Name Date Period. Calculater Permitted MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Transcription

1 PreAP Precalculus Spring Final Exam Review Name Date Period Calculater Permitted MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Simplify the expression. 1) csc π - x cos (-x) 1) 1 B) -1 C) -csc x D) cos x ) 1 1- cos x cos x csc x B) csc x C) sec x D) csc x ) ) 1 - sinx sin x - csc x sin x B) -sin x C)cosx D) -cos x ) Find all solutions in the interval [0, π). ) sinx - cosx = 0 ) x = π, π, π, π B) x = π, π C)x = π D) x = π, π 6 ) sin x = sin x ) 0, π, π B) 0, π C) π, π D) 0, π Find the exact value by using a half-angle identity. 6) cos - π 8 6) B) C) 1 + D) 1 - Perform the indicated operation. Write the result in standard form. ) ( + 9i) 16-81i B) i C)9 + i D) -6 + i ) Find the measures of two angles, one positive and one negative, that are coterminal with the given angle. 8) π 8) 6π ; - 1π B) 9π ; - 9π C) 9π ; - 6π D) 1π ; - 6π A-1

2 9) 8π 9) 18π ; - π B) 1π ; - π C) 1π ;- 1π D) π ; - 18π Write an equation for a sine curve that has the given amplitude and period, and which passes through the given point. ) Amplitude, period π/6, point (1/, 0) ) y = sin π 6 x - π B) y = sin 1x - C)y = sin 1x - π D) y = sin 6x - Use the arc length formula and the given information to find the indicated quantity. 11) r = 1 ft, θ = 9 ; find s 1 1 π ft B) 68 ft C)96 ft D) π ft 11) Convert the angle to decimal degrees and round to the nearest hundredth of a degree. 1) B) 0. C) 0.1 D) 0. 1) Solve the problem. 1) A car wheel has a 1-inch radius. Through what angle (to the nearest tenth of a degree) does the wheel turn when the car rolls forward ft? 198. B) 18. C) 19. D) ) 1) A boat sails for hours at 1 mph in a direction How far south has it sailed (to the nearest mile)? mi B) mi C) mi D) 1 mi 1) 1) The radius of a car wheel is 1 inches. How many revolutions per minute is the wheel making when the car is travelling at mph. Round your answer to the nearest revolution. 018 rpm B) 11 rpm C)6 rpm D) 99 rpm 1) 16) The minute hand of a clock is 6 inches long. What distance does its tip move in 8 minutes? 8 π in. B) 90 π in. C) 1 π in. D) π in. 16) 1) A ship travels 6 km on a bearing of 19, and then travels on a bearing of 9 for 11 km. Find the distance of the end of the trip from the starting point, to the nearest kilometer. 1 km B) 168 km C)18 km D) km 1) 18) A generator produces an alternating current according to the equation I = 6 sin 1πt, where t is time in seconds and I is the current in amperes. What is the smallest time t such that I = 8? 1 0 sec B) 1 8 sec C) 1 0 sec D) 1 0 sec 18) A-

3 Use the product, quotient, and power rules of logarithms to rewrite the expression as a single logarithm. Assume that all variables represent positive real numbers. 19) logm y - 9 logm x 19) logm y 9x B) logm y x18 C)logm y x9 D) logm y x11 Find all solutions to the equation in the interval [0, π). 0) sin x = -sin x 0) 0, π, π, π B) π, π, π, π C) π 8, 9π 8 D) No solution Find an algebraic expression equivalent to the given expression. 1) sin (arcsec u) u - 1 u B) u u + 1 u + 1 C) u + 1 D) u - 1 1) Write the expression using only the indicated logarithms. ) log (x + y) using natural logarithms ln ln (x + y) B) ln (x + y) ln C)ln (x + y) + ln D) ln (x + y) ln ) Use a calculator to find the approximate value of the expression. Express your answer in radians and round to three decimal places. ) csc-1 (-1.8) ).6 B) -. C).98 D).090 ) csc-1 (.1) 0. B) C).8 D) -.8 ) Solve the equation. ) Solve cot θ = for θ, where 0 θ 90 B) 60 C) D) 0 ) 6) (6 - x) = 16 B) - C) D) 6) Solve for x in the given interval. ) sec x = -, π x π ) π B) π C) π 6 D) π A-

