# MATH 1710 College Algebra Final Exam Review

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1 MATH 7 College Algebra Final Eam Review MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. ) There were 80 people at a pla. The admission price was \$ for adults and \$ for children. The admission receipts were \$770. How man adults and how man children attended? A) 9 adults and 88 children 90 adults and 90 children C) 9 adults and 38 children D) 90 adults and 90 children ) Use the graph of f to sketch a graph of the inverse of f using a dashed curve. ) ) A) C) D)

2 Solve the logarithmic equation smbolicall. 3) log 8 = 3 + log A) = 8 9 = 3/ C) = 9/8 D) = 3 3) Use common or natural logarithms to solve the eponential equation smbolicall. ) ( - 3) = ) A) = -3. = 3. C) = -3 D) = 3 ) ) The graph of = f() gives the speed limit along a rural highwa after traveling miles. (i) Evaluate f(), f(33), and f(3). (ii) At what -values is the graph discontinuous? A) 0, 7, 7; f(3), f(), f(), f(30), and f(3) 0, 0, 7; f(), f(), f(8), f(3), and f() C) 7, 7., 7; f(), f(8), f(30), f(3), and f() D) 7., 7, 90; f(), f(), f(8), f(30), and f(3) ) Let f() compute the cost of a rental car after das of use at \$0 per da. What does f - () compute? A) The number of das rented for 0 dollars The cost of rental for das C) The cost of rental for 0 das D) The number of das rented for dollars ) Solve the logarithmic equation smbolicall. 7) ln 3 + ln = ln 9 A) = = e9 8 C) = 9 8 / D) = 0 7)

3 Identif the slope, -intercept, and -intercept. 8) 3 8) A) Slope: ; -intercept: ; -intercept: - Slope: ; -intercept: -; -intercept: C) Slope: 3; -intercept: -; -intercept: D) Slope: -; -intercept: ; -intercept: - Find the probabilit of the compound event. 9) If two 8-sided dice are rolled what is the probabilit that both numbers will be even? A) 3 33 C) D) 9) Complete numerical representations for the functions f and g are given. Evaluate the epression, if possible. ) (g f)() ) f() g() - A) - C) - D) Compute the average rate of change of f from to. Round our answer to two decimal places when appropriate. Interpret our result graphicall. ) f() = -3 +, = - and = - A) 3; the slope of the line passing through (-, f(-)) and (-, f(-)) is 3. -; the slope of the line passing through (-, f(-)) and (-, f(-)) is -. C) -3; the slope of the line passing through (-, f(-)) and (-, f(-)) is -3. D) ; the slope of the line passing through (-, f(-)) and (-, f(-)) is. ) ) In Countr X, the average hourl wage in dollars from 9 to 99 can be modeled b ) f() = 0.077( - 9) if 9 < ( - 970) if Use f to estimate the average hourl wages in 90, 970, and 990. A) \$0.73, \$3.03, \$.7 \$3., \$0.3, \$.7 C) \$0.73, \$.7, \$.7 3

4 3) If an object is dropped off of a tower, the velocit, V, of the object after t seconds can be obtained b multipling t b 3 and adding to the result. Epress V as a linear function of t. A) V(t) = t V(t) = t- C) V(t) = 3t + D) V(t) = 3 + t 3 3) Solve the inequalit smbolicall. Epress the solution set in interval notation. ) A) (-, ] (-, ) C) [, ) D) (, ) ) Specif the domain of the function. ) f() = + - A) < 0 0 C) > 0 D) All real numbers ) ) A store is discounting all regularl priced items b 30%. (i) Find a function f that computes the sale price of an item having a regular price of. (ii) If an item normall costs \$ 99., what is its sale price? A) f() = - 30; \$9. f() = 0.3; \$9.8 C) f() = - 0.3; \$99. D) f() = - 0.3; \$39.8 ) Solve the equation. 7) r + = A) - -, C) No solution D), 7) 8) Determine whether the ordered triple (, 9, -) is a solution of the sstem of equations z = z = z = 3 A) Yes No 8) 9) The perimeter of a rectangle is cm. One side is cm longer than the other side. Find the lengths of the sides. A), 9 3, 8 C) 3, D), 9) Solve. 0) There are women running in a race. How man first, second, and third place possibilities can occur? A) 0 C) D) 0) ) In how man was can 7 people line up for pla tickets? A) 7 83,3 C) D) 00 )

