086a STA: A.A.9 TOP: Domain and Range KEY: real domain, rational 4 ANS: PTS: REF: 0864a STA: A.S.8 TOP: Correlation Coefficient 5 ANS: 5 C (x)5 ( ) = 040x PTS: REF: 0865a STA: A.A.6 TOP: Binomial Expansions 6 ANS: 4 x + y + 4x = 5 x + 4x y = (x + ) + y = 9 PTS: REF: 0866a TOP: Equations of Circles

9 ID: A 7 ANS: 4 4m 0m = 40m = 8 5m = m 5 PTS: REF: 0867a STA: A.N. TOP: Operations with Radicals 8 ANS: = 9,70 PTS: REF: 0868a STA: A.S.0 TOP: Permutations 9 ANS: A = 5000e PTS: REF: 0869a STA: A.A. TOP: Evaluating Exponential Expressions 0 ANS: = 0 8 =.5 PTS: REF: 0860a STA: A.A.0 TOP: Sequences KEY: difference or ratio ANS: cos θ = cos θ = θ = 60,00 PTS: REF: 086a STA: A.A.68 TOP: Trigonometric Equations KEY: basic ANS: yes. y = 80(.048) PTS: REF: 086a STA: A.S.7 TOP: Regression KEY: exponential ANS: a b b a b a a b = a b b a a b b a = PTS: REF: 086a STA: A.A.7 TOP: Complex Fractions 4 ANS: sin P = y x + y = 8 = ( 8) 89 csc P = 89 8 PTS: REF: 0864a STA: A.A.6 TOP: Determining Trigonometric Functions 4

10 ID: A 5 ANS: 8π 9 80 π = 60 PTS: REF: 0865a STA: A.M. TOP: Radian Measure KEY: degrees 6 ANS: x + = 5 x x + 9 = 5x 5 0 = 5x x 4 0 = (5x + 7)(x ) x = 7 5, PTS: 4 REF: 0866a TOP: Exponential Equations KEY: common base not shown 7 ANS: 4x 5x 0 4x 4x 5 0 and x or 4x 5 0 and x x + 9x 0 0 (4x 5)(x + 6) 0 x 5 4 and x 6 x 5 4 x 5 and x 6 4 x 6 PTS: 4 REF: 0867a STA: A.A.4 TOP: Quadratic Inequalities KEY: one variable 8 ANS: 5, 7.8 PTS: 4 REF: 0868a STA: A.S.4 TOP: Dispersion KEY: interquartile range, variance 9 ANS: S = = A = ( 04)( 057)( 7) 5,490 PTS: 6 REF: 0869a STA: A.A.74 TOP: Heron s Formula 5