Intermediate Algebra / MAT 135 Spring 2017 Master ( Master Templates) $6.70 $9.90 $

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1 Midterm Review #1 Intermediate Algebra / MAT 135 Spring 2017 Master ( Master Templates) Student Name/ID: 1. Solve for. 6 + k = C 2. Solve for. 2 = M 3. At the cit museum, child admission is and adult admission is. On Tuesda, three times as man adult tickets as child tickets were sold, for a total sales of $6.70 $9.90 $ How man child tickets were sold that da? Two trains leave stations miles apart at the same time and travel toward each other. One train travels at 75 miles per hour while the other travels at 65 miles per hour. How long will it take for the two trains to meet? Do not do an rounding. hours 5. The length of a rectangle is longer than its width. If the perimeter of the rectangle is 5 ft 30 ft, find its area. Midterm Review #1 Page 1 / 20

2 6. An allo is a miture of metals. Suppose that a certain allo is made b miing grams of an allo that 44% 56 contains copper with grams of pure copper. Answer the questions below. Do not do an rounding. 200 (a) How man grams of copper are in the resulting miture? grams (b) What percentage of the resulting miture is copper? % 7. In the lab, Ivan has two solutions that contain alcohol and is miing them with each other. He uses milliliters less of Solution A than Solution B. Solution A is alcohol and Solution B is alcohol. How man milliliters of Solution A does he use, if the resulting miture has 12% 16% 44 milliliters of pure alcohol? 100 D E 8. The sets and are defined as follows. D = 1 E = < 7 D E D E Write and using interval notation. If the set is empt, write. 9. Solve the compound inequalit. 2v 2 10 and Write the solution in interval notation. If there is no solution, enter. 4v 6 2 Midterm Review #1 Page 2 / 20

3 10. Solve the compound inequalit. 3 4 < 22 or + > Graph the solution on the number line Solve for = 5 v 12. Solve for. 1 3v = v Solve Graph the solution to the inequalit on the number line < Midterm Review #1 Page 3 / 20

4 15. Solve < 7 6, 6 4, Find an equation for the line that passes through the points and. 17. Write equations for the vertical and horizontal lines passing through the point. vertical line: horizontal line: 2, 4 = Consider the line. 5, 2 (a) Find the equation of the line that is parallel to this line and passes through the point. 5, 2 (b) Find the equation of the line that is perpendicular to this line and passes through the point. Midterm Review #1 Page 4 / 20

5 19. For each relation, decide whether or not it is a function. Relation 1 Relation 2 D o m a i n R a n g e D o m a i n R a n g e lake 6 moon paper 8 d pencil chair rock 5 z cloud pencil 8 m lake Function Function Not a Function Not a Function Relation 3 Relation 4 Domain Range Domain Range c 2-6 c b 2-9 b 5 2 c c 2-1 Function Not a Function Function Not a Function 20. Suppose that the relation is defined as follows. H = 4, 4, 8, 0, 5, 8, 1, 7 H H Give the domain and range of. Write our answers using set notation. Midterm Review #1 Page 5 / 20

21. Find the domain of the function. u = 30 + 6 Write our answer using interval notation. 22. Keiko is driving to San Francisco.

6 21. Find the domain of the function. u = Write our answer using interval notation. 22. Keiko is driving to San Francisco. Suppose that the remaining distance to drive (in miles) is a linear function of her driving time (in minutes). When graphed, the function gives a line with a slope of below.. See the figure Keiko has miles remaining after minutes of driving. How man miles were remaining after minutes of driving? Remaining distance in miles Driving time in minutes 23. The Jackson famil and the Hernandez famil each used their sprinklers last summer. The Jackson famil's sprinkler was used for hours. The Hernandez famil's sprinkler was used for hours. There was a combined total output of 70 L per hour? L Jackson famil's sprinkler: Hernandez famil's sprinkler: of water. What was the water output rate for each sprinkler if the sum of the two rates was Midterm Review #1 Page 6 / 20

7 24. The Roal Fruit Compan produces two tpes of fruit drinks. The first tpe is pure fruit juice, and the second tpe is pure fruit juice. The compan is attempting to produce a fruit drink that contains pure fruit juice. How man pints of each of the two eisting tpes of drink must be used to make that is 75% 70% 95% 75% 180 pure fruit juice? First fruit drink: pints Second fruit drink: pints pints of a miture 25. Use substitution to solve the sstem = 7 = = 2 5 = 26. Solve the following sstem of equations = = Factor completel: 3v Factor Midterm Review #1 Page 7 / 20

8 29. Factor Factor u 3 v 31. Solve for. 6v 2 30v = Solve for = 11 u 33. Solve for. 2u 2 + u + 21 = u 3 2 If there is more than one solution, separate them with commas. 34. The area of a rectangle is, and the length of the rectangle is more than double the width. Find the dimensions of the rectangle. 45 d 2 1 d Midterm Review #1 Page 8 / 20

35. For the following right triangle, find the side length. Round our answer to the nearest hundredth. 12 10 36. The hpotenuse of a right triangle is long.

