# Diaz Math 080 Midterm Review: Modules A-F Page 1 of 7

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1 Diaz Math 080 Midterm Review: Modules A-F Page 1 of 7 1. Use the rule for order of operations to simplif the epression: Perform the indicated operations and simplif: 7( + ) 6(5 9) 3. If a = 3, b = 1 and c =, what is the value of 3a 10b + c?. Solve for : 3 1 = Solve for : = Solve t = (a + z) for a Solve for : 5(3 3) 1 = Solve for : (6 + 6) + 6(3 + ) + = Solve for : 15 = 3 ( ) Solve: 3 3 = Solve: 3 = The sum of four consecutive even integer numbers is 8. Find the four numbers. 13. One angle in a triangle has a measure that is three times as large as the smallest angle. The measure of the third angle is 0 degrees more than the smallest angle. Find the measure of the largest angle. 1. Solve: 5 3 > 1 Be sure to write our answer in interval notation. 15. Solve: 3 < < 1 Be sure to write our answer in interval notation. 16. Graph the solution to the inequalit (5 + ) 17. What is the interval for the graph below? Courtne and Sarah both leave the mall at the same time, but in opposite directions. If Sarah travels 6 mph faster than Courtne and after 5 hours the are 170 miles apart, how fast is each traveling? 19. Find the slope of the line that passes through the points (13, 1) and (6, 3). 0. Find the slope of the line Santiago Canon College

2 Diaz Math 080 Midterm Review: Modules A-F Page of 7 1. Write an equation for the graph, where depends on Rewrite in slope-intercept form, and then state the slope and -intercept. 8 6 = 9 3. Graph the line = 1 3. Find the equation of the line passing through the points ( 1, ) and (, ). Write our answer in the form = m+b. 5. Write an equation of a line parallel to = and passes through the point (, 3). 6. Write an equation of a line perpendicular to = 5 5 and passes through the point ( 10, 3). 7. Solve and graph the solution: 6 > + 10 or Be sure to write our answer in interval notation. 8. Solve and graph the solution: < 6 1 and Be sure to write our answer in interval notation. 9. Solve the inequalit: 17 1 > or Be sure to write our answer in interval notation. 30. Solve the inequalit: 9 5 < + 10 and + 9. Be sure to write our answer in interval notation. 31. Solve the inequalit: < 5. Be sure to write our answer in interval notation. 3. Solve the inequalit: > 38. Be sure to write our answer in interval notation. + = 33. Is (1, 1) a solution to the sstem? 5 = 11 5 = Is ( 3, 1) a solution to the sstem? 8 + = 0 5 = 35. Solve the sstem b graphing: 7 = = Solve the sstem b substitution: = = 37. Solve the sstem b elimination (addition): 1 1 = z = Solve the sstem. Give our answer as (,, z): 5 + z = z = Santiago Canon College

3 Diaz Math 080 Midterm Review: Modules A-F Page 3 of You need 330 ml of a 0% alcohol solution. On hand, ou have a 35% alcohol miture and a 90% alcohol miture. How much of each miture will ou need to obtain the desired solution? 0. A boat travels upstream for 10 miles in 18 hours and returns in 1 hours traveling downstream in a local stream of water. What is the rate of the boat in still water and the rate of the current? Round to two decimal places, if necessar. 1. Turke the Pigeon travels the same distance of 96 miles in 3 hours against the wind as it does traveling hours with the wind in local skies. What is the rate of Turke the Pigeon in still air and the rate of the wind?. If Ben has 3 times as man dimes as quarters and the have a combined value of 385 cents, how man of each coin does he have? 3. Kat invests a total of \$5,500 in two accounts paing % and 1% annual interest, respectivel. How much was invested in each account if, after one ear, the total interest was \$1,10.. Given the following functions, find each of the values (f + g)(3) and (f g)( 1): f() = 5 1 g() = 7 5. Given the following functions, find each (f + g)() and (f g)(): f() = g() = When P () = 7 3 1, evaluate P ( 5). What is the ordered pair? (i.e., what is the point on the graph?) Your answer should be of the form (, ). 7. Given the function below, evaluate f(): f() = Match each graph with the name of its function. Graphs of Functions A. B. C. D. E. F. G. H. I. Santiago Canon College