4 Evaluate without using a calculator. 8) sec β, if sin β = - and tan θ > 0 8) B) C) D) - 91 Find the area. Round your answer to the nearest hundredth if necessary. 9) Find the area of the triangle with the following measurements: B = 8, a = 1 cm, c = cm 16.6 cm B) 9.9 cm C)1 cm D).9 cm 9) Use a calculator to evaluate the function. Round your answer to decimal places. 0) csc B) C). D) ) Write the expression as the sine, cosine, or tangent of an angle. 1) cos π cos π 11 + sin π sin π 11 1) cos 1π B) cos 8π C)sin 8π D) sin 1π Give the exact value. ) cot π ) B) C)1 D) Find the angle in degrees that describes the compass bearing. ) NW 0 B) 9. C). D) 1 ) Use basic identities to simplify the expression. ) sinθ + tanθ + cosθ cosθ B) tanθ C) sin θ D) secθ ) ) cos θ + csc θ sin θ sinθ ) secθ B) cscθ C) 1 D) tanθ Write each expression in factored form as an algebraic expression of a single trigonometric function. 6) secx + secx tanx - tanx tanx - 1 B) secx - C)secx + D) secx 6) A-

5 Using the Difference Quotient, find the average rate of change of the function over the given interval. ) f(x) = 6x + x +, [-, ] 80 B) 118 C) 9 D) 01 ) Suppose that θ is in standard position and the given point is on the terminal side of θ. Give the exact value of the indicated trig function for θ. 8) (-, ); find sin θ. 8) - B) - 1 C) 1 D) Rewrite with only sin x and cos x. 9) cos x + sin x 1 + sin x + sin x B) 1 + sin x C)1 + sin x D) 1 - sin x + sin x 9) Convert the radian measure to degree measure. Use the value of π found on a calculator and round answers to two decimal places. 0) -1. 0) -98. B) -9.9 C) D) Find an exact value. 1) sin -11π 1 1) - 6 B) 6 - C) 6 + D) Assume that θ is an acute angle in a right triangle satisfying the given conditions. Evaluate the indicated trigonometric function. ) sin θ = ; cot θ ) B) C) D) Find the value of the unique real number θ between 0 and π that satisfies the given conditions. ) cos θ = - and tan θ > 0 ) π B) π C) π D) π Describe the transformations required to obtain the graph of the function f(x) from the graph of the function g(x). ) f(x) = cos x ; g(x) = cos x ) Vertical shrink by a factor of 1 B) Horizontal shrink by a factor of 1 C)Horizontal stretch by a factor of D) Vertical stretch by a factor of A-

6 Determine whether the given function is positive or negative for values of t in the specified quadrant. ) Quadrant II, cot t Negative B) Positive ) Convert from degrees to radians. Use the value of π found on a calculator and round answers to four decimal places, as needed. 6) 16 6) 9π B) 9π C) π D) π Use the fundamental identities to find the value of the trigonometric function. ) Find csc θ if cot θ = - and cos θ < 0. 6 B) 1 C) D) - 6 ) State whether the given measurements determine zero, one, or two triangles. 8) C = 0, a =, c = 16 One B) Two C) Zero 8) Two triangles can be formed using the given measurements. Solve both triangles. 9) B = 6, b =, c = A = 8.6, C = 6., a = 1.1; A = 0., C = 1.6, a = 1.1 B) A = 1., C =.6, a = 1.1; A = 69.6, C = 16., a = 1.1 C)A = 8.6, C = 6., a = 0.8; A = 0., C = 1.6, a = 1. D) A = 1., C =.6, a = 8.; A = 69.6, C = 16., a = 8. 9) Decide whether a triangle can be formed with the given side lengths. If so, use Heron's formula (SSS Area formula) to find the area of the triangle. 0) a = 6. 0) b = 6. c = B) 166. C) No triangle is formed. D) 1. A-6

7 Answer Key Testname: PRECAL SPRING FINAL REVIEW AND TEST 01 UNDERCLASSMEN 1) A ) A ) B ) A ) A 6) C ) D 8) D 9) A ) B 11) D 1) C 1) B 1) C 1) B 16) A 1) A 18) B 19) B 0) A 1) A ) D ) B ) A ) D 6) D ) A 8) A 9) A 0) C 1) B ) C ) D ) D ) B 6) B ) B 8) C 9) D 0) C 1) A ) D ) B ) C ) A 6) A ) A 8) A 9) C 0) D A-