Honors Pre-Calculus. Multiple Choice 1. An expression is given. Evaluate it at the given value

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1 Honors Pre-Calculus Multiple Choice. An epression is given. Evaluate it at the given value, (A) (B) 9 (C) 9 (D) (E). Simplif the epression. (A) + (B) (C) (D) (E) 7. Simplif the epression. (A) (B) (C) (D) ( + ) (E) 7 7. Simplif the epression (A) (B) (C) 7 (D) (E) 7. Simplif the epression (A) (B) (C) (D) 9 9 (E) Simplif the epression. 9 (A) (B) (C) (D) (E) 7. Epress the function in the form f g. H A) f, g B) f, g C) f, g D) f, g E) f, g nd Semester Final Review. Epress the function in the form f gh. j 7 (A) f, g, 7 h (B) f, g, h 7 (C) f 7, g, h (D) f 7, g, h 9. Find the domain of g f, if f and g. (A) (B) (C) (D). Simplif the epression. 9 (A) (B) 9 9 (C) 9 (D) (E) 9 9. Determine whether the given value is a solution of the equation., (A) es (B) no. Solve the equation. w w (A) (B) (C) 9 (D) (E) 9 z. Solve the equation. z 7 9 (A) 9 (B) 7 (C) (D) (E). Solve the equation. (A) (B) (C) (D) (E) 9. Solve the equation. (A) (B) (C) (D) (E). Solve the equation. t t (A) (B) (C) (D) (E) 7. Find all real solutions of the equation. 7 (A) none of these (C),,,,,,,, (D) (B), (E),,

2 . Find all real solutions of the equation. (A), (B) (C) (D), (E) 9. Find all real solutions of the equation. (A) = (B) = 7, = (C) = 7, = (D) =, = (E) =. Solve the linear inequalit. Epress the solution using interval notation. 7 A), B), C), D), E),. Solve the nonlinear inequalit. Epress the solution using interval notation.,,,, A) B) C), D), E),,. Solve the nonlinear inequalit. Epress the solution using interval notation., 9,,, A) B) C), 7, D),, E),,. A riverboat theater offers bus tours to groups on the following basis. Hiring the bus costs the group $, to be shared equall b the group members. Theater tickets, normall $ each, are discounted b cents times the number of people in the group. How man members must be in the group so that the cost of the theater tour (bus fare plus theater ticket) is less than $ per person? A. at least members B. at least members C. at least members D. at least members E. at least members. Solve the inequalit. Epress the solution using interval notation. A), B), C), D), E),. Solve the inequalit. Epress the solution using interval notation. 9 A) [, ) B) [, 7) C) [, ) D) [, ) E) [ 7, ). Solve the inequalit. Epress the answer using interval notation. 9 A) B) [, ] C), D),, E),, 7. A set of real numbers is graphed) Find an inequalit involving an absolute value that describes the set. 7 A) 7 B) 7 C) 7 D) 7 E). Solve the nonlinear inequalit. Epress the solution using interval notation and graph the solution set. A),, B),, C),, D),, 9. Evaluate the function f at f(). A) f() = B) f() = C) f() = D) f() = 7 E) f() =. Evaluate the function f at f (). A) f() =. B) f() =.7 C) f() =. D) f() =. E) f() =. Find the domain of the following function: 9 f A) (-, ) B) [, ) C) (, ) D) [, ) E) (-, ]. What is the domain and range of the function that is graphed below? (A) Domain: ( 7, ), Range: [, ] (B) Domain: (-, ), Range: [, ] (C) Domain: [ 7, ], Range: [, ] (D) Domain: [ 7, ], Range: (-, ) (E) Domain: [, ], Range: [ 7, ]. What is the average rate of change of the function f between = and =? A) B) 7 C) D) E). What is the average rate of change of the function f between = and =? A) B) 7 C) D) E). The graph of the function is sketched as follows: Determine the interval on which the function is increasing. A) (, ) B) (, ) C) (, ) D) (, ) E) (, ) - - -

