HNRS ALGEBRA B Semester Eam Review The semester B eamination for Honors Algebra will consist of two parts. Part is selected response on which a calculator will NT be allowed. Part is short answer on which a calculator will be allowed. Items with a smbol net to the item number indicate that a student should be prepared to complete items like these with or without a calculator. The formulas below will be provided in the eamination booklet. Compound Interest Formula (continuous): A Pe rt r Compound Interest Formula (n times per ear): A P n nt Arithmetic Sequence and Series: a a n d n a a a n d n Sn n n Geometric Sequences and Series: an n ar Sn a n r r Conic sections formulas on net page MCPS 0 0
HNRS ALGEBRA B Semester Eam Review Conic Sections Equation of a circle with center at hk, with radius r: h k r Equations of a parabola with verte at hk, with p the distance from verte to focus and verte to directri : ; opens up if p 0, opens down if p 0. p h p k or k h ; opens right if p 0, opens left if p 0. p k p h or h k Equations of an ellipse with center at hk,, a b: Major ais horizontal: Major ais vertical: h k a b h k b a Equations of a hperbola with center at hk, : Transverse ais horizontal: Transverse ais vertical: h k a b k h a b MCPS 0 0
HNRS ALGEBRA B Semester Eam Review. Given the sequence,, 8, 9,... Write the recursive rule for the sequence. a a n Write an eplicit rule for the sequence. an c. Use a formula to determine the th term of the sequence. d. Use a formula to determine the sum of the first fifteen terms of the series 8 9.... Given the sequence,, 7, 0,... Write the recursive rule for the sequence. a a n Write an eplicit rule for the sequence. an c. Use a formula to determine the 60 th term of the sequence. d. Use a formula to determine the sum of the first 60 terms of the series 7 0.... A balloon is filled with,000 cm of helium. It immediatel begins losing helium such that it loses one-fourth of its helium each d How much helium will the balloon have lost (correct to three places after the decimal point) b the end of the ninth da?. A theater is designed with 0 seats in the first row, seats in the second row, 6 seats in the third row, and so on. If there are thirt rows of seats in the theater, how man seats are in the theater?. Rewrite using rational eponent notation. 7 MCPS 0 0
HNRS ALGEBRA B Semester Eam Review 6. Rewrite using radical notation. 7 8 7 7. Evaluate each epression. 9 8 7 c. 7 d. 0 8. Simplif each of the following. Assume that all variables represent positive numbers. An eponents in our answers should be positive. ab 6 6 c. d. a abc 7 b c e. 0 f. 8 g. 8 h. 8 g. a a 0 a 9. Graph each function and state its domain and range. 0. Describe how to obtain the graph of g from the graph of g, f 8, g f c. 7, g f f. MCPS 0 0
HNRS ALGEBRA B Semester Eam Review. Match each function to its graph. 8 f g c. h d. m e. s Graph Graph Graph Graph Graph MCPS 0 0
HNRS ALGEBRA B Semester Eam Review. The approimate time, t, in seconds, that it takes an object to fall a distance, d, in feet is d given b the formula t 0.9. Sammi is parachuting and falls feet before 6 opening her parachute. How long does it take Sammi to fall this distance?. A car travelling on Interstate 70 was involved in an accident. To approimate the speed of the car at the time of the accident, the police use the function s 8d, where s is the speed in miles per hour, and d is the length of the skid mark on the highwa in feet. The driver said that he was traveling at 0 miles per hour. What should the length of the skid mark be (correct to three places after the decimal point) if the driver was indeed travelling 0 miles per hour?. Solve each equation. Make sure to check for etraneous solutions. 6 0 c. 76 d. 8 6 e. 9. Graph each function. Identif the -intercept, the asmptote, the domain, range, and whether the function is increasing or decreasing. f g c. h d. j e e. m e 6. In 900, the population of a town was,000. The population increased at an average rate of.% per ear. What was the population (to the nearest whole number) in 90? What was the population (to the nearest whole number) in 90? 7. A cit has a population of 0,000. Due to a loss of jobs in the area, the population decreases at a rate of % per ear. Write an eponential model that describes this situation. What is the epected population of the town (to the nearest whole number) in ten ears? MCPS 0 0 6
HNRS ALGEBRA B Semester Eam Review 8. A savings account pas % interest compounded monthl. You deposit $6,000 into the account. If ou neither add nor withdraw an mone from the account, how much mone (to the nearest cent) will ou have in five ears? 9. You deposit $,000 in an account. The bank pas.% interest compounded continuousl. If ou neither add nor withdraw mone from this account, how much mone (to the nearest cent) will ou have in the account after eight ears? 0. In a bacterial culture, the number B of bacteria is modeled b the equation 0.7t B, 000e, where t represents the number of hours since noon. How man bacteria (nearest whole number) will be present at :00 p.m.? How man hours (correct to three decimal places) will it take for there to be 0,000 bacteria?. The population of a count toda is,000 and is growing eponentiall according to the rt function At Pe, where P is toda s population, r is the growth rate epressed as a decimal, and t is the number of ears from tod Ten ears from toda, the population is epected to be 66,000. At what rate (correct to three decimal places) is the count growing?. Write each equation in eponential form. log 0000 log6 6 c. log8 d. ln 7 m. Rewrite each equation in logarithmic form. 6 m e c. 0 00000. Evaluate each epression. log8 log c. log00 d. log9 7 e. log6 8 d. log 0 MCPS 0 0 7
