Honors Algebra II Final Exam: 2012 L I 1. Multiple Choice Identify the choice that best completes the statemenr or answers the question.

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1 Naie: Class: 1 Date: ID: A Honors Algebra II Final Exam: 01 L I 1 Multiple Choice Identify the choice that best completes the statemenr or answers the question. f) 1. The formula S 3Qfd relates the speed S in miles per hour a car was traveling to the length d in feet that the car skidded when brakes were applie The variable f is the coefficient of friction, which varies depending on the road surface and the condition of the tires. Wbic1its of numbers contain the value of S for f=o.8andd=51? (j7 p integers, rational numbers, real numbers irrational numbers, real numbers whole numbers, integers, rational numbers, real numbers natural numbers, whole numbers, integers, rational numbers, real numbers Simplify by combining like ternis, X 4L x x 3x x 4x x Solve for x. State any restrictions on the variables. 3. ax+bx±9=7 a, x= ;ab x= ;a+h9 a+b a+b+9 x= ;ao,b9 x= a+b+9 a+b 4. Supposef(x) = 4x andg(x) x + 1. f(s) Find the value of. g(3) l- 4 Find an equation for the line: 5. through (, 6) and perpendicular toy = x v=-x+- y=-x+ v=-x+-

2 ID: A Solve the system by graphing Ix+y+1 =0 4xy= ct C. 4 N/ 4 4 x 4 x infinite (0, 0) -4/ x 4 x (0,i)

3 ID:A 7. A rental car agency charges a flat fee of $3.00 plus $3.00 per day to rent a certain car. Another agency charges a fee of $30.50 plus $3.5 per day to rent the same car. Write a system of equations to represent the cost c for renting a car at each agency for d days. Using a graphing calculator, find the number of days for which the costs are the same. Round your answer to the nearest whole day. Ic = 3.OOd Ic = 3.5d Ic = 3.OOd Ic = 3.5d Ic = 3.OOd Ic = 3.5d Ic = 3.OOd d Ic = 3.5d Without graphing, classify each system as independent, dependent, or inconsistent. = 4x + 6 I8x+y= 1 independent inconsistent dependent Solve the system by the method of substitution. I5xv= L5x 3y = 15 (0,5) (5,0) (5,1) (1,5) 10. Use the elimination method to solve the system. 0.18f 0.3g = 3 L0.15g 0.9f = 5.55 f7,g5 f5,g7 II. Find a quadratic function tq model the values in the table, Predict the value of v for x = 6. x l 0 y 3 10 f5,g7 f5,g7 - -x--- y = x + lv 58 v = x x--60 v=xv58 v=lv+v+;58 3

4 . ±. 8x4; ID: A A1. Dalco Manufacturing estimates that its weekly profit, F, in hundreds of dollars, can be approximated by the formula P = 3x + 6x + 10, where x is the number of units produced per week, in thousands. How many units should the company produce per week to earn the maximum profit? Find the maximum weekly profit. 1,000 units; $1300 3,000 units; $100 1,000 units; $600,000 units; $ Identify the vertex and the y-intercept of the graph of the function y vertex: (, 5); vertex: (, 5); y-intercept: 7 y-intercept: 7 vertex: (, 5); vertex: (, 5); l y-intercept: 1 y-intercept: 9 3(x + ) + 5. Factor the expression x (5x + 3)(x + 5) (x + 3)(5x 5) Ic 15. 1&x 40x + 5:(4 5) (4x (4x + 5)(4x 5) 16. 9x 16 (3x + 4)(3x 4) ) (3x± 4)(3x 4) \ 17. c3 51 a, (c 8)(c + 8c + 64) (c 8)(c + 8c + 64) (5x + 3)(x 5) (5x 5)(x 3) (4x + 5) (4x + 5) (3x + 4)(3x 4) (3x 4) (c + 8)(c + 8c + 64) (c 8)(c 8c 64) Solve the equatlon by finding squatejoots.. ) x = \ -,, \ C Simplify using the imagina number i i /i 5if 5J 0. Write 4x(x + 5x 3) in standard form. Then classify it by degree and number of terms. x + 9x 4; quintic binomial x5 quintic trinomial 0x 5 8x4; quintic binomial 0x 5 lox 4; quartic binomial 1. Write a polynomial function in standard form with zeros at 5, 4, and 1.. (.. f(x)=x3_x_19x_9 f(x)=x 31x +60x9 f(x)=x 3x l9x+0 f(x)=x3+0x_x_19 4 V U

5 ID: A Divide using synthetic division. j \). (x4 + x3 3 15x 3x 77x 75x x3+15x_3x_.5 3. Use synthetic division x 36) (x 4) 5 find P() forp(x) x4 x3 x + 9x + 19 x+19x x+9 to = + lox Use the Rational Root Theorem to + x 7x 4 = 0. Do not 4,,1, x3 noroots Verne has 1,,4 list all find the actual roots. 3 3x 6x possible rational roots of 1,,4 4,l,1,4 I the - polynomial equation 6 math books to up a has 4 to line up more line up his There are orders can Verne 10 first and 1 90 ways second way line on students participating in the bee be chosen? in The Booster Club dogs, sells meals at shelf. Jenny English books books than Jenny? s a spelling bee. In 45 ways how many ways 3,68,800 ways basketball games. Each meal cheeseburgers, or tacos, and combinations are there? possible meal a choice of root beer, lemonade, comes with milk, I can a L / on the students who a sheifrmn how many go choice of hamburgers, pizza, hot coffee, In how many ways can 3 from 5 to I singers be selected who came an audition? tea, or col How many Simplify J l8a i4b a3b&j 90x SA h6. Assume that all variables are positive. 4i4b noneofthese 3x.f 4l8x 5x-J noneofthese Add if possible J + 5Ji 9&Ji 7/ not 7fi possible to simplify 5

6 JiE ID: A Multiply. 3. (8_)(9+) 7.\Ji J 7 Solve the equation. 33. Jx = Let /) = t + 6 and g(x) = 8 4 cl Find (g 1) (7) Findtheinverseofy = 7x 3. ix + 3 x 3 a v=±q C I v + 3 I x=q. =±j 36. An initial population of 895 quail increases at an annual rate of 7%. Write an exponential function to model the quail population -) C. i 3 f(x) = 895(1.07)v 1(x) = 895(0.07)x /(x) = 895(7)x f(x) = ( ) 37. Find the annual percent increase or decrease that y = 0.35(.3)t models. 30% increase 30% decrease 130% increase 65% decrease 38. For an annual rate of change of 31%, find the corresponding growth or decay factor \ = 3 Write the equation in logarithmic form = 1.96 log 6l,96 = 4 logl,96 = 46 log 1,96 4 log 4 1,96 = 6 Evaluate the logarithm. 40. log

7 C) Nane: ID: A 41. Solvelog(4x+ 10) = Write the expression as a single natu al logarithm. 4. 3Inxlnc ln ln(x3 + c) In(x3 3c Inx 43. Simp1ifye3. 3 I I 3e 3e 3 Short Answer 44. In an experiment, a petn dish with a colony of bacteria is exposed to cold temperatures and then warmed again. Find a quadratic model for the data in the table. Use the model to estimate the population of bacteria at 9 hours. Time (hours) Population (l000s) is( J 7

8 ID: A Essay 45. Write the equation of the line that contains the point (8, 3) and is perpendicular to 4x equation. Write the equation in standard form. Show your work. N S w = 10. Graph the l 1 \ \ -4 I-c L 8