Pre-Calc 12 Final Exam Review Ch 1 Transformations 1. and b) f ( x ) translated 4 units to the right. =, what point must be on the following?

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1 Pre-Calc Final Eam Review Ch Transformations. If f ( ) =, find the equation of a) f ( ) Name: and b) f ( ) translated units to the right.. If ( a, b ) is a point on the graph of f ( ) a) f ( + 0) b) ( ) =, what point must be on the following? f + + c) f +. If f ( ) = +, find the equation of a) its inverse b) a reflection in the -ais.. The graph of f ( ) = is shown below. Sketch the graphs of: a) f c) f + ( ) b) f ( + ) f d) ( + ). Given f ( ) = and g ( ) = +, find: a) g ( ) f ( ) b) g f ( ) c) g f ( ) Ch Polnomials. What is the remainder when ( ) + is divided b +? ( ). Divide + b +.. Solve b factoring: a) = 0 b) + = 0. Sketch the graph of: =.. Find the equation of a polnomial that has zeroes at,, and has a -intercept of.

2 . A rectangular prism has dimensions 0cm b 0cm b cm. When each dimension is increased b the same amount, the new volume is 008cm. What are the dimensions of the new prism? 8. A cereal bo is a rectangular prism with a volume of 00cm. It is times as wide as it is deep and cm taller than it is wide. What are the dimensions of the bo? Ch Radical and Rational Functions. Determine the domain and range of each: a) = ( + ) b) f ( ) = +. Solve: a) = b) + =. Sketch: a) = and b) = 8. Given =, find the equations of all asmptotes, the coordinates of an holes, the + and -intercepts, and the domain. Sketch a graph. Ch Logarithms. Write as a single log: + a b c b) log + log log log + log log a) log log log c) ( ) ( ) ( ). Find the eact value of: a) log log log 9 b) 9 c) log log. Simplif: 9 ( ) log. If log = m and log = n, rewrite the following in terms of m and n: a) log ( 9 ) b) log9 ( ). Solve for algebraicall: + + a) 8 = b) = log log log 8 log c) ( + ) = d) ( )( ) =. Balonium decas from 000 atoms to 0 atoms in seconds. What is the half-life of Balonium? (Answer to two decimal places). An earthquake off the coast of Tofino was measured as. on the Richter scale. Eperts epect the net major earthquake to be about times stronger. What will the Richter scale number of this earthquake be?

3 8. Milk has a ph of.0 and apples are about 800 times more acidic. Find the ph of apples. 9. Sketch: =. Determine the domain, range and equations of an asmptotes. 0. Sketch: log ( ) = +. Determine the domain, range and equations of an asmptotes.. What is the domain of: log ( ) +? Ch Trig Part. Convert into degrees: a) π b).. Convert into radians: a) 80 b) 0. A pendulum 0 cm in length swings through an arc length of 0 cm. What is the angle in degrees?. For each, sketch the angle and determine: i) a coterminal angle and ii) the reference angle a) 90 b) π π c). Given that (,8) is on the terminal arm of angle θ in standard position, find the eact values of the following trig ratios. a) b) secθ c) cotθ. Given = and θ is in quadrant III, find the eact values of: a) b) cscθ c) tanθ. Given a = where a > 0 and cscθ < 0, find the eact value of. a 8. Find the eact values of: π a) cos b) π sec c) π sin 9. Given = and secθ < 0, what is the eact value of angleθ if 0 θ < π? 0. Determine the amplitude, period, phase shift, vertical displacement and the range of: a) cosπ = cos π + = b) ( )

