The semester B examination for Algebra 2 will consist of two parts. Part 1 will be selected response. Part 2 will be short answer. n times per year: 1

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1 ALGEBRA B Semester Eam Review The semester B eamination for Algebra will consist of two parts. Part 1 will be selected response. Part will be short answer. Students ma use 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 used. The trace function should not be used. 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. Quadratic Formula: b b ac If a b c 0, then a Factoring: a b aba ab b a b aba ab b Compound Interest: Continuousl: A A P rt Pe n times per ear: 1 r n nt Arithmetic Sequence and Series: a1 an a1 ( n1) d an a1 ( n 1) d Sn n n Geometric Sequence and Series: an n 1 ar 1 n 1 S n 1 r a 1 r MCPS

2 ALGEBRA B Conic Sections: Semester Eam Review Circle r Center 0,0 radius r Parabola 1 p or opens up if p 0, opens down if p 0 Verte 0,0 p 1 p or opens right if p 0, opens left if p 0 p Verte 0,0 p distance from verte to focus and from verte to directri Ellipse 1 a b major ais horizontal Center 0,0 a b 1 b a major ais vertical Center 0,0 a b a distance from center to verte c distance from center to focus c a b Hperbola 1 a b transverse ais horizontal Center 0,0 1 a b transverse ais vertical Center 0,0 a distance from center to verte c distance from center to focus c a b MCPS

3 ALGEBRA B 1. Given the sequence, 1, 8, 19, Semester Eam Review Write the recursive rule for the sequence. a1 a n Write an eplicit rule for the sequence. an c. What is the 1 th term? d. What is the sum of the first fifteen terms of the sequence?. Given the sequence 1,, 7, 10, Write the recursive rule for the sequence. a1 a n Write an eplicit rule for the sequence. an c. What is the 60 th term? d. What is the sum of the first sit terms of the sequence?. A balloon is filled with 000 cm of helium. It immediatel begins losing helium such that it loses one fourth of its helium per d 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

4 ALGEBRA B. Rewrite using rational eponent notation. Semester Eam Review Rewrite using radical notation Evaluate c. 7 1 d Simplif each of the following. Assume all variables are positive. ab c. d. a abc 1 7 b c e. 10 f. 81 g. 8 h. 18 i. a a 10 a 1 9. Graph each function and state its domain and range. 10. Describe how to obtain the graph of g from the graph of f. g, f 8 g, f 11. The approimate time t, in seconds, that it takes an object to fall a distance d, in feet, is d t Sammi is parachuting and falls 1600 feet before she opens her parachute. How long does it take Sammi to fall this distance? MCPS

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 (our answer should be correct to three places after the decimal point)?

5 ALGEBRA B Semester Eam Review 1. 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 (our answer should be correct to three places after the decimal point)? 1. Solve. Check for etraneous solutions. 6 0 c. 7 6 d Match each function to its graph. 1 f f c. f d. f 1 e. f 1 i. ii. iii. iv. v. MCPS

6 ALGEBRA B Semester Eam Review 1. Graph the function. Identif the -intercept, the asmptote, state the domain and range, and whether the function is increasing or decreasing. c. 16. In 1900, 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 190? What was the population (nearest whole number) in 190? 17. 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? 18. 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? 19. 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 (to the nearest whole number) of the town in 10 ears? 0. You deposit $1,000 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? 1. Graph the function f e. State the -intercept, the asmptote, the domain, the range, and whether the function is increasing or decreasing.. In a bacterial culture, the number b of bacteria present is modeled b where t represents time in hours since 1:00 noon. b e. 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 10,000 bacteria? MCPS

7 ALGEBRA B. Rewrite each equation in eponential form. 1 log log616 c. log d. ln 7 m Semester Eam Review. Rewrite each equation in logarithmic form. 16 e c , 000. Evaluate each epression. log81 log1 c. log Simplif each epression using the inverse relationship between logarithms and eponents. 11 log11 log c. ln e d. ln e 7. 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. 8. Solve each equation. Your answer ma be eact or correct to three decimal places. 0 c d. e 9 e. 6 f. ln g. log 8 h. log 1 i. log 6 log 9 j. MCPS

8 ALGEBRA B 9. Write an eponential function of the form points 0, and 11, Semester Eam Review ab whose graph passes through the 0. 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 1 f() f() f() f() f() f() 0 1. The number of bacteria () in a culture is a function of the number of hours () the culture has been growing. The initial number of bacteria present in a culture is 0; the number of bacteria in the culture for each hour is represented in the table below What tpe of function best models this data? Write a function that models the dat c. Predict how man bacteria there will be after 9 hours. MCPS

9 ALGEBRA B. Match each equation to its graph: Semester Eam Review c. d. 1 i. ii. iii. iv.. Match each equation to its graph: e e c. e d. log10 e. log 1 i. ii iii. 10 iv. v. MCPS

10 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.. If varies inversel as, and when, find when 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. c. 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? 7. Graph each function. Identif the horizontal and vertical asmptotes. Identif the - and -intercepts. State the domain and range. c. 1 d. 8. Perform the indicated operations. Simplif the result Perform the indicated operations and simplif. 1 c. 1 MCPS

ALGEBRA B 0. Solve each equation. Check for etraneous roots. Semester Eam Review 8 1 1 7 1 1. Match each equation to its graph. 1 c. d. i. ii. iii.

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.

11 ALGEBRA B 0. Solve each equation. Check for etraneous roots. Semester Eam Review Match each equation to its graph. 1 c. d. i. ii. iii. iv.. 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. c. The set of all points equidistant from a given point. d. The set of all points that is equidistant from a given point and a given line. MCPS

ALGEBRA B. Sketch the graph of each equation. Semester Eam Review 6 0. Write the equation of a circle that passes through the point, the origin. and whose center is.

12 ALGEBRA B. Sketch the graph of each equation. Semester Eam Review 6 0. Write the equation of a circle that passes through the point, the origin. and whose center is. Sketch the graph of the equation 16 and state the center and radius. 6. An ellipse has a center at 00,. One verte is at the point 010 the point 80,. Write an equation of the ellipse., and a co-verte is at 7. Describe the graph of the equation Sketch the graph of each equation. Identif the center and the vertices Match each equation to its graph c d. 1 e. 1 f i ii iii iv v vi MCPS

13 ALGEBRA B Semester Eam Review Practice Student Produced Response questions 0. Evaluate 1. Evaluate 16. Solve. Evaluate log 8 0. / / / / / / / / MCPS

The formulas below will be provided in the examination booklet. Compound Interest: r n. Continuously: n times per year: 1

The formulas below will be provided in the examination booklet. Compound Interest: r n. Continuously: n times per year: 1 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