# Friday, January 29, :15 a.m. to 12:15 p.m., only

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2 Part I Answer all 7 questions in this part. Each correct answer will receive credits. For each statement or question, choose the word or expression that, of those given, best completes the statement or answers the question. Record your answers on your separate answer sheet.  1 A survey is to be conducted in a small upstate village to determine whether or not local residents should fund construction of a skateboard park by raising taxes. Which segment of the population would provide the most unbiased responses? (1) a club of local skateboard enthusiasts () senior citizens living on fixed incomes () a group opposed to any increase in taxes (4) every tenth person 18 years of age or older walking down Main St. Use this space for computations. Which angle does not terminate in Quadrant IV when drawn on a unit circle in standard position? (1) 00 () 80 () 50 (4) x y The expression is equivalent to xy (1) () x y xy () xy (4) x y Algebra /Trigonometry Jan. 16 []

3 4 Which relation does not represent a function? Use this space for computations Domain Range Domain (1) () Range Domain Range Domain Range () (4) 5 In the diagram below, the spinner is divided into eight equal regions. D C B A E F G H Which expression represents the probability of the spinner landing on B exactly three times in five spins? (1) 8 C ( 5) 1 ( 4 5) 5 () 5 C ( 8) 1 ( 8) 7 () 8 C ( 1 5) 5 ( 4 5) (4) 5 C ( 1 8 ) ( 7 8 ) Algebra /Trigonometry Jan. 16 [] [OVER]

4 6 6 The expression 7a b c is equivalent to Use this space for computations. bc (1) () a bc () (4) 18 a 9 6 bc 6 5 a b c a 7 The amount of money in an account can be determined by the formula A Pe rt, where P is the initial investment, r is the annual interest rate, and t is the number of years the money was invested. What is the value of a \$5000 investment after 18 years, if it was invested at 4% interest compounded continuously? (1) \$967.0 () \$10,19.08 () \$ (4) \$10,7.17 x 8 What is 1 x 1 x expressed as a single fraction? (1) x 1 x 1 () () x 1 x (4) x 1 ( x 1) x 1 ( x 1) Algebra /Trigonometry Jan. 16 

5 9 What is the total number of points of intersection of the graphs of the equations x y 8 and y x? (1) 1 () () (4) 0 Use this space for computations. 10 Given the sequence: x, (x y), (x y), Which expression can be used to determine the common difference of this sequence? (1) x (x y) () x ( x y) () (x y) (x y) (4) ( x y) ( x y) 11 In a circle with a diameter of 4 cm, a central angle of 4π radians intercepts an arc. The length of the arc, in centimeters, is (1) 8π () 16π () 9π (4) π 1 Which graph is the solution to the inequality 4 x 6 5 7? (1) () () (4) Algebra /Trigonometry Jan. 16  [OVER]

6 1 What is the sum of the roots of the equation x 6x 0? (1) () () (4) Use this space for computations. 14 The scores of 1000 students on a standardized test were normally distributed with a mean of 50 and a standard deviation of 5. What is the expected number of students who had scores greater than 60? (1) 1.7 () 46 () (4) If T 10x, then log T is equivalent to y (1) (1 log x) log y () (1 log x) log y () log(1 x) log y (4) (1 log x) log y 16 Which statement regarding correlation is not true? (1) The closer the absolute value of the correlation coefficient is to one, the closer the data conform to a line. () A correlation coefficient measures the strength of the linear relationship between two variables. () A negative correlation coefficient indicates that there is a weak relationship between two variables. (4) A relation for which most of the data fall close to a line is considered strong. Algebra /Trigonometry Jan. 16 

7 17 What is the value of cos n π? (1) 1 () 0 n 1 Use this space for computations. () 1 (4) 1 18 The roots of the equation 4(x 1) x are (1) imaginary () real, rational, unequal () real, rational, equal (4) real, irrational, unequal 19 If f(x) x x 4, then f(x ) is equal to (1) x x 7 () x 9x 1 () x x 1 (4) x 9x 5 0 The expression x(i ) xi 1 is equivalent to (1) x 7xi () 5x () 7x (4) 9x 1 If the terminal side of angle θ passes through the point (, 4), what is the value of sec θ? (1) 5 () 5 4 () 5 (4) 5 4 Algebra /Trigonometry Jan. 16  [OVER]

8 When the inverse of tan θ is sketched, its domain is (1) 1 θ 1 () 0 θ π () π θ π (4) θ Use this space for computations. What is the third term of the recursive sequence below? a 1 6 a n 1 a n 1 n (1) 11 () 1 () 5 (4) 4 4 What is the equation of a circle with its center at (0, ) and passing through the point (, 5)? (1) x (y ) 9 () x (y ) 18 () (x ) y 9 (4) (x ) y 18 5 If angles A and B are complementary, then sec B equals (1) csc(90 B) () cos(b 90 ) () csc(b 90 ) (4) cos(90 B) Algebra /Trigonometry Jan. 16 

