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Practice Problems -- Exam I
Do all work on your own paper. Show your steps.
1.Write the set described by listing its elements: {x x is an even integer greater than 8}.
2. Write the set listed using set builder notation: {. . ., -2, -1, 0, 1, 2, 3}.
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3. Simplify each expression: a. –9(2) –(-3)(-2)
2
b.
10 " 24 + ("6)
16 # ("5)
4. Simplify each expression: a. "3(2x "1) + 5(x + 3) " 2x
b. 2 + 3(3a " 5) " 7(4a + 6)
5. Solve the equation:
3 ! 2(x ! 4) = 5 ! x
!
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! solution, no solution or an infinite
6. Find the solution set. State whether there is a unique
number of solutions.
5x + 5 = 3(x – 3) + 2x
7. Solve for x: 2(x – 6) = 5 – {2x – [4(x – 3) – 5]}
8. Solve for x:
3x ! 5
2x
+2=
4
3
9. Solve for m: y = mx + b
10. Solve for y: 2x – 3y = 5
11. Solve for a: S =
3a + b
2
12. Evaluate the formula for D, with the given values:
D = b 2 ! 4ac when a = 2, b = –3, c = – 5
13. A real estate agent earned $6300 commission on a property sale of $210,000. What is
her rate of commission?
14. A print shop charges $60 for the first 100 booklets printed plus $0.20 for each additional
booklet. If Wyonia Jackson paid $84, how many booklets did she have printed?
15. Seaside Village hired 27 lifeguards for the summer season. The number of men was
5 less than 3 times the number of women. How many men did they employ?
16. The perimeter of a triangle is 45 cm. The second side is 3 centimeters longer than the
first side. The third side is 3 centimeters shorter than triple the length of the first side.
Find the length of each side.
17. How many liters of 30% alcohol solution and 80% alcohol solution must be mixed to
obtain 100 L of 50% alcohol solution?
18. Sam Wood invested some money at 4.5% simple interest and 1000 more than four times
that amount at 6%. His total annual income for one year from the two investments was
$801. How much did he invest at each rate?
19. Two cars leave Flint at the same time, traveling in opposite directions. The car that is
traveling north is moving 9 miles per hour faster than the car traveling south. If the
two cars are 405 miles apart after 3 hours, find the speed of each car.
20. A truck leaves Portland traveling at 40 mph. Two hours later a car leaves from the same
spot, traveling 65 mph along the same route as the truck.
a. How long will it take for the car to overtake the truck?
b. How many miles had the vehicles traveled when the car caught up with the truck?
21. The sum of the least and greatest of three consecutive integers is 32 more than the middle
integer. What are the integers?
22. Solve the inequality and graph your answer on a number line.
5x ! 1 " 3(x ! 2)
23. Solve the inequality and express your answer in interval notation.
!10 < ! 2x + 6 " 4
24. Solve and graph your answer on a number line.
x < 3 and x > ! 4
25. Solve x + 1 > 2 and 2x < 6 . Express answer in interval notation.
26. Solve 2x + 4 > 8 or "3x > 9 and graph your answer on a number line.
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27. A parking garage charges $1.25 for the first hour and $0.75 for each additional hour or
part thereof. What is the maximum length of time you can park in the garage if you wish to
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pay no more than $3.75? Set up an inequality to work this problem.
28. Graph the inequality on the number line:
x "5
29. Solve the inequality for x, leaving your answer as an inequality:
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30. Find the solution set to each of the following:
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x < 4
a. 3x " 5 = 7
b. 3x " 2 > 7
c. 5 " 2x # 9
31. Find the slope of the line shown in the graph.
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32.
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a. Find the slope of the line passing through the points (4, –1) and (–2, –5).
b. What is the slope of the line y = 12 ?
c. What is the slope of the line x = –1?
d. If the slope of the line through the points (6, 1) and (4, y) is 3, find the value of y.
33. If one point on a graph is (–6, 6) and the slope of the line is – 32 , find the y-intercept of the graph.
34. Draw a graph of the line y = – 23 x + 4
35. What is the slope of a line perpendicular to the line y – 3 = 0?
36. Find the equation of a line perpendicular to the line y = –3x + 2, passing through the
point (6, 3).
37. Determine whether the following pairs of lines are parallel, perpendicular, or neither.
a.
6x + 2y = 8
4x – 9 = –y
b.
x + 3y = 9
y = 3x + 6
c.
y = – 23 x + 5
2x + 3y = 8
38. Find the equation of the line through (3, -2) and (-1, 6). Express your answer in both
standard form and slop-intercept form.
39. Put in standard form: y =
1
x " 4.
3
40. Graph by first finding the x- and y- intercepts. 5x " 2y = "10
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41. Graph the equation
x = –5
a. What is the domain?
b. What is the range?
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For problems 42 – 45, use coordinate axes (x- and y-axes) to graph.
42. Graph y > 2x – 1.
43. Graph 3x + 2y ≥ 12.
44. Graph x < –3.
45. Graph y ≤ 12 x.
46. Does this set represent a function? Why or why not? State the domain and range.
{(9, –8), (–8, 9), (8, 1)}
47. Does this set represent a function? Why or why not? State the domain and range.
2
1
–1
1
48. Write the set of ordered pairs represented by the given diagram. Determine whether this
relation is also a function. Tell why or why not. Also give the domain and the range.
1
a
2
3
b
49. Determine whether the following graph represents a function. Explain why.
Domain:
Range:
50. Determine whether the following graph represents a function. Explain why
Domain:
•
Range:
2
51. h(x) = –x + 3x + 10.
Find h(–4).
52. The number of accidents, N, in one month involving drivers x years of age can be
2
approximated by the function N(x) = 2x – 150x + 4000. Find the approximate number
of accidents in one month that involved 19-year-olds.
53. A salesperson receives a weekly salary of $300 plus an 8% commission based on total
weekly sales. The salesperson’s total weekly earnings, P, can be calculated using the
formula P(s) = 0.08s + 300, where s represents the total weekly sales.
a. Find the salesperson’s weekly earnings when the total weekly sales are $3152.
b. What were the weekly sales if the total weekly earnings were $450?
54. Rachel Greene plans to decorate dolls to sell at a craft fair. She spent $49.50 on
materials for decorations, and the dolls cost $6.50 each.
a. Write a function expressing the cost, C(x), of the project in terms of the number of
dolls decorated, x.
b. Determine the cost of decorating 50 dolls.
c. How many dolls can be decorated with a budget of $439.50?