FoM3 Midterm Review 2014

Transcription

1 FoM3 Midterm Review 01 Short Answer Solve the equation Evaluate the expression for the given value of the variable(s) Simplif the expression. Simplif. Write the answer in standard form. 11. The expression models the height of an object t seconds after it has been dropped from a height of 1900 feet. Find the height of an object after falling for 3. seconds. 1. Suppose and. Find the value of. 13. Graph the equation x + =. 7. (6 3) (3 + 5 ) Factor the expression. Write in standard form an equation of the line passing through the given point with the given slope.. 1. slope = ; ( 5, ) 15. A canner processed 175 pounds of strawberries in 6.5 hours. The canner processed 390 pounds in 1 hours. a. Write a linear equation to model the weight of strawberries S processed in T hours. b. How man pounds of strawberries can be processed in 7 hours? 16. A group of people attended a ball game. There were three times as man children as adults in the group. Set up a sstem of equations that represents the numbers of adults and children who attended the game and solve the sstem to find the number of children who were in the group. 17. Solve the sstem of inequalities b graphing. 1. An exam consists of two parts, Section X and Section Y. There can be a maximum of 0 questions. There must be at least 15 more questions in Section Y than in Section X. Write a sstem of inequalities to model the number of questions in each of the two sections. Then solve the sstem b graphing. 19. Find the values of x and that maximize the objective function P = 3x + for the graph. What is the maximum value?

2 Solve the quadratic equation b completing the square Rewrite the equation in vertex form.. 9. Find the zeros of. Then graph the equation. 0. Your computer suppl store sells two tpes of inkjet printers. The first, tpe A, costs $137 and ou make a $50 profit on each one. The second, tpe B, costs $100 and ou make a $0 profit on each one. You can order no more than 100 printers this month, and ou need to make at least $00 profit on them. If ou must order at least one of each tpe of printer, how man of each tpe of printer should ou order if ou want to minimize our cost? 1. Use vertex form to write the equation of the parabola.. Write in vertex form. 3. Solve b factoring. = 0. Simplif using the imaginar number i. 5. Find. 6 6 O 6 x Divide using snthetic division. 31. Use the Rational Root Theorem to list all possible rational roots of the polnomial equation. Do not find the actual roots. 3. Find the roots of the polnomial equation. 33. For the equation, find the number of complex roots and the possible number of real roots. 3. Graph the exponential function. 35. An initial population of 90 quail increases at an annual rate of 15%. Write an exponential function to model the quail population. 36. Graph. 37. The half-life of a certain radioactive material is 5 hours. An initial amount of the material has a mass of 1 kg. Write an exponential function that models the deca of this material. Find how much radioactive material remains after hours. Round our answer to the nearest thousandth. 3. Suppose ou invest $500 at an annual interest rate of 6.7% compounded continuousl. How much will ou have in the account after 10 ears?

3 Write the equation in logarithmic form. Evaluate the logarithm. Graph the logarithmic equation. Write the expression as a single logarithm.. Solve. 5. Solve. 6. Write the expression as a single natural logarithm. 7. Simplif.. Solve. 9. Write an equation of a parabola with a vertex at the origin and a focus at ( 7, 0). 50. Identif the vertex, focus, and directrix of the graph of. Expand the logarithmic expression. 51. Write a recursive formula for the sequence 3, 5, 7, 9, 11,... Then find the next term Write an explicit formula for the sequence, 5,, 1,,... Then find. 53. The table shows the predicted growth of a particular bacteria after various numbers of hours. Write an explicit formula for the sequence of the number of bacteria. Hours (n) Number of Bacteria Viola makes gift baskets for Valentine s Da. She has 11 baskets left over from last ear, and she 57. Use summation notation to write the series for 11 terms. plans to make more each da. If there are 10 work das until the da she begins to sell the baskets, how man baskets will she have to sell? 5. For the series, find the first and the last 55. Write the explicit formula for the sequence. Then find the fifth term in the sequence. 56. A large asteroid crashed into a moon of a planet, causing several boulders from the moon to be propelled into space toward the planet. Astronomers were able to measure the speed of one of the projectiles. The distance (in feet) that the projectile traveled each second, starting with the first second, was given b the arithmetic sequence 3, 31, 39, 7,.... Find the total distance that the projectile traveled in seven seconds. term. 59. The da before the parade, the school band s starting point was changed. The band director called three band members. Each of these band members called 6 other band members. Then all of these band members called three members. How man band members, including the band director, are notified of the new starting point? 60. Find the slope of the line.

4 6 6 6 x 6

5 FoM3 Midterm Review 01 Answer Section SHORT ANSWER , (g 5)(g ) ft O 1 x 1 1. x + = 15. S = 310T 30; 190 lb 16. ; 11 adults, 33 children

6 17. O x maximum value at (9, 0); of tpe A 60 of tpe B , x

7 . 9. 0, 5, x , 1, 1, complex roots; 1, 3, 5, or 7 real roots x 35.

8 x ; kg 3. $ none of these x vertex ( 3, 5), focus ( 3, 3), directrix at = 7

9 51. ; ; baskets 55. ; feet , band members 60.