Math 260
Ch1 practice test
1. Consider the following set of numbers. Classify each number as Natural, Whole, Integers, Rational, or
Irrational numbers.
{1.001, 0.333..., -π, -6, 9, 11/15, √15, 3.14, 15/3}
2. Find the indicated set if given the following. (Select all that apply.)
(a)
(b)
3. Evaluate each expression.
4. Express each repeating decimal as a fraction in lowest terms.
5. Evaluate each expression:
6. Evaluate each expression:
7. Simplify the expression. Assume the letters denote any real numbers:
8. Simplify the expression. Assume x denotes any real number:
9. Simplify the expression and eliminate any negative exponent(s). Assume that all letters denote positive
numbers.
10. Answer the following questions. (Consider that there are 365 days per year.)
If you have one hundred million (108) dollars in a suitcase, and you spend ten thousand (104) dollars each day,
how many years would it take you to use all the money? Give your answer rounded to the nearest
11. Factor the expression completely. Begin by factoring out the lowest power of each common factor.
x5/2 - 49x1/2
12. Factor the expression completely. Begin by factoring out the lowest power of each common factor.
13. Factor the expression completely.
14. Perform the multiplication or division and simplify:
15. Perform the multiplication or division and simplify:
16. Simplify the compound fractional expression.
17. Simplify the compound fractional expression.
18. Simplify the fractional expression. (Expressions like these arise in calculus.)
19. Solve the equation by completing the square.
20. Use the discriminant to determine the number of real solutions of the equation. Do not solve the equation.
x2 + m x - n = 0, n > 0
21. Find all real solutions of the equation. (If there are extra answer boxes, enter NONE in the last boxes.)
22. Find all real solutions of the equation. (If there are extra answer boxes, enter NONE in the last boxes.)
23. Find all real solutions of the equation. (If there are extra answer boxes, enter NONE in the last boxes.)
24. Find all real solutions of the equation. (If there are extra answer boxes, enter NONE in the last boxes.)
25. Find all real solutions of the equation. (If there are extra answer boxes, enter NONE in the last boxes.)
26. A woman earns 15% more than her husband. Together they make $82560 per year. What is the husband's
annual salary?
27. Helen earns $7.50 per hour at her job, but if she works more than 35 hours in a week she is paid 1.5 times
her regular salary for the overtime hours worked. One week her gross pay was $375.00. How many overtime
hours did she work that week?
28. A movie star, unwilling to give his age, posed the following riddle to a gossip columnist. "7 years ago, I was
14 times as old as my daughter. Now I am 7 times as old as she is." How old is the star?
29. A father is 4 times as old as his daughter. In 7 years, he will be three times as old as she is. How old is the
daughter now?
30. Mary has $6.00 in nickels, dimes, and quarters. If she has twice as many dimes as quarters and sixty-five
more nickels than dimes, how many coins of each type does she have?
31. A bottle contains 750 mL of fruit punch with a concentration of 50% pure fruit juice. Jill drinks 100 mL of
the punch and then refills the bottle with an equal amount of a cheaper brand of punch. If the concentration of
juice in the bottle is now reduced to 48%, what was the concentration in the punch that Jill added?
32. Stan and Hilda can mow the lawn in 60 min if they work together. If Hilda works twice as fast as Stan, how
long does it take Stan to mow the lawn alone?
33. A box with a square base and no top is to be made from a square piece of cardboard by cutting 4 inch
squares from each corner and folding up the sides, as shown in the figure. The box is to hold 324 in3. How big a
piece of cardboard is needed?
34. Solve the linear inequality. Express the solution using interval notation and graph the solution set.
35. Solve the nonlinear inequality. Express the solution using interval notation and graph the solution set.
36. Solve the nonlinear inequality. Express the solution using interval notation and graph the solution set.
37. Solve the nonlinear inequality. Express the solution using interval notation and graph the solution set.
38. Solve the nonlinear inequality. Express the solution using interval notation and graph the solution set.
39. Solve the absolute value inequality. Express the solution using interval notation and graph the solution set.
40. Solve the absolute value inequality. Express the solution using interval notation and graph the solution set.
41. Solve the inequality. Express the answer using interval notation. (Do not use mixed numbers in your
answers.)
42. Solve the inequality. Express the answer using interval notation. (Do not use mixed numbers in your
answers.)
43. A car rental company offers two plans for renting a car.
Plan A: $25 per day and 25¢ per mile
Plan B: $65 per day with free unlimited mileage
For what range of miles will plan B save you money? Give your answer as an interval (in miles). (Round the
answer to the nearest lower whole mile.)
44. A telephone company offers two long-distance plans. For how many minutes of long-distance calls would
plan B be financially advantageous?
Plan A: $25 per month and 5 per minute
Plan B: $4 per month and 15¢ per minute
45. Which of the points C(-6, -1) or D(3, 2) is closer to the point E(-2, 1)?
46. Test the equation for symmetry.
47. Test the equation for symmetry.
48. Test the equation for symmetry.
49. Find an equation of the circle that satisfies the given conditions. Give your answer using the form (x - h)2 +
(y - k)2 = r2.
Endpoints of a diameter are P(1, 1) and Q(7, 9)
50. Find the slope of the line through P and Q.
P(-1,-8), Q(9,0)
51. Find an equation of the line that satisfies the given conditions.
through (8, 6); parallel to the x-axis
52. Find an equation of the line that satisfies the given conditions.
through (8, 6); parallel to the y-axis
53. Find an equation of the line that satisfies the given conditions.
through (1,-2); parallel to the line x + 2y = 6
54. Find an equation of the line that satisfies the given conditions.
through (1/6, -2/5); perpendicular to the line 5x - 10y = 1
55. Find an equation of the line that satisfies the given conditions.
through (-8, -9); perpendicular to the line passing through (-5, 3) and (6, 1)
56. The manager of a furniture factory finds that it costs $2200 to manufacture 100 chairs in one day and $5000
to produce 300 chairs in one day.
Assuming that the relationship between cost C and the number of chairs produced x is linear, find an equation
that expresses this relationship.
57. If Ben invests $3000 at 4% interest per year, how much additional money must he invest at 5 1/2% annual
interest to ensure that the interest he receives each year is 4 1/2% of the total amount invested?
58. A movie star, unwilling to give his age, posed the following riddle to a gossip columnist. "3 years ago, I was
10 times as old as my daughter. Now I am 7 times as old as she is." How old is the star?
59. Mary has $6.00 in nickels, dimes, and quarters. If she has twice as many dimes as quarters and ninety-eight
more nickels than dimes, how many coins of each type does she have?
60. A bottle contains 450 mL of fruit punch with a concentration of 50% pure fruit juice. Jill drinks 100 mL of
the punch and then refills the bottle with an equal amount of a cheaper brand of punch. If the concentration of
juice in the bottle is now reduced to 48%, what was the concentration in the punch that Jill added?
61. Stan and Hilda can mow the lawn in 30 min if they work together. If Hilda works twice as fast as Stan, how
long does it take Stan to mow the lawn alone?