Intermediate Algebra Test
1. Simplify
a.
b.
c.
d.
2. Perform the indicated operation:
a.
b.
c.
d.
3. Perform the indicated operation:
a.
b.
c.
d.
4. Factor
a.
b.
c.
d.
5. Factor
a.
b.
c.
d.
6.
a.
b.
c.
d.
7.
a.
b.
c.
d.
8. Simplify
a.
b.
c.
d.
9. Rationalize the denominator of
a.
b.
c.
d.
10. Solve the equation for x: 3(2-x) = 2x - 1
a.
b.
c.
d.
11. Solve the equation for x:
a. -12
b. 10
c. -10
d. 12
12. How long must a wire be to reach from the top of a 30-foot (ft) pole to a point on the
ground 20 ft from the base of the pole?
a. 36 ft
b. 24.5 ft
c. 38 ft
d. 35ft
13. Solve the equation for x:
a.
b.
c.
d.
-10
12
-12
10
14. Find the real solutions of the equation by factoring:
a. -3, 2
b. 3, -2
c. -3, -2
d. 3, 2
15. Find the real solutions of the equation by factoring:
a.
b.
c.
d.
16. Which of the following is equivalent to 2x + 7 > 3x - 2
a.
b.
c.
d.
x<9
x>9
x < -9
x > -9
17. Solve the equation for
:
a.
b.
c.
d.
18. The roots of
a.
b.
c.
d.
are:
19.Use the quadratic formula to solve:
a.
b.
c.
d. No real roots
20. Solve
a.
b.
c.
d.
21. Use the quadratic formula to solve:
a.
b.
c.
d.
22. Solve:
a. 2, 1
b. -2, -1
c. -2, 1
d. 2, -1
23. Solve
a.
b.
c.
d.
24.
2x + y = 7,
x – y = 2,
In the solution of the system of equations above, what is the value of x?
a. 3
b. 9
c. 5
d.
25. Solve the sytem: {2x + 3y = 1, - x + y = -3}
a. x = -2, y = -1
b. x = - 2, y = 1
c. x = 2, y = 1
d. x = 2, y = -1
26. The y-intercept for 5x + 4y = 12 is is:
a. 3
b. 4
c. 12
d. 7
27. How many feet does a wheel with a diameter of 16 inches travel after 4 revolutions?
a.
b.
c.
d.
201.06
16.76
50.27
4.19
28. In the figure shown, ABCD is a square, with each side of length 6 feet. The width of
the border (shaded portion) between the outer square EFGH and ABCD is 2 feet. Find the
area of the border.
a.
b.
c.
d.
36
12
64
24
29. The manager of store wants to market 100 pounds of a new blend of tea that will sell
for $4.50 per pound. The manager mixes Earl Grey tea, selling for $5 per pound, with
Orange Pekoe tea selling for $3 per pound to produce the 100 pounds. How many pounds
of the Earl Grey tea and the Orange Pekoe tea are required?
a. Earl Grey: 75 pounds; Orange Pekoe: 25 pounds
b. Earl Grey: 25 pounds; Orange Pekoe: 75 pounds
c. Earl Grey: 30 pounds; Orange Pekoe: 70 pounds
d. Earl Grey: 35 pounds; Orange Pekoe: 65 pounds
30. Trent can deliver his newpapers in 30 minutes. It takes Sue 20 minutes to do the
same route. How long would it take them to deliver the newspapers if they work
together?
a. 15 minutes
b. 10 minutes
c. 12 minutes
d. 8 minutes
31. Jose has test scores of 86, 80, 84 and 90. What score does Jose need on the next exam
in order to have an average score of 80?
a.
b.
c.
d.
80
75
70
60
32. A motorboat heads upstream on a river that has a current of 3 miles per hour. The
trip upstream takes 5 hours and the return trip takes 2.5 hours. Identify the correct
equation in order to determine the speed of the motorboat. (Assume that the motorboat
maintains a constant speed relative to the water.)
a. 2.5 (r - 3) = 5(r + 3)
b. 5(r – 3) = 2.5(r + 3)
c. 5(r + 3) = 2.5 (r – 3)
d. 5(r – 3) = 2.5 (r)
33. Find the dimensions of a rectangle whose perimeter is 26 meters and whose area is 40
square meters.
a. 5 meters by 8 meters
b. 4 meters by 10 meters
c. 3 meters by
meters
d. 2meters by 20 meters
34. Which of the following is a graph of a circle?
a.
b.
c.
d.
35. In which quadrant is the point (-3,4)?
a.
b.
c.
d.
I
II
III
IV
36. Find the distance between the points
a.
b.
c.
d.
and
37. A quick sketch of
is best illustrated by:
a.
b.
c.
d.
38. If
, determine
a.
b.
c.
d.
11
-11
-19
19
39. A quick sketch of
is best illustrated by:
a.
b.
c.
d.
40. A quick sketch of
a.
b.
c.
d.
is best illustrated by: