FGCU 6th Annual Math Competition 2008 Precalculus - Individual Exam

Size: px

Start display at page:

Download "FGCU 6th Annual Math Competition 2008 Precalculus - Individual Exam"

Sheena Little
6 years ago
Views:

1 FGCU 6th Annual Math Competition 008 Precalculus - Individual Eam Find the domain of the rational function. ) f() = A) all real numbers B) { -, } C){ -,, -} D) { 0, -9} Solve the equation b epressing each side as a power of the same base and then equating eponents. ) e + 7 = e0 A) -7 B) C) - D) 7 Find the eact value of the epression, if possible. Do not use a calculator. ) sin- sin 6π 7 A) 7 6π B) π 7 C) 6π 7 D) 7 π ) sin(sin-π). A) π B) 0 C)π D) Not Definted Solve the equation on the interval [0, π). ) cos + sin - = 0 A) π 6, π 6 B) π, π, π, π C)0, π, π 6, π 6 D) π, π 6) cos = A) π C) π, π, π, π B) π D) π 6, π 6 Solve the equation on the interval [0, π). 7) tan cos + tan + cos + = 0 A) π, π, 7π B) 0, π, 7π C) π, 7π, π D) 0, π, π Use a right triangle to write the epression as an algebraic epression. Assume that is positive and in the domain of the given inverse trigonometric function. 8) sin(tan- ) A) + + B) + + C) + D) - -

2 Find an equation for the graph. 9) A) = cos π B) = cos π C) = cos π D) = cos π Find the standard form of the equation of the ellipse satisfing the given conditions. 0) Major ais horizontal with length 0; length of minor ais = ; center (0, 0) A) = B) 00 + = C) = D) = Convert the equation to the standard form for a parabola b completing the square on or as appropriate. ) = 0 A) ( - ) = -( - ) B) ( + ) = -( + ) C)( + ) = -( - ) D) ( - ) = ( - ) Find the location of the center, vertices, and foci for the hperbola described b the equation. ) ( + ) - ( + ) = 6 A) Center: (-, -); Vertices: (-6, -) and (-, -); Foci: (- - 7, -) and (- + 7, -) B) Center: (, ); Vertices: (, ) and (6, ); Foci: (- 7, ) and ( + 7, ) C)Center: (-, -); Vertices: (-, -) and (-, -); Foci: (- + 7, -) and (- + 7, -) D) Center: (-, -); Vertices: (-6, ) and (-, ); Foci: (- - 7, ) and (- + 7, )

3 Solve the problem. ) A satellite following the hperbolic path shown in the picture turns rapidl at (0, 6) and then moves closer and closer to the line = as it gets farther from the tracking station at the origin. Find the equation that describes the path of the satellite if the center of the hperbola is at (0, 0). (0, 6) = A) 6 - ( = B) ) 9-6 = C) 6 - = D) 9 ( ) - 6 = Rewrite the equation in a rotated ''-sstem without an '' term. Epress the equation involving ' and ' in the standard form of a conic section. ) = 0 A) ' 9 + ' = B) ' = - ' C)' = - ' D) ' + ' 9 = Eliminate the parameter t. Find a rectangular equation for the plane curve defined b the parametric equations. ) = 7 cos t, = 7 sin t; 0 t π A) - = 9; -7 7 B) + = 7; -7 7 C) + = 9; -7 7 D) - = 7; -7 7 Solve the problem. 6) A radio transmission tower is 0 feet tall. How long should a gu wire be if it is to be attached feet from the top and is to make an angle of 0 with the ground? A) 00.0 feet B) 76.0 feet C) 88.7 feet D) 7.8 feet An object is attached to a coiled spring. The object is pulled down (negative direction from the rest position) and then released. Write an equation for the distance of the object from its rest position after t seconds. 7) amplitude = 9 cm; period = seconds A) d = -9 cos π t B) d = -9 cos πt C)d = -9 sin πt D) d = - cos 9 πt Find the eact value of the epression. Do not use a calculator. 8) + sin 7 + sin A) - B) C) D) 0

