PreCalculus First Semester Exam Review

Transcription

1 PreCalculus First Semester Eam Review Name You may turn in this eam review for % bonus on your eam if all work is shown (correctly) and answers are correct. Please show work NEATLY and bo in or circle the answers. If you do not have correct work and answers for any problem, you will not get the etra credit! You will be allowed to use a scientific/graphing calculator and a formula sheet during the eam. 1) State the domain and range of the function. Note: You should be able to give answers in set notation and/or interval notation. a) f ( ) = c) f ( ) = 1 1 b) ( ) f = 5 d) ( ) f = ) Which type of discontinuity (jump, removable, or infinite), if any, occurs at the given -value? a) f ( ) = : = 9 b) f ( ) = : = f = : = 4 c) ( )

2 ) Evaluate f ( ) for ( ) 4, if 1 f = 10, if 1 < <, if 4) Given that f ( ) = + 5 and ( ) ( ) a) f g ( ) b) g ( 5) g = + 1, determine c) f ( ) + g ( ) d) f ( ) g ( ) e) g ( ) i f ( ) g = ( ) for 5) Determine the inverse of (a) f ( ) = and (b) ( ) 6) Given f ( ) = 9, graph ( ) f. Page of 1

3 7) Determine whether the graph is symmetric to the -ais, y-ais, or origin. a) = y 1 b) y = 8) Determine whether the functions are odd or even. f = + a) ( ) f = 5 + b) ( ) 4 f = 4 c) ( ) 7 9) Describe the end behavior of the following functions. 4 a) f ( ) = f = b) ( ) 5 c) f ( ) = e d) f ( ) + 1 = 10) Determine the -value(s) of any relative minimum(s) and relative maimum(s) for the graph of f = ( ) Page of 1

4 11) The distance d ( t ) in feet an object travels when dropped from a high place is given by d ( t) 16t =, where t is the time in seconds after the object is dropped. Determine the average rate of change in feet per second from to 4 seconds. 1) Solve f = + 5 has a zero of 1, with a multiplicity of, what is another zero of? 1) If ( ) 4 Show work! 14) Describe the domain of the following functions. a) f ( ) = 1 b) g ( ) = 5 1 c) h ( ) = ) Divide ( 4 1) + + by ( + ) 16) State the number of possible real zeros and the number of turning points of ( ) 5 f = Page 4 of 1

5 17) List all possible rational zeros of ( ) f = ) Determine whether ( 1) and ( + ) are factors of ( ) f = ) Solve + =. Evaluate. 0) 16 1) 5 Simplify. ) ln e ) log 4) 5 5) 5 ( ) 6) (4 ) 1 Page 5 of 1

6 Solve. 7) e = 15 1) 4 = 1/ 8) log 5( ) = ) ( ) ( ) log + + log = 4 4 9) = 0 b g b g ) log n + log n + 4 = ) ln ( + ) ln ( 1) = ln ( ) b g b g 4) log 9 1 = log 4 16 Condense. 5) log10 log 5 + log 1 6) ln 4 + ln 8 Epand. 7) log( y ) 8) log y Page 6 of 1

7 9) $, is invested at 1% for 4 years. Determine the value in the account if interest is compounded (a) continuously (b) monthly and (c) quarterly. 40) Convert from degrees to radians. a) 10 b) 0 41) Convert from radians to degrees. a) 5 18 b) 7 4 4) Determine one positive and one negative coterminal angle for each of the following: a) 18 b) 15 4) Evaluate the following without a calculator: 5 a) cos 6 b) tan 4 c) sin d) 5 sec e) cos 70 f) csc 0 44) Determine all si trig functions for angle θ θ Page 7 of 1

8 45) If θ is a second quadrant angle and sinθ =, determine the remaining 5 trig functions. 46) Given cos θ =, θ, determine sin θ and tanθ. 5 47) Determine the value of the epression in degrees (remember there is only one answer). a) Sin 1 1 b) Cos 1 1 c) Tan ( ) 48) Epress each angle in terms of a reference angle. a) sin 15 b)sin 50 c) cos15 49) Sketch y = sin and y = cos for. State the domain, range, period, and amplitude. 50) Sketch the other 4 trig functions. State the domain, range and period. Page 8 of 1

9 51) Evaluate the following without a calculator: 1 a) sin ( tan ( ) ) b) sin 1 7 cos 6 5) Given the parent function h( ) = what transformations occur in the graph of ( ) ( ) j = 5. 5) Which of the following functions are 1-1 functions? 1 f ( ) =, g ( ) =, h ( ) = + 1, and j ( ) = 54) Graph: y = 4 cos( ) 55) Determine the amplitude and period of the graph at the right. 56) Determine the amplitude and period of y = 1+ sin ( ). 57) The graph of y = cos + translates the graph of cos y = how many units vertically and horizontally? Page 9 of 1

10 58) State the equation of the graph in terms of cosine. 59) State the equation of the graph in terms of sine. 4 60) Solve each equation over the interval: 0 θ < 60 a) cosθ sinθ = 0 b) sin θ + cosθ = 0 61) Use angle addition to determine the eact value of: Remember: when using angle addition for tangent, it is easier to use the 60 family than the 0 family. a) cos75 b) sin75 c) tan75 6) Evaluate each of the following: a) 5 5 sin cos + cos sin b) 7 7 cos cos + sin sin c) 1 tan 65 + tan 55 1 tan 65 tan 55 d) 8 cos 1 Page 10 of 1

11 6) Given that 1 sin A = with A <, and 1 cos B = with B <. Evaluate the following: 5 a) sin( A B) b) cos( A + B) c) cos A 64) If tanθ =, evaluate tan(15 +θ ) 5 65) Solve for 0 θ < a) sinθ = 1 b) sin θ + cosθ = 4cosθ c) cotθ = d) sin θ sinθ = 1 e) cos θ = f) cosθ sinθ = sinθ 4 Page 11 of 1

12 66) Determine the general solutions. a) cosθ + = 0 b) sinθ = 0 c) sin θ = 1 d) cos sin = sin θ θ θ 67) Simplify: a) cos + sin tan b) sin sin c) sin u cot u d) sin α (sinα csc α ) e) tan ( θ ) f) cos( + θ ) g) cos 4θ sin 4 θ h) cos 6 1 Page 1 of 1