5 Write the sstem of linear equations that the augmented matri represents. ) A) + + 3z = - + 7z = = + + 3z = z = = C) + + 3z = - + 7z = = ) Graph the eponential function. 3) = - 3) A) C) D) Specif the domain of the function. ( + 8)( - 8) ) f() = + A) > 8, -8 C) D) All real numbers )

6 Use the graph of f to sketch a graph of the inverse of f using a dashed curve. ) ) A) C) D) Use the graph to determine whether the function is one-to-one. ) ) A) No Yes

7 Graph the eponential function. 7) = 3 7) A) C) D) Use common or natural logarithms to solve the eponential equation smbolicall. 8) (7 + 3) = 8) A) = - ln ln + = - ln 3 ln C) = ln ln - 7 D) = ln 3 ln Compute the average rate of change of f from to. Round our answer to two decimal places when appropriate. Interpret our result graphicall. 9) f() = 3 -, = and = A) -3; the slope of the line passing through (, f()) and (, f()) is ; the slope of the line passing through (, f()) and (, f()) is -7. C) 3; the slope of the line passing through (, f()) and (, f()) is 3. D) 7; the slope of the line passing through (, f()) and (, f()) is 7. 9) If possible, find the matri product of AB. 30) A = - 3 ; B = ) A) AB = AB = C) AB = 0 - D) AB = - 9-7

8 Use the graph to determine whether the function is one-to-one. 3) 3) A) No Yes Find an equation that shifts the graph of f b the indicated amounts. 3) f() = ; right units, up units A) = - ( - ) + = ( - ) + C) = ( + ) - D) = - ( - ) + 3) 33) If dollars is deposited ever four weeks (3 times a ear) into an account paing an annual interest rate r, epressed in decimal form, then the amount A n in the account after n ears can be 33) approimated b the formula A n = + r/3 3n -. r/3 If a retirement account pas 9% annual interest, determine how much a 0-ear-old worker would have to deposit in this account ever weeks in order to have a million dollars at age. A) \$8.0 \$. C) \$80. D) \$,. Use the discriminant to determine the number of real solutions. 3) w - w + = 0 A) Two real solutions No real solutions C) One real solution 3) Write the sstem of linear equations that the augmented matri represents. 3) A) = - = - z = -3 = 0 = z = C) = - = - z = 0 D) = = z = 3 3) 8

9 3) 3) The graph of = f() gives the speed limit along a rural highwa after traveling miles. (i) What are the maimum and minimum speed limits along this stretch of highwa? (ii) Estimate the miles of highwa with a speed limit of 0 miles per hour. A) Maimum 70 mph; minimum 0 mph; miles Maimum mph; minimum mph;. miles C) Maimum 0 mph; minimum 3 mph; 0 miles D) Maimum 0 mph; minimum mph; 0 miles Find a smbolic representation for f - (). 37) f() = - 9 A) f-() = + 9, 0 Not a one-to-one function 37) C) f-() = ( - 9) D) f-() = + 9 Find an equation that shifts the graph of f b the indicated amounts. 38) f() = + - 7; left units, down 8 units A) = ( + ) + ( + ) - = ( + ) + ( - ) - C) = ( - ) + ( + ) + D) = ( - ) + ( - ) + 38) Find the median of the set of data. 39) 3, 3, 7, 3,,, 8 A) 3 C) 7 D) 39) 9