4 Diaz Math 080 Midterm Review: Modules A-F Page of 7 Names of the Functions (a) Reciprocal Function (b) Absolute Value Function (c) Cube Root Function (d) Cube Function (e) Constant Function (f) Identit Function (g) Square Root Function (h) Square Function (i) Linear Function 9. Use the graphs A. I. above to match each graph with the formula of the function. Formulas of Functions (a) f() = (b) f() = (c) f() = (d) f() = (e) f() = 1 (f) f() = 3 (g) f() = m + b (h) f() = 3 (i) f() = 50. Select all of the following graphs which represent as a function of. A. B. C. D. 51. What is the domain of the function: f() = What is the domain of the function: f() = A rocket is launched at t = 0 seconds. Its height, in meters above sea-level, as a function of time is given b h(t) =.9t + 11t What is the independent variable and its units? What is the dependent variable and its units? 5. The cost C(), where is the number of miles driven, of renting a car for a da is \$7 plus \$0.95 per mile. What is the slope of the linear function and its units? What is the -intercept and its units? What is the linear function, C()? 55. If f() is a linear function and given f(3) = 8 and f(11) =, determine the linear function. 56. Given the function below, evaluate f( 3): f() = Simpif: ( ) 58. Evaluate at = Perform the indicated operations: ( ) ( ) + ( ) 60. Multipl and simplif completel: 5 3( ) 61. Multipl and simplif completel: (3 5)(3 + 1) 6. Multipl: ( 3) ( + ) 63. Perform the following operation and simplif: (9 7) 6. Multipl and add like terms: (3z + 1)(3z 1) Santiago Canon College

5 Diaz Math 080 Midterm Review: Modules A-F Page 5 of Multipl and simplif: 3(3t + )(t ) 66. Simplif the epression completel: Find the quotient and remainder using long division for (( 6 ) ) Simplif: 69. Find 1 1 ( ) f () using long division for g 5 f() = g() = Let f() = + and g() = Find and simplif (f g)() 71. Factor Completel: Factor Completel: Factor Completel: Factor completel: r Factor completel: Factor completel: Factor completel: Solve for p: p = 1p 79. Solve for : + 5 = Solve for z when f(z) = 0, where f(z) = 0z 3z The length of a rectangle is 5 inches longer than it is wide. If the area is 66 square inches, what are the dimensions of the rectangle? 8. The product of two positive integer numbers is 1 and the sum of the same two numbers is 10. Find the numbers. 83. A rocket is launched at t = 0 seconds. Its height, in feet, above sea-level, as a function of time, t, is given b When does the rocket hit the ground after it is launched? h(t) = 16t + 8t + 8 Santiago Canon College

6 Diaz Math 080 Midterm Review: Modules A-F Page 6 of 7 Answers t z No solution; contradiction , , 7 1. The four consecutive even integers are 18, 0,, and. 13. The largest angle was (, ) ( ), [, ) 17. (, 1] 18. Each are traveling 1 mph and 0 mph = +. The slope is 3 and the -intercept is 3.. = 5. = 5 6. = (, 1] (3, ) 8. [ 3, ) 9. (, 1] (3, ) 30. [0, 3) ( 31. 9, 7 ) ( 3., 8 ) (, ) False 3. True 35. ( 3, 1) 36. (3, ) 37. No Solution; contradiction 38. ( 1,, 1) 39. You will need 300 ml and 30 ml of each solution. 0. The rate of the boat in still water is 8.33 mph and the rate of the current is 1.67 mph. 1. The rate of Turke the Pigeon in still air is 0 miles per hour and the rate of the wind is 8 miles per hour.. Ben has 7 quarters and 1 dimes. 3. Kat invested \$16,500 and \$9,000 in each account.., 0 5. (f + g)() = ; (f g)() = ; ( 5, 189) A i; B h; C d; D b; E a; F g; G f; H c; I e A g; B d; C f; D c; E e; F i; G a; H h; I b 50. A; C; D 51. 1, 5} 5. All Real Numbers 53. t is the independent variable and its units is seconds; h(t) is the dependent variable and its units is feet Santiago Canon College

7 Diaz Math 080 Midterm Review: Modules A-F Page 7 of 7 5. \$0.95; dollars per mile; \$7; dollars; C() = f() = z t t quotient: 3+1; remainder: or (5 + 8) 7. ( + 3) ( ) 73. ( 5) ( ) 7. (r + 11)(r 11) 75. ( + )( 1) 76. (3 )( 5) 77. (5 + 3)( ) 78. p = 1, 79. = 5, z = 3, inches and 11 inches 8. 7,3 83. after 7 seconds Santiago Canon College

### Diaz Math 080 Midterm Review: Modules A-F Page 1 of 7

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