3 . How man units must we shift the graph of f to obtain the graph of f? A) left B) left C) right D) right E) left 7. The graph of a function is given as follows: Determine the average rate of change for the function between the indicated values of the variable. A) B) C) D). The graph of a function is sketched as follows: Determine the average rate of change of the function between the indicated values A) B) C) - D) E) - 9. The table shows the number of CD plaers sold in a small electronics store in the ears as follows: Year CD plaers sold What was the average rate of change of sales between 99 and 999? (A) 7 CD plaers/ear (B) 9 CD plaers/ear (C) CD plaers/ear (D) CD plaers/ear (E) 7. CD plaers/ear. Suppose the graph of f is given. Describe how the graph of the function can be obtained from the graph f of f. f to the right units, stretch verticall b a factor of, and then shift (A) Shift the graph of downward units. (B) Shift the graph of f to the left units, stretch verticall b a factor of, and then shift downward units. (C) Shift the graph of f to the right units, stretch verticall b a factor of, and then shift downward units. (D) Shift the graph of f to the left units, stretch verticall b a factor of, and then shift upward units. (E) Shift the graph of f to the left units, stretch verticall b a factor of, and then shift downward units.. Determine the end behavior of P A) - as and as - B) as and - as - C) - as and - as - D) as and as - E) as and - as -. Find the quotient and remainder using long division. (A) The quotient is 7 ; the remainder is. (B) The quotient is 7 ; the remainder is. (C) The quotient is 7 ; the remainder is. (D) The quotient is 7 ; the remainder is. (E) The quotient is 7 ; the remainder is.. Find the quotient and remainder using snthetic division. 7 (A) The quotient is 9 the remainder is. (B) The quotient is 9 the remainder is. (C) The quotient is 9 the remainder is. (D) The quotient is 9 there is no remainder. (E) The quotient is 9 the remainder is.. Use snthetic division and the Remainder Theorem to evaluate P, for P. A) B) C) D) E) 7. Find all rational zeros of the polnomial. P 9 A) =,, B) = -,, -, C) =, -, D) = -,, -, E) = -,,, -. Find a polnomial of degree that has zeros 7, 7, and. A) 9 9 B) 9 9

4 C) 9 9 D) 9 9 E) Find a polnomial of degree that has zeros of,, and, and where the coefficient of is. A) 9 B) 9 C) 9 D) 9 E) 9. List all possible rational zeros given b the Rational Zeros Theorem (but don't check to see which actuall are zeros). Q A), B),,, C), D),,, E),,, 9. List all possible rational zeros given b the Rational Zeros Theorem (but don't check to see which actuall are zeros). f A),,,,, B),,,,, C),,,,,,,,,,, D),,,,,,,,,,, E),,,,,,,,,,,. Find the real and imaginar part of the comple number i. A) Real part =, Imaginar part =. B) Real part =, Imaginar part =. C) Real part = i, Imaginar part =. D) Real part =, Imaginar part = i.. Evaluate the epression ( + 9i)( i) and write the result in the form a + bi. A) + 99i B) 9 i C) 9 + i D) + 9i. Find all solutions of the equation 9 and epress them in the form a + bi. A) = 7i B) = 7i, = 7i C) = 7i, = 7 D) = 7, = 7. A polnomial P is given. P Find all zeros of P, real and comple., i, i A) B), i, i C) D), i E). Factor the polnomial P completel and find all its zeros. A) i, -i, -, B), -, C) i, -i, -, D) i, -i, - E),,. Find the polnomial P of degree, and zeros i and i, and constant coefficient. A) B) 9 C) D) E). Find the polnomial with real coefficients of the smallest possible degree where i and + i are zeros and the coefficient of the highest power is. A) B) C) D) E) 7. The population of a certain species of bird is limited b the tpe of habitat required for nesting. The population behaves according to the logistic growth model nt where t is measured. t. 7. e in ears. What size does the population approach as time goes on? A) B) C) 7 D) E). Radioactive iodine is used b doctors as a tracer in diagnosing certain throid gland disorders. This tpe of iodine decas in such a wa that the mass remaining after t das is given b the function. t mt 7e where m(t) is measured in grams. Find the mass at time t =. A). g B). g C) g D) 7 g E) g 9. If $, is invested at an interest rate of % per ear, compounded monthl, find the amount of the investment at the end of ears. A) $9 B) $ C) $77 D) $ E) $9. The rate at which a batter charges is slower the closer the batter is to its maimum charge C. The time (in hours) required to charge a full discharged C batter to a charge C, is given b t kln C where k is a positive constant that depends on the batter. For a certain batter, k =.. If this batter is full discharged, how long will it take to charge that is % of its maimum charge C? Round to four decimal places. A). hour B). hour C). hour D). hour. Solve the equation. e e A) =, = B) =.9 C) =.7, = D) =, = E) =., =

