HONORS ALGEBRA B Semester Eam Review The semester B eamination for Honors Algebra will consist of two parts. Part will be selected response on which a calculator will not be allowe Part will be short answer on which a calculator will be allowe The following smbol applies to this review: Indicates that a student should be prepared to complete a question like this with or without a calculator. If a calculator is used to find points on a graph, the appropriate calculator function (i.e. zero, intersect, minimum or maimum) should be use The trace function should not be use Decimal approimations must be accurate to three places after the decimal point. Unless otherwise specified, the domain of an function f is assumed to be the set of all real numbers for which f is a real number. The formulas below will be provided in the eamination booklet. Compound Interest: Continuousl: A A P rt Pe n times per ear: r n nt Arithmetic Sequence and Series: a an a ( n) d an a ( n ) d Sn n n Geometric Sequence and Series: an n ar n S n r a r MCPS 0 0
HONORS ALGEBRA B Conic Sections: Semester Eam Review Circle h k r Center hk, Parabola p h p k or k h opens up if p 0, opens down if 0 p k p h or h k opens right if p 0, opens left if 0 p Verte hk, p Verte hk, radius r p = distance from verte to focus and from verte to directri h k a b major ais horizontal Center hk, a b h k b a major ais vertical Center hk, a b a distance from center to verte c distance from center to focus c a b h k a b transverse ais horizontal Center hk, k h a b transverse ais vertical Center hk, a distance from center to verte c distance from center to focus c a b Ellipse Hperbola MCPS 0 0
HONORS ALGEBRA B. Given the sequence,, 8, 9, Semester Eam Review Write the recursive rule for the sequence. a a n Write an eplicit rule for the sequence. an Use a formula to determine the th term of the sequence. 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 Use a formula to determine the 60 th term of the sequence. Use a formula to determine the sum of the first sit 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 per da. How much helium will it 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 0 rows in the theater, how man seats are there? MCPS 0 0
HONORS ALGEBRA B Semester Eam Review. Rewrite using rational eponent notation. 7 6. Rewrite using radical notation. 7 7. Evaluate. 9 8 7 7 0 8. Simplif each of the following. Assume all variables are positive. ab 6 6 a abc 7 b c e. 0 f. 8 g. 8 h. 8 i. 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 g, f 8 g f 7, f. MCPS 0 0
HONORS 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 t 09.. 6 Sammi is parachuting and falls feet before she opens her parachute. How long does it take Sammi to fall this distance?. A car traveling 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 00 6 is the speed in miles per hour and d is the length of the skid mark in feet. The driver said he was traveling at 0 miles per hour. s. d, where s What should be the length of the skid mark (correct to three decimal places)?. Solve. Check for etraneous roots. 6 0 7 6 8 6 e. 9. Match each function to its graph: f f f f e. f i. ii. iii. iv. v. MCPS 0 0
HONORS ALGEBRA B Semester Eam Review. Graph the function. Identif the -intercept, the asmptote, state the domain and range, and whether the function is increasing or decreasing. 6. Graph the function. State the -intercept, the asmptote, the domain, the range, and whether the function is increasing or decreasing. e e 7. In 900, the population of a town was,000. The population increased at an average rate of.% per ear. What was the population (nearest whole number) in 90? What was the population (nearest whole number) in 90? 8. A town has a population of 0,000. Due to a loss of jobs in the area, the population of the town decreases at a rate of % per ear. Write an eponential model that describes this situation. What is the epected population of the town (nearest whole number) in 0 ears? 9. A luur car originall costs $7,000. It depreciates at a rate of % per ear. What will the car be worth (to the nearest dollar) after ears? What will the car be worth after t ears? 0. An account pas % interest compounded monthl. You deposit $6,000 into the account. If ou do not deposit or withdraw mone from the account, how much mone (to the nearest cent) will be in the account in ears?. You deposit $,000 in an account to save mone for a car. The bank pas 7.% interest. If ou neither deposit nor withdraw an mone from the account, how much mone (to the nearest cent) will be in the account after 6 ears if the interest is compounded continuousl? MCPS 0 0 6
HONORS ALGEBRA B Semester Eam Review. In a bacterial culture, the number b of bacteria present is modeled b where t represents time in hours since :00 noon. b, e 07 000. t, How man bacteria (nearest whole number) will be present at :00 PM? How long (correct to three decimal places) will it take for there to be over 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 toda. Ten ears from toda, the population is epected to be 7000. At what rate (correct to three decimal places) is the count growing?. Rewrite each equation in eponential form. 0 log 0000 log66 log ln 7 m. Rewrite each equation in logarithmic form. 6 e 0 00, 000 6. Evaluate each epression. log8 log log00 log9 7 e. log86 f. log00 0 7. Simplif each epression using the inverse relationship between logarithms and eponents. log log lne ln e e. log f. log0000 MCPS 0 0 7