10 0) Brand A soup contains 883 milligrams of sodium. It is recommended that a person requiring 000 calories dail consume 00 mg of sodium or less per da. Graph the function, f, that computes the number of mg of sodium in cans of soup together with = 00, = 000, 3 = 700 in [0, 0), ] b [0, 8000, 00]. Use the intersection-of-graphs method to find how man cans of soup contain,, and 3 dail allowances of sodium. A) C) 8 allowance = 3 cans; allowances = cans; 3 allowances = 8 cans D) 8 allowance = cans; allowances = cans; 3 allowances = 7 cans allowance = cans; allowances = 8 cans; 3 allowances = 3 cans allowance = 3 cans; allowances = cans; 3 allowances = 8 cans Answer the question. ) In the ʺBig Bucksʺ lotter game, a person is to pick digits from 0 to 9 in correct order. If a number can be repeated, how man was are there to pla the game? A), 0,000 C),08,7 D),000 )

11 Use the graph of f to determine the intervals where f is increasing and where f is decreasing. ) ) A) increasing: (-, 0); decreasing (0, ) increasing: (-, ); decreasing (, ) C) increasing: (, ); decreasing (-, ) D) increasing: (-, ); decreasing: never Solve the sstem of linear equations. 3) = -0 + = - A) (0, -) (-, -) C) No solutions D) (0, -) 3) ) To convert a temperature from degrees Celsius to degrees Fahrenheit, ou multipl the temperature in degrees Celsius b.8 and then add 3 to the result. Epress F as a linear function of c. A) F(c) = 33.8c F(c) =.8c + 3 C) F(c) =.8 + 3c D) F(c) = c ) Use the discriminant to determine the number of real solutions. ) (-3 - ) = -3 A) One real solution No real solutions C) Two real solutions ) ) Determine whether the ordered triple (7,, -) is a solution of the sstem of equations z = z = z = A) Yes No )

12 Identif an horizontal asmptotes in the graph. 7) 98 7) A) = 7 = 7 C) = 0 D) None 8) 8) A) = 0 None C) = 9 D) = -9 Find a smbolic representation for f - (). 9) f() = ( - 9) A) f-() = + 9 Not a one-to-one function 9) C) f-() = + 9 D) f-() = + 9 If possible, find the matri product of AB. 0) A = 3-0 ; B = 0-0) A) AB = AB = C) AB = 0 0 D) AB = Specif the domain of the function. ) f() = - A) All real numbers > C) D) )

13 Use the discriminant to determine the number of real solutions. ) t - t + = 0 A) No real solutions One real solution C) Two real solutions ) Solve the equation. 3) m = 7 3) A), - - 3, 3 C) 3, - 3 D) No solution Find A - without a calculator. ) A = 0 - A) A - = 0-8 A - = 8-0 C) A - = 8-0 ) Make a scatterplot of the data. ) {(0., 0.33),(0.87, 0.89),(0.09, 0.8),(0., 0.),(0., -0.7), (0., 0.77),(0.78, 0.77),(0., -0.0)} ) A) C) D)

14 ) The cost for labor associated with fiing a washing machine is computed as follows: There is a fied charge of \$ for the repairman to come to the house, to which a charge of \$9 per hour is added. Find an equation that can be used to determine the labor cost, C(), of a repair that takes hours. A) C() = + 9 C() = - 9 C) C() = ( + 9) D) C() = 9 + ) Specif the domain of the function. 7) f() = + ( + 8)( - ) A) -, -8, > 0 C) All real numbers D) -, -8, 7) Use the graph of f to determine the intervals where f is increasing and where f is decreasing. 8) 8) A) increasing: (-, 0); decreasing (0, ) increasing: (0, ); decreasing (-, 0) C) increasing: (-, ); decreasing: never D) increasing: never; decreasing: (-, )