5 . Solve the logarithmic equation for. loglog loglog A) = B) =.9 C) = 7 D) = E) =. Solve the inequalit. e e A), ) B) (-, ) C) (-, ) D) (-, ) E) (-, ). Find the time required for an investment of $, to grow to $, at an interest rate of % per ear, compounded quarterl. A) ears B) ears C) none of these D) ears E) ears. A sum of $, was invested for ears, and the interest was compounded semiannuall. If this sum amounted to $, in the given time, what was the interest rate? A).9 % B) none of these C). % D).9 % E). %. The population of a certain cit was, in 99, and the observed relative growth rate is % per ear. In what ear will the population reach 9,? A) B) C) D) none of these E) 7. Radium- has a half-life of s. How long will it take for 9% of a sample to deca? A) 9. s B).9 s C) 9.7 s D). s E). s 7 A) (, ) B) (, ) C) (, ) D) (, ) E) (, ) f a whose graph is given.. State the range of the function. h 9. Find the eponential function A) f B) f C) f D) f E) f 7. State the range of the function e. A) (, ) B) (, ) C) (, ) D) [, ) E) (, ) 7. What is the asmptote of the function e? A) = B) = C) < D) = E) > 7. Epress the equation ln in eponential form. A) e B) e C) e D) e E) none of these 7. Epress the equation in logarithmic form. A) none of these B) log C) log D) log E) log ln 7. Evaluate the epression. e A) e B) none of these C) ln D) E) e 7. Find the function of the form loga whose graph is given. A) log B) log log C) D) log E) none of these 7. Use the Laws of Logarithms to rewrite the epression below in a form with no logarithm of a product, quotient, or power. loga 7 z (A) log a + log a + 7 log a z loga (B) loga7loga z (C) log a log a 7 log a z (D) log a + log a + 7 log a z (E) log a log a + 7 log a z 77. Use the Laws of Logarithms to rewrite the epression below in a form with no logarithm of a product, quotient, or power. ln 9 z A) ln ln ln z B) ln ln ln z C) ln ln ln z D) ln ln ln z Use the Laws of Logarithms to rewrite the epression below in a form with no logarithm of a product, quotient, or power. log z A) log log log z B) log log log z C) log log log z D) log log log z 79. Rewrite the epression as a single logarithm. log log A) log B) C) D) E) ln

6 . Rewrite the epression below as a single logarithm. log log log A) ln 7 B) log 7 C) log 7 D) log log 7 E). Solve the equation. e e A) =, = B) = ln C) = ln, = D) =, = E) = ln, = log. Solve the logarithmic equation for. A) = 7 B) = 7 D) none of these E) = 7. Solve the logarithmic equation for. log log log log C) = 9 A) = B) =.9 C) = 7 D) = E) = Short Answer. Perform the addition and simplif.. Perform the subtraction and simplif.. Find the length in the figure, if the shaded area is 9 in. 7. Perform the multiplication and simplif.. Determine whether the given value is a solution of the equation. (A) = (B) = 9. Solve the equation. t t 9. Solve the equation b factoring. 9. Solve the equation b completing the square. Find all real solutions of the equation Simplif ab t 9. Simplif s 9. Simplif: Simplif: Multipl: 9. Multipl: Factor: m m m 9. Factor:. Factor:. Factor:. Factor:. Multipl:. Simplif each radical and combine if possible: 7. Simplif each radical and combine if possible: 7. Simplif each radical and combine if possible: 7. Rationalize and simplif: 9. Rationalize and simplif:. Simplif:. Simplif: 7. Simplif: 9 f, determine the graph of. If w?. Find the domain of the function. g. Sketch the graph of the piecewise defined function. if f if if. Sketch the graph of the piecewise defined function. if f if