9 35. For the following right triangle, find the side length. Round our answer to the nearest hundredth The hpotenuse of a right triangle is long. The longer leg is longer than the shorter leg. Find the side lengths of the triangle. Length of the shorter leg: Length of the longer leg: Length of the hpotenuse: m m m 10 m 2 m 37. Find all ecluded values for the epression. That is, find all values of for which the epression is undefined. 7t 2t + 10 t If there is more than one value, separate them with commas. f 38. The function is defined below. f = Find all values of that are NOT in the domain of. If there is more than one value, separate them with commas. f Midterm Review #1 Page 9 / 20

10 39. For each epression, simplif if possible. 2 + v = v + 2 v + 4 v 4 = 40. Simplif. v 2 + 6v + 9 3v v Simplif Multipl Simplif our answer as much as possible. 43. Multipl Simplif our answer as much as possible. Midterm Review #1 Page 10 / 20

11 44. Divide Simplif our answer as much as possible. 45. Divide Simplif our answer as much as possible. 46. Divide Simplif our answer as much as possible. 47. Find the least common denominator of and Find the least common denominator of and Find the least common denominator of and. 6 Midterm Review #1 Page 11 / 20

12 50. Add. 10a 3 b a u 4b 2 d 3 Simplif our answer as much as possible. 51. Subtract Simplif our answer as much as possible. 52. Subtract Simplif our answer as much as possible. 53. Add Simplif our answer as much as possible. 54. Add. 2c + 7 9c + c + 4 6c Simplif our answer as much as possible. Midterm Review #1 Page 12 / 20

13 55. Add Simplif our answer as much as possible. 56. Simplif. u 3 u u 2 9 4u 57. Simplif Simplif Midterm Review #1 Page 13 / 20

14 59. Simplif Simplif Midterm Review #1 Page 14 / 20

15 Midterm Review #1 Answers for class MAT 135 Spring 2017 Master 1. = C 6 k 2. = 2M tickets hours 5. 50ft 2 6. (a) How man grams of copper are in the resulting miture? 144 grams (b) What percentage of the resulting miture is copper? 56.25% 7. Number of milliliters of Solution A: 8. D E =, D E = 1, = 2 Midterm Review #1 Page 15 / 20

16 12. v = 3, No solution vertical line: horizontal line: 18. = = 2 = 4 Equation of parallel line: Equation of perpendicular line: = = Midterm Review #1 Page 16 / 20

17 19. Relation 1 Relation 2 D o m a i n R a n g e D o m a i n R a n g e lake 6 moon paper 8 d pencil chair rock 5 z cloud pencil 8 m lake Function Function Not a Function Not a Function Relation 3 Relation 4 Domain Range Domain Range c c b c b c Function Not a Function Function Not a Function 20. domain range = 4, 8, 5, 1 = 4, 0, 8, , miles 23. Jackson famil's sprinkler: per hour Hernandez famil's sprinkler: 40 L 30 L per hour Midterm Review #1 Page 17 / 20

18 First fruit drink: pints 36 Second fruit drink: pints 25. = 1 = = 4 = v 2 v + 2 v u 25 15u + 9u v = 0, , 33. u = 3, Length: Width: 10 d 4.5 d Midterm Review #1 Page 18 / 20

19 36. Length of the shorter leg: Length of the longer leg: Length of the hpotenuse: 6 m 8 m 10 m t = 5 = 8, v v + 2 v + 4 v 4 = 1 Cannot be simplified v v Midterm Review #1 Page 19 / 20

20 d a 6 bu 20a 3 b 3 d c c u Midterm Review #1 Page 20 / 20

Intermediate Algebra / MAT 135 Spring 2017 Master ( Master Templates)

Test 1 Review #1 Intermediate Algebra / MAT 135 Spring 017 Master ( Master Templates) Student Name/ID: 1. Solve for. = 8 18. Solve for. = + a b 3. Solve for. a b = L 30. Two trains leave stations miles