15 Make a scatterplot of the data. 9) {(, ),(-, 3),(8, ),(-, -9),(-, -),(, 3),(, 9),(3, ),(, ),(, )} 9) A) C) 80 D) Find the probabilit of the compound event. 0) Two -sided dice are rolled. What is the probabilit the sum of the two numbers on the die will be 3? A) C) 7 D) 8 8 0) Find A - without a calculator. ) A = A) A - = 0 3 A - = 0 3 C) A - = )

16 Graph the eponential function. ) = 3-3 ) A) C) D) Solve the quadratic equation. 3) = 0 A) -,, - C), - D) -, 3) ) = 0 A) - ± ± 7 C) - ± 7 D) - ± ) ) + 8 = - A) - ± - ± C) - ± D) -8 ± ) Use common or natural logarithms to solve the eponential equation smbolicall. ) ( + ) = log A) = log - log log log = - C) = - D) = + log log log )

17 7) Sketch a graph that depicts the amount of water in a 0 -gallon tank. The tank is initiall full, and then a pump is used to take water out of the tank at a rate of gallons per minute. The pump is turned off after minutes. At that point, the pump is changed to one that will pump water into the tank. The change takes minutes and the water level is unchanged during the switch. Then, water is pumped into the tank at a rate of gallons per minute for 3 minutes. A) 7) 0 0 (0, 0) 0 30 (, 3) (0, 0) (, 30) (7, 30) (, 3) C) 0 0 (0, 0) (, ) (, 3)

18 D) 0 0 (0, 0) 0 30 (, 3) 0 (, ) (7, ) Solve. 8) In how man was can the letters in the word PAYMENT be arranged if the letters are taken at a time? A) 8 C) 0 D) 80 8) Solve the sstem of linear equations. 9) + 8 = = - A) (, -) (, 0) C) (, ) D) No solutions 9) Use the given graph to find the -intercepts. 70) 8 70) A) -, -, C) -, - D), Answer the question. 7) In how man was can ou answer the questions on an eam that consists of true-false questions? A) 0 C) D) 8 7) Solve the inequalit smbolicall. Epress the solution set in interval notation. 7) A) (, ) [, ) C) (-, ) D) (-, ] 7) 8

19 Solve the equation. 73) k - = - A) -3 -, C) 3, -3 D) 3 73) 7) 7) The graph of = f() depicts the amount of cash in dollars that a bank teller has at his station after minutes. (i) When did the largest withdrawal occur? (ii) How much was it? A) After minutes; \$0 After. minutes; \$0 C) After 37. minutes; \$0 D) After 37. minutes; \$0 7) Determine whether the ordered triple (-3, -, ) is a solution of the sstem of equations z = z = z = - A) No Yes 7) 7) The inequalit T describes the range of monthl average temperatures T in degrees Fahrenheit at a Cit X. (i) Solve the inequalit. (ii) If the high and low monthl average temperatures satisf equalit, interpret the inequalit. A) -.7 T.; The monthl averages are alwas within. of 0 F. -7. T.; The monthl averages are alwas within. of 0 F. C) 37.3 T.7; The monthl averages are alwas within.7 of 0 F. D) 3.9 T 7.; The monthl averages are alwas within 7. of 0 F. 7) Find the probabilit of the compound event. 77) Urn A has balls numbered through 8. Urn B has balls numbered through 3. What is the probabilit that a is drawn from A followed b a from B? A) C) D) 8 77) 9