7 7. A man is running around a circular track m in circumference. An observer uses a stopwatch to record the runner's time at the end of each lap, obtaining the data in the table. Time (s) Distance (m) (a) What was the man's average speed (rate) between s and s? Please round our answer to the nearest hundredth. (b) What was the man's average speed (rate) between 7 s and 9 s? Please round our answer to the nearest hundredth. For the following, graph, determine the domain and range, and determine where the graph is increasing.. f 9. f. f.. f. f f. f. Determine where the function is increasing.. A function is given. Determine the average rate of change of the function between the values of the variable. g ;, h 7. Evaluate the following piecewise defined function at f 7. f f, f, and if if f to evaluate the fol-. Use the function lowing epressions and simplif. f a 9. For the function f, find f a h f a h. Find the domain of the function. h 7.. The graph of g is given. Sketch the graph of the g function.. In a certain countr, income ta T is assessed according to the following function of income. if, T. if,,,. if, (A) Find T(,). (B) Find T(,). (C) Find T(,).. Assume f is a one-to-one function. If f, find f.. Use f and g to evaluate f g. 7. Find the inverse function of f. 9. Find the inverse function of f Find the maimum or minimum value of the function. f t 7t t. Find the maimum or minimum value of the function. g 9 9. A function f is given. f. Sketch the graph of f. Use the graph of f to sketch the graph of f. Find f.. A one-to-one function is given. f. Find the inverse of the function. Graph both the function and its inverse on the same screen to verif that the graphs are reflections of each other in the line =.. Find the coordinates of the function verte and its intercepts.. Find the coordinates of the function verte and its intercepts.. Find its maimum or minimum value of the function :. Find its maimum or minimum value of the func- tion 7:. Find the domain and range of the function f. If a ball is thrown directl upward with a velocit of ft/s, its height (in feet) after t seconds is given

8 b tt. What is the maimum height attained b the ball? 7. A quadratic function is given. f Find the maimum or minimum value of the quadratic function f.. The number of apples produced b each tree in an apple orchard depends on how densel the trees are planted. If n trees are planted on an acre of land, then each tree produces 7 n apples. So the number of apples produced per acre is An n7 n. How man trees should be planted per acre in order to obtain the maimum ield of apples? 9. Use the given graphs of f and g to evaluate the epression. (A) g f (B) g g. A manufacturer finds that the revenue generated b selling units of a certain commodit is given b the function R, where the revenue R() is measured in dollars. (a) What is the maimum revenue? (b) How man units should be manufactured to obtain this maimum?. Find the function in general form whose graph is a parabola with verte (, ) and that passes through the point (, ).. Use f and g to evaluate the epression. (A) f f (B) g g. Find the domain of the function. f. Determine the equation of the piece-wise function.. Determine k so that - is a factor of f k 7. Determine if is an upper bound for P 7. Graph the following function:, f,,. Determine if is a lower bound for P 9. Find all the real zeros of the polnomial. P 7. Find all the real zeros of the polnomial. P 7. Two polnomials P and D are given. Divide P b D, and epress P in the form P D R D 7. P,. Use snthetic division and the Remainder Theorem to evaluate Pc. P 7, c. Find all rational zeros of the polnomial, and then find the irrational zeros, if an. Whenever appropriate, use the Rational Zeros Theorem, the Upper and Lower Bounds Theorem, Descartes' Rule of Signs, the quadratic formula, or other factoring techniques. 7. Find the equation of the graph in factored form. A) degree B) degree Find the remainder given. Factor completel and graph. f 7 7. Factor completel and graph. f. Factor completel and graph. f 9. Factor completel and graph. f 9 7. Factor completel and graph. f 7. Perform the addition and write the result in the form a + bi. i i 7. Perform the subtraction and write the result in the.. i.. i form a + bi.