4 . Write the equation of a sine curve that has a minimum at (, ) and the net maimum at (, ).. On a tpical da at an ocean port, the water has a minimum depth of m at :00am. The maimum depth of 0 m occurs hours later. Assume that the relationship between the depth of water and time is a sinusoidal function. Write an equation for the depth of water at an time, t hours. Ch Trig Part. Simplif the following epressions: a) csc b) cos( ) cos( ) + sin ( ) sin ( ) c) csc( A) sin A d) 8cos ( ). If cotθ = and cos 0 θ <, find the eact value of sin ( θ π ) +.. Solve: sin + = 0 if a) 0 < π and b) over all real numbers.. Solve: cot = if a) 0 < π and b) over all real numbers.. Solve: cos = if a) 0 < π and b) over all real numbers.. Solve algebraicall with eact values: sin + sin + = 0 over all real numbers.. Prove: tanθ cos θ a) + = secθ secθ b) cscθ + cotθ = 8. Determine the restrictions on : tan sec if 0 < π. Ch Combinatorics. A couple is planning an evening out. The have a choice of restaurants for dinner, movies following dinner and coffee shops for after the movie. How man different was can the plan the evening if the choose one of each?. How man different was are there to arrange the letters in TSAWWASSEN if: a) there are no restrictions b) if the first letter must be an S c) if the As must be together

5 . The winner of a lotter chooses vehicles from a warehouse that contains different cars, 9 different trucks and different motorccles. How man different choices of vehicles are possible if there must be at least one car?. Codes with digits are made from the digits,,,,,,, 8. a) If repetitions are allowed, how man different -digit codes are there? b) If repetitions are not allowed and each code must contain odd digits followed b even digits, how man different codes can be made?. A class of students is made up of bos and 0 girls. From this class, a group of students is chosen. a) Determine the number of different groups of that can be formed if there must be girls and bos in the group. b) Determine the number of different groups of that can be formed if there must be at most bo in each group.. In a standard deck of cards, how man different -card hands contain at least face cards?. Solve algebraicall: a) 90 n P = b) ( n ) 8. Simplif: ( n ) ( n + ) ( n! )!!. 9. Determine the th term in the epansion of ( ) 0. In the epansion of ( ) a b, determine the middle term. Answer Ke: Ch +. a) = b) =. a), a b. a) = b) =. a) b) n! =!! + c) a +, b + b) ( a, b )

6 c) d) a) + + b) c) Ch.. ( ) +. a) =, =, = b) =, =, = + = +.. ( )( )( ). a), or (, ], [, ) - b) < <, > or (, ),(, ) cm cm cm 8. cm 0cm cm Ch. a), 0 b),. a) = b) =, =.. asmptotes:, = = hole: (,) intercepts: (,0) and (,0 ) domain:, or (, ),(, ),(, ) Ch. a) log 8a b c log c) ( ) b) log log =. a) b) c)

7 . 8. a) + m + n b) m n + +. a).. seconds = b) =. c) = d) = 9. Domain and Range: R, > Asmptote: = Domain and Range: >, R Asmptote: = < < Ch. a) 0 b) -8.. a) π π b). 8.. a) R: 0 b) R: π π c) R: 9 9. a) b). a) b) c). a 8. a) b) c) a 9. π 0. a) amp:, period:, p.s: 0, vd: down, range: 8 b) amp:, period: π, p.s: right π, vd: up, range: π nπ. a) period:, asmp: =, n is odd b) period: π, asmp: = nπ, n is odd 0 π π π π. = sin +, = cos ( ) +. = sin ( ) +, = cos ( + ) + Ch. a) tan b) cos( ) c) sec A π π d) cos.. a) =, π π π π b) = + nπ, + nπ, n I. a) =, b) = π + nπ, n I

8 π π π 9π π π. a) =,,, b) = + nπ, + nπ, n I.. a) b) + cos θ sin θ + 8. π π 0,, Ch. 9. a) 00 b) 0 c) a) 8 b) 88. a) 00 b) a) n = 0 b) n = ( )( ) ( ) a b + n + n n ( ) π π = + nπ, + nπ, n I ( cscθ + ) ( ) ( ) cscθ + sin ( θ ) sin ( θ ) sin θ sin ( θ ) cos θ sin cotθ ( θ )