HONORS ALGEBRA B Semester Eam Review 8. The graph below illustrates a relationship between the functions 7 and log7. What is the relationship between the two functions? Eplain how the relationship is determined from the graph. 9. Graph the function. State the asmptote, the domain, the range, and whether the function is increasing or decreasing. 0 log ln 0. Solve each equation. Your answer ma be eact or correct to three places after the decimal point. 0 0 0 e 9 e. 6 f. ln g. log 8 h. log i. log 6 log 9 k. j. 0 6 l. 0 m. 8 n. ln 7 8. Write an eponential function of the form ab whose graph passes through the given points. 0, and, 0, and 00, MCPS 0 0 8
HONORS ALGEBRA B Semester Eam Review. For each set of data below: Based on the patterns of change, which tpe of function best fits the data: linear, quadratic, radical, eponential, or logarithmic? Write the function that best fits the dat f 6 6 6 0 f 0 0 8 6 f 0 f 0 9 6 0 f 00 00 00 0 0 9 6 f 0. 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 P t who have heard the rumor t minutes after the rumor starte t 0 Pt 6 8 6 What tpe of function best models this data? Write a function that models the dat (calculator ok) Predict how man people will have heard the rumor after 9 hours. MCPS 0 0 9
HONORS ALGEBRA B. Match each equation to its graph: Semester Eam Review i. ii. iii. iv.. Match each equation to its graph: e e e log0 e. log 0 i. ii iii. iv. v. MCPS 0 0 0
HONORS ALGEBRA B Semester Eam Review 6. Write an equation relating the variables. Use k for the constant of variation. s varies directl as r. varies inversel as. t varies directl as r and inversel as s. V varies jointl with r and h. e. F varies jointl with m and n, and inversel as the square of v. 7. If varies inversel as, and when, find when 0. 8. The time t required to empt a pool varies inversel as the rate r of the pump. One 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. Find the constant of variation k. How long will it take to empt the same pool with a pump that can empt it at the rate of 00 gallons per minute? 9. If varies directl with and inversel as z, and 9 when and z, find when and z 0. 0. 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 illuminate The intensit of light from an overhead fiture to a dining room table feet below the fiture is lu. Write an equation that represents the relationship between I and What will the intensit (correct to three decimal places) be if the fiture is raised to a height of 6. feet above the table?. Graph each function. Identif the horizontal and vertical asmptotes. State the domain and range. MCPS 0 0
HONORS ALGEBRA B Semester Eam Review. Perform the indicated operations. Simplif the result. 0 6 8 8 7 6. Perform the indicated operations and simplif. e. 7 9 8. Solve each equation. Check for etraneous roots. 8 7 MCPS 0 0
HONORS ALGEBRA B Semester Eam Review. Match each equation to its graph. i. ii. iii. iv. 6. Identif each locus of points in the plane. The set of all points such that the sum of the distances from two fied points to each point on the locus is a constant. The set of all points such that the difference of the distances from two fied points to each point on the locus is a constant. The set of all points equidistant from a given point. The set of all points that is equidistant from a given point and a given line. MCPS 0 0
HONORS ALGEBRA B Semester Eam Review 7. Sketch the graph of each equation. Identif the focus and directri. 6 0 8. Write the equation of a circle that passes through the point, the origin. and whose center is 9. Sketch the graph of the equation 6and state the center and radius. 0. An ellipse has a center at 00,. One verte is at the point 00 the point 80,. Write an equation of the ellipse., and a co-verte is at. Describe the graph of the equation. 6 6. Sketch the graph of each equation. Identif the center and the vertices. 6 6 9 6 MCPS 0 0
HONORS ALGEBRA B Semester Eam Review. Match each equation to its graph. 8 9 9 6 e. f. 6 i ii iii iv v vi. For each of the following equations, name the conic section. For parabolas, name the focus, directri, equation of the ais of smmetr, and the direction in which the parabola opens. For circles, name the center and the length of the radius. For ellipses, name the vertices, co-vertices, and foci. For hperbolas, name the foci and the vertices. 6 9 0 9 MCPS 0 0
HONORS ALGEBRA B Semester Eam Review. For each of the following equations of conic sections: Identif the tpe of coni Write the equation in standard form. 0 9 8 8 0 9 6 8 0 6. Match each equation to its graph. i. ii. 6 9 iii. iv. 7. Solve each sstem of equations for and. 9 0 9 6 MCPS 0 0 6
HONORS ALGEBRA B Semester Eam Review Practice Student Produced Response questions 8. Evaluate 9. Evaluate 6 60. Solve 6. Evaluate log0 8. / /... 0 0 0 6 6 6 6 7 7 7 7 8 8 8 8 9 9 9 9 9. / /... 0 0 0 6 6 6 6 7 7 7 7 8 8 8 8 9 9 9 9 60. / /... 0 0 0 6 6 6 6 7 7 7 7 8 8 8 8 9 9 9 9 6. / /... 0 0 0 6 6 6 6 7 7 7 7 8 8 8 8 9 9 9 9 MCPS 0 0 7