9 7. Evaluate the epression and write the result in the i form a + bi. i 7. Evaluate the epression and write the result in the form a + bi. i 7. Find all solutions of the equation and epress them in the form a + bi. 7. Find a polnomial with integer coefficients that satisfies the given conditions. Q has degree, and zeros and 7i 77. Find all zeros of the polnomial. 7. Find all zeros of the polnomial. P Determine the equation of the function whose graph is:. Find all asmptotes (if an). r For problems -, find the following: (a) Determine the -intercept(s). (b) Determine the -intercept(s). (c) Determine the vertical asmptote(s). (d) Determine the horizontal asmptote(s).. s. r 9 9. r Graph the following:. r.. s. r 7. r r 9. f( ) 9. f( ) 9. f( ) 9. f( ) 9. f( ) 9. f( ) 9. f( ) 9. f( ) 97. f( ) 9. f( ) 99. f( ) 7. f( ). f( ). f( ). Solve for. log. Solve for : e.. Use a graphing device to find all solutions of the equation, correct to two decimal places. e. When a certain medical drug is administered to a patient, the number of milligrams remaining in the patient's bloodstream after t hours is modeled b. t Dt e. How man milligrams of the drug remain in the patient's bloodstream after hours? Please give the answer to one decimal place. 7. A hot bowl of soup is served at a dinner part. It starts to cool according to Newton's Law of Cooling so that its temperature at time t is given b. t Tt 9e where t is measured in minutes and T is measured in F. (a) What is the initial temperature of the soup? Please round the answer to the nearest integer. (b) What is the temperature after min? Please round the answer to the nearest integer. (c) After how long will the temperature be F? Please round the answer to the nearest integer.. For a certain tpe of tree the diameter D (in feet) depends on the tree's age t (in ears) according to. the logistic growth model Dt.. t 9.e Find the diameter of a -ear-old tree. 9. A certain strain of bacteria divides ever three hours. If a colon is started with 9 bacteria, then the time t (in hours) required for the colon to grow log N / 9 to N bacteria is given b t. log Find the time required for the colon to grow to a million bacteria.. Use the Change of Base Formula and a calculator to evaluate the logarithm, correct to si decimal places. log 9 7. A car dealer sells a used car for $,. He offers the buer paments of $ per month for ears. What interest rate is the car dealer charging?. How much mone should be invested monthl at % per ear, compounded monthl, to have $ in months?

10 . Ebbinghaus' Law of Forgetting states that if a task is learned at a performance level P, then after a time interval t the performance level P satisfies the equation logplogp clogt. Use the Ebbinghaus Forgetting Law to estimate a student's score on a biolog test two ears after he got a score of 7 on a test covering the same material. Assume c =. and t is measured in months.. Radioactive iodine is used b doctors as a tracer in diagnosing certain throid gland disorders. This tpe of iodine decas in such a wa that the mass remaining after t das is given b the function. 7t mt e where is measured in grams. (a) Find the mass at time t =. Please round the answer to the nearest integer. (b) How much of the mass remains after das? Please round the answer to the nearest integer.. If $, is invested in an account for which interest is compounded quarterl, find the amount of the investment at the end of ears for the following interest rates. (a) %. (b).%. (c) 7%. (d) %.. A sum of $, is invested at an interest rate of 9% per ear, compounded semiannuall. (a) Find the value A(t) of the investment after t ears. (b) Use the graph of A(t) to determine when this investment will amount to $,. Please give the answer to two decimal places. 7. What is the monthl pament on a -ear mortgage of $, at 9% interest? What is the monthl pament on this same mortgage if it is to be repaid over a ear period?. Solve for : 9. Solve for : ln. Solve for : log.. Solve the equation.. Solve the equation State the range of the function. h 7. State the range of the function e. Determine the domain and range of the function h. Graph f log. 7. Graph the function. State the domain, range, and asmptote.. Graph. 9. Use the definition of the logarithmic function to find. (a) log (b) log.. Find the domain of the function. f log. Use the Laws of Logarithms to epand the epression. log AB. Use the Laws of Logarithms to epand the epression. ln 9. Use the Laws of Logarithms to combine the epression. log log log. Use the Laws of Logarithms to combine the epression. log log logz. Given that log7 a and log7 c, find the following: A) log7 ac c B) log7 a C) log7 a D) log7 c