HNRS ALGEBRA B Semester Eam Review. Simplif each epression using the inverse relationship between logarithms and eponents. log d. ln e e. 6. Let f log7 and 7 g. log c. ln e log f. log00 What is the relationship between f and g? How are their graphs related? 7. Graph each function. State the asmptote, domain, range, and whether the function is increasing or decreasing. log ln 8. Solve each equation. Your answer should be eact, meaning a whole number, a fraction, or an epression involving logarithms or the number e. 0 c. e 9 d. 0 0 e. f. ln g. log 8 h. log i. log 6 j. log 9 k. 0 l. 8 9. Solve each equation. Write our answer correct to three places after the decimal point. 0 6 ln 7 8 c. e 7 0. Write an eponential equation of the form pair of points. ab whose graph passes through the given 0, and,,0 and,00 MCPS 0 0 8
HNRS ALGEBRA B Semester Eam Review. A rumor is spreading through a town that aliens from Mars will be landing on Earth tomorrow. The table below shows the number of people t minutes after the rumor was started. Pt who have heard the rumor t 0 P t 6 8 6 Write a function that best models this dat Use our function to predict how man will have heard the rumor after 9 minutes.. For each set of data below, Based on the patterns of change, which tpe of function best models the data: linear, quadratic, radical, eponential, or logarithmic? Write the function that best models the dat f 6 6 6 0 g 0 0 c. 8 6 h d. 0 j 0 9 6 e. 0 k 00 00 00 0 f. 0 9 6 m 0 MCPS 0 0 9
HNRS ALGEBRA B Semester Eam Review. Match each equation to its graph. c. Graph Graph Graph MCPS 0 0 0
HNRS ALGEBRA B Semester Eam Review. Match each equation to its graph. e e c. e d. log ( ) e. log Graph Graph Graph Graph Graph MCPS 0 0
HNRS ALGEBRA B Semester Eam Review. Write an equation relating the variables. Use k for the constant of variation. s varies directl as r. varies inversel as. c. t varies directl as r and inversel as s. d. V varies jointl with r and h. e. F varies jointl with m and n, and inversel as the square root of v. 6. If varies directl with and when, find when 0. 7. The time t required to empt a pool varies inversel as the rate r of the pump. ne pool takes 60 minutes to empt at the rate of 0 gallons per minute. Write an equation that represents the relationship between t and r. Determine the constant of variation k. c. How long will it take to empt the same pool with a pump that operates at a rate of 00 gallons per minute? 8. If varies directl as and inversel as z, and 9 when and z, determine the value of when and z 0. 9. The intensit of light (I), measured in lu, is inversel proportional to the square of the distance (d) between the light source and the object that is being illuminated. The intensit of light from an overhead bulb to a table feet below it is lu. Write an equation that represents the relationship between I and d. What will the intensit (correct to three decimal places) be if the bulb is raised to a height of 6. feet above the table? 0. Graph each function. Give the equation of an asmptotes and state the domain and range. f g c. h d. j = MCPS 0 0
HNRS ALGEBRA B Semester Eam Review. Perform the indicated operations and simplif the result. 0 6 c. 8 8 7 6 d. e. f. g. h. 7 9 8. Solve each equation. Check for etraneous solutions. c. 8 7. Identif each locus of points in the plane b its description. The set of all points such that the sum of the distances from two fied points to each point on the locus is the same. The set of all points equidistant from a given point. c. The set of all points such that the difference of the distances from two fied points to each point on the locus is the same. d. The set of all points that is equidistant from a given point and a given line.. Sketch the graph of each equation. Identif the focus and the directri. 0 MCPS 0 0
HNRS ALGEBRA B Semester Eam Review. Write the equation of the circle that passes through the point, and whose center is at the origin. 6. Sketch the graph of the equation 6 and state the center and radius. 7. A ellipse is centered at the origin. ne verte is at the point 0,0 and a co-verte is at the point 8, 0. Write the equation of the ellipse. 8. Describe the graph of the equation 6 6 9. Sketch the graph of each equation. Identif the center and the vertices. 6 9 6 For items 0 through, do the following. Name the conic section that is represented b the equation. If a parabola, name the verte, focus, directri, ais of smmetr and the direction which the parabola opens. If a circle, name the center and the length of the radius. If an ellipse, name the center, vertices, co-vertices, foci, and its orientation. If a hperbola, name the center, vertices, foci, and its orientation. 0.... 6 9 0 9 MCPS 0 0
HNRS ALGEBRA B Semester Eam Review. Match each equation to the graphs below. 8 9 c. 9 6 d. e. f. 9 Graph Graph Graph Graph Graph Graph 6 MCPS 0 0
HNRS ALGEBRA B Semester Eam Review. Graph each equation. c. d. 6 9 For items 6 through 9, Name the conic section represented b the equation. Write the equation in standard form. 6. 7. 8. 9. 9 8 8 0 9 6 8 0 60. Solve each sstem of equations for and. 9 0 9 6 MCPS 0 0 6
HNRS ALGEBRA B Semester Eam Review Grid-in practice: For items 6 through 6, grid-in and bubble the correct answer. 6. log9 7 6. The equation of the horizontal asmptote of f 7 is =. 6. The eponent of the variable when 8 is written eponentiall. 6 6 6 / /.... 0 0 0 0 6 6 6 6 7 7 7 7 8 8 8 8 9 9 9 9 / /.... 0 0 0 0 6 6 6 6 7 7 7 7 8 8 8 8 9 9 9 9 / /.... 0 0 0 0 6 6 6 6 7 7 7 7 8 8 8 8 9 9 9 9 MCPS 0 0 7