20 Determine the equation of the line described. Put the answer in the slope -intercept form, if possible. 78) Through (, -), perpendicular to -8-7 = -3 A) = = C) = D) = ) 79) Let f() compute the time in hours to travel miles at miles per hour. What does f - () compute? A) The miles traveled in hours The hours taken to travel miles C) The hours taken to travel miles D) The miles traveled in hours 80) The inequalit T - 9 describes the range of monthl average temperatures T in degrees Fahrenheit at a Cit X. (i) Solve the inequalit. (ii) If the high and low monthl average temperatures satisf equalit, interpret the inequalit. A) 3 T ; The monthl averages are alwas within 9 of F. 8 T ; The monthl averages are alwas within of F. C) 8 T; The monthl averages are alwas greater than or equal to 8 F. D) T ; The monthl averages are alwas less than or equal to F. 79) 80) Find the median of the set of data. 8) 3, 77,,, 3, 97 A) 33 C) 8. D) 8) 8) A salesman sold \$0 more than the rest of the sales staff. If the sales total for the da was \$ 0, how much did the rest of the sales staff sell? A) \$70 \$ C) \$00 D) \$00 8) Solve the logarithmic equation smbolicall. 83) log 8 = 8.7 A) = 8.7/8 = C) = 0.7 D) = 9 83) 8) In order to receive a B in a course, it is necessar to get an average of 80% correct on two one-hour eams of 0 points each, on one midterm eam of 00 points, and on one final eam of 00 points. If a student scores 90, and 8 on the one-hour eams, and 8 on the midterm eam, what is the minimum score on the final eam that the person can get and still earn a B? A) 397 C) 307 D) 77 8) Find the median of the set of data. 8) 78,, 9, 3, 97,, A) 9 C) 80 D) 3 8) Use the compound interest formula to determine the final value of the given amount. 8) \$,000 at 9% compounded quarterl for 7 ears A) \$,88.9 \$,37. C) \$,93.7 D) \$,37. 8) 0

21 87) \$,000 at % compounded semiannuall for 7 ears A) \$378. \$.97 C) \$.97 D) \$7. 87) 88) The table lists the average composite scores on a national entrance eam for selected ears. 88) Year Score (i) Make a line graph of the data. (ii) If the graph represents a piecewise-linear function f, find a smbolic representation for the piece of f located on the interval [98, 988]. A) f() = if f() = 3. if

22 C) f() =.7 if D) f() = if

23 Use the given graph to find the -intercepts. 89) 89) A), -, C) -, D) -, - Approimate f() to four decimal places. 90) f() = 3.e -., = -.9 A) C) 0.0 D) ) 9) Your compan uses the quadratic model = to represent the average number of new customers who will be signed on () weeks after the release of our new service. How man new customers can ou epect to gain in week? A) 8 customers 09 customers C) 8 customers D) 037 customers 9) Find a smbolic representation for f - (). 9) f() = A) f-() = 7-3 f -() = C) f-() = + 3 D) Not a one-to-one function 7 9) 93) f() = A) f-() = + 3 Not a one-to-one function 93) C) f-() = 3-3 D) f-() = ) The following table gives the outside temperature in degrees Fahrenheit on a winter da in Death V California. Time 7:00 am 8:00 am 9:00 am :00 am :00 am Temperature ( F) Calculate the average rate of change in temperature between 7:00 am and :00 am. Round our ans to two decimal places when appropriate. A). F.33 F C).3 F D) 3.98 F 9) 3

24 Answer Ke Testname: COLLEGE ALGEBRA FINAL EXAM REVIEW ) B ) D 3) B ) D ) C ) D 7) C 8) B 9) D ) C ) C ) A 3) C ) C ) D ) D 7) B 8) B 9) B 0) B ) D ) A 3) D ) D ) C ) B 7) D 8) B 9) C 30) D 3) B 3) B 33) B 3) B 3) D 3) D 37) A 38) A 39) B 0) A ) D ) B 3) A ) B ) B ) A 7) B 8) A 9) B 0) A

25 Answer Ke Testname: COLLEGE ALGEBRA FINAL EXAM REVIEW ) C ) B 3) C ) C ) C ) A 7) A 8) B 9) D 0) D ) A ) A 3) D ) C ) C ) A 7) B 8) D 9) B 70) C 7) C 7) D 73) C 7) D 7) B 7) D 77) D 78) C 79) A 80) A 8) B 8) D 83) B 8) B 8) B 8) B 87) C 88) B 89) B 90) D 9) A 9) B 93) D 9) B

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