11 Answer Section ) A ) B ) B ) A ) C ) C 7) B ) A 9) A ) D ) A ) D ) E ) A ) E ) C 7) D ) 7 ) ) in. ) E 9) E ) B ) D ) C ) B ) E ) D ) D 7) A ) B 9) C ) E ) A ) C ) C ) A 7) ) = is not a solution; = is a solution 7 9) t 9), 9), 7 7 9), 9) a b t 9) s 7 9) 9) ) 7 9) m m 7 m 99) ) 9 ) ) ) D ) B 7) D ) C 9) D ) E ) C ) A ) D ) B ) E ) B 7) B ) B 9) C ) B ) D ) 7) ) 9) ) ) 9 ) 7 ) ) (-, ] ) ) ) B ) D ) D ) D ) C 7) D ) A 9) E ) D ) E ) A ) D ) B ) A ) B 7) A ) D 9) A 7) B 7) B 7) B 7) C 7) D 7) B 7) C 77) B 7) C 79) A ) E ) E ) B ) A ) ) )

12 7) A) 7 ) B) 9 ) ) - - D: (-, ) R: [-, ) Inc: (, ) ) D: (-, ) R: (-, ) Inc: (-, ) ) ) - D: (-, ) (, ) R: (-, ) (, ) Inc: none D: (-, ] R: (-, ] Inc: (-, ) D: (-, ) R: (-, -] Inc: (-, ) ) (-, ) ) h 7) f() =, f() =, f(7) = f a a a ) 9) ) ) a ah h 7, ) D: (-, ) R: (-, ) Inc: (-, ) ) (A) (B) (C) ) ) 9 ) f 7 ) f 7 7) 9 ) -7 9) f D: (-, ) (, ) R:(, ) Inc: (-, )

13 ) f ) f ) verte (, ); -intercepts, ; -intercept ) verte (, ); -intercepts, ; -intercept ) ma = ) min = ) D = (-, ), R = [-, ) ) feet 7) = ) 9) A) B) ) A) $ B) ) ) A) 9 B) ) [, ] ) f ) ) Yes 7) 7) f ) f f 9) 7) f ) Yes 9), ),, ) P ) P ),, P a ) A) B) Pa ) 7) i 7) i 7) i 7) -i 7 7) i 7) Q 9 77),, i, i 7) 9, i, i 79) f ) VA: =, = ; SA: = + ) (A) = ; (B) = ; (C) =, = ; (D) = ) (A) = 9; (B) = 9; (C) = ; (D) =

14 ) (A) no solution; (B) = ; (C) =, = ; (D) = ) 9) ) ) ) ) - 9) 7) ) - 9) ) - - 9)

15 9) ) 97) 9) 99) ) ) 7 ).7 ).,. ) 9. 7) (A) ; (B) ; (C) 7 ). 9). ).7 ).% ) $. ) ) (A) ; (B) ) (A) $,. (B) $,. (C) $,9. (D) $,.7 ) (A) 9 t. (B). 7) $. ).9 9) (,.9) ). ), - ), - ) (, ) ) (-, ) ) Domain: (-,); Range: (-, ) ) )

16 7) ) Domain: (-, ). Range: (, ). Asmptote: =. 9) (A) ; (B) ) (-, ) ) log A log B lnln 9ln ) ) ) log log z ) A) - B) -9 C) D)

(C), 5 5, (B) 5, (C) (D), 20 20,

(C), 5 5, (B) 5, (C) (D), 20 20, Reg. Pre-Calculus Multiple Choice. An epression is given. Evaluate it at the given value, (A) 0 (B) 9 9 (D) 0 (E). Simplif the epression. (A) (B) (D) (E) 0. Simplif the epression. (A) (B) (D) ( + ) (E).