4 Find the domain of the composite function f g. 9) f() = + 7, g() = 7 A) (-, 0) (0,-) (-, ) B) (-, ) C)(-, -7) (-7, 0) (0, ) D) (-, -7) (-7,-) (-, 0) (0, ) Epress the given function H as a composition of two functions f and g such that H() = (f g)(). 0) H() = - - A) f() = +, g() = - B) f() = -, g() = - C)f() = -, g() = - D) f() = -, g() = - Find the vertical asmptote(s), if an, of the graph of the rational function. + 7 ) f() = A) = 9 B) = -9, = 7 C) = 9, = -7 D) no vertical asmptote Find the polnomial P() with real coefficients having the specific degree, leading coefficient, and zeros. ) degree:, leading coefficient: -, zeros:, + 6i A) B) C) D) Determine whether the given function is one-to-one. If it is one-to-one, find its inverse. 7 ) f() = - 8 A) f-() = B) Not one-to-one C)f-() = D) f-() =

5 Match the function with its graph. ) ) = sin () ) = cos () ) = sin () ) = cos () A) B) -π -π π π - -π -π π π C) D) - -π -π π π - -π -π π π A) A, C, D, B B) A, D, C, B C)A, B, C, D D) B, D, C, A Solve the equation. ) π + arccos () = π 6 A) = B) = C) = - D) = Solve the problem. 6) A domed ceiling is a parabolic surface. For the best lighting on the floor, a light source is to be placed at the focus of the surface. If 7 m down from the top of the dome the ceiling is 7 m wide, find the best location for the light source. A) 0. m down from the top B). m down from the top C).8 m down from the top D) 0.8 m down from the top Identif the conic section represented b the equation. 7) = 0 A) parabola B) ellipse C) hperbola D) circle

6 Graph the hperbola. 8) - = A) B) C) D) Solve the logarithmic equation. 9) log ( - ) + log ( - ) = A) B) -, C) -, D) Epand the epression. 0) ln ( + ) 9 + A) 6 ln - ln - ln B) ln ( + ) + ln ( + ) C) ln ( + ) - ln ( + ) D) ln ( + ) ln ( + ) Find the domain of f and write it in interval notation. ) f() = log () 7 A), B) (-, 0) (0, ) C)(0, ) D) (, ) 6

7 Solve the problem. ) Technolog matri A, representing interindustr demand, and matri D, representing consumer demand for the sectors in a two-sector econom, are given. Use the matri equation X = (I - A)-D to find the production level X that will satisf both demands. A = , D = 7 A) X = B) X = C) X = D) X = ) The graph of a logarithmic function of the form = loga( - c) is given. Use the graph to determine a and c A) a = ; c = B) a = ; c = C)a = ; c = D) a = ; c = Use the inverse trig functions to epress the angle in terms of the indicated unknown side. ) b A Use one of the inverse trig functions csc- or sec- to epress angle A in terms of b. A) A = csc- b B) A = sec- b C)A = sec- b D) A = csc- b Which answer choice is equivalent to the given epression? ) + sin + - sin A) sec - sin B) csc C) tan D) sec 7

8 Answer Ke Testname: PRECALCULUS INDIVIDUAL EXAM - MATH COMPETITION 008 ) A ) A ) B ) D ) C 6) C 7) A 8) B 9) D 0) A ) C ) A ) C ) D ) C 6) B 7) B 8) B 9) A 0) D ) A ) C ) A ) D ) B 6) A 7) D 8) D 9) A 0) C ) B ) A ) B ) C ) D 8

Name Please print your name as it appears on the class roster.

Name Please print your name as it appears on the class roster. Berkele Cit College Practice Problems Math 1 Precalculus - Final Eam Preparation Name Please print our name as it appears on the class roster. SHORT ANSWER. Write the word or phrase that best completes