9 6 The legs of a right triangle are represented by x and x. The length of the hypotenuse of the right triangle is represented by Use this space for computations. (1) x 4 () () x 4 (4) x x 7 What are the amplitude and the period of the graph represented by the equation y cos θ? (1) amplitude: ; period: π () amplitude: ; period: 6π () amplitude: ; period: π (4) amplitude: ; period: 6π Algebra /Trigonometry Jan. 16  [OVER]

10 Part II Answer all 8 questions in this part. Each correct answer will receive credits. Clearly indicate the necessary steps, including appropriate formula substitutions, diagrams, graphs, charts, etc. For all questions in this part, a correct numerical answer with no work shown will receive only 1 credit. All answers should be written in pen, except for graphs and drawings, which should be done in pencil.  8 Solve algebraically for x: x Algebra /Trigonometry Jan. 16 

11 9 Factor completely: x x x 6 Algebra /Trigonometry Jan. 16  [OVER]

12 0 Solve algebraically for the exact value of x: log 8 16 x 1 Algebra /Trigonometry Jan. 16 

13 1 Determine how many eleven-letter arrangements can be formed from the word CATTARAUGUS. Algebra /Trigonometry Jan. 16  [OVER]

14 Express 10 in radian measure, to the nearest hundredth. Algebra /Trigonometry Jan. 16 

15 Determine the area, to the nearest integer, of SRO shown below. R S 8 17 O Algebra /Trigonometry Jan. 16  [OVER]

16 4 Prove that the equation shown below is an identity for all values for which the functions are defined: csc θ sin θ cot θ cos θ Algebra /Trigonometry Jan. 16 

17 5 Find the difference when 4 x 5 8 x 7 9 x is subtracted from x 4 x 9. Algebra /Trigonometry Jan. 16  [OVER]

18 Part III Answer all questions in this part. Each correct answer will receive 4 credits. Clearly indicate the necessary steps, including appropriate formula substitutions, diagrams, graphs, charts, etc. For all questions in this part, a correct numerical answer with no work shown will receive only 1 credit. All answers should be written in pen, except for graphs and drawings, which should be done in pencil.  6 Find the exact roots of x 10x 8 0 by completing the square. Algebra /Trigonometry Jan. 16 

19 7 The table below gives the relationship between x and y. x y Use exponential regression to find an equation for y as a function of x, rounding all values to the nearest hundredth. Using this equation, predict the value of x if y is 46.1, rounding to the nearest tenth. [Only an algebraic solution can receive full credit.] Algebra /Trigonometry Jan. 16  [OVER]

20 8 Solve the equation cos x cos x algebraically for all values of x in the interval 0 x 60. Algebra /Trigonometry Jan. 16 

21 Part IV Answer the question in this part. A correct answer will receive 6 credits. Clearly indicate the necessary steps, including appropriate formula substitutions, diagrams, graphs, charts, etc. A correct numerical answer with no work shown will receive only 1 credit. The answer should be written in pen.  9 Given: DC 10, AG 15, BE 6, FE 10, m ABG 40, m GBD 90, m C 90, BE ED, and GF FB A 15 G F 40 B 10 6 E C 10 D Find m A to the nearest tenth. Find BC to the nearest tenth. Algebra /Trigonometry Jan. 16  [OVER]

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23 Tear Here Tear Here Reference Sheet Area of a Triangle Law of Cosines K _ 1 ab sin C a b + c bc cos A Functions of the Sum of Two Angles Functions of the Double Angle sin (A + B) sin A cos B + cos A sin B sin A sin A cos A cos (A + B) cos A cos B sin A sin B cos A cos A sin A tan A + tan B cos A cos tan (A + B) A 1 1 tan A tan B cos A 1 sin A Functions of the Difference of Two Angles tan A tan A 1 tan A sin (A B) sin A cos B cos A sin B cos (A B) cos A cos B + sin A sin B Functions of the Half Angle tan A tan B tan (A B) 1 + tan A tan B sin _ 1 A 1 cos A Law of Sines a sin A b sin B c cos _ 1 A 1 + cos A sin C tan _ 1 Sum of a Finite Arithmetic Series A 1 cos A 1 + cos A S n n(a 1 + a n ) Sum of a Finite Geometric Series S n a 1(1 r n ) Binomial Theorem 1 r (a + b) n n C 0 a n b 0 + n C 1 a n 1 b 1 + n C a n b n C n a 0 b n n (a + b) n nc r a n r b r r = 0 Algebra /Trigonometry Jan. 16 []

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25 Tear Here Tear Here Scrap Graph Paper This sheet will not be scored.

26 Scrap Graph Paper This sheet will not be scored. Tear Here Tear Here

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28 ALGEBRA /TRIGONOMETRY Printed on Recycled Paper ALGEBRA /TRIGONOMETRY

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