Intermediate
Algebra
Review
Problems for the final
1. Find the x and y intercepts of
a. 
b. 
2. Complete the given ordered pairs so that each ordered pair satisfies the given equation.
(-1,_____) (
,4), 
3. Graph 
in a rectangular
coordinate system.
4. Determine the slope of each line and
write the equation of each line in the form of 
.
a. (-2, 2) (3, -3)
b. (4, 3) (2, 0)
c. x = -3
d. y = 2
5. Given (-3, -1), (4, 3):
a. Find the slope
b. Find
the equation of the line and write the equation of each line in the form of 
.
c. Find the y-intercept
6. Given (3, 7), (-11, 7)
a. Find the slope
b. Find
the equation of the line and write the equation of each line in the form of 
.
c. Find the y-intercept
7. Find k so
that the line through (2,k) and (-3, -5) has slope 
.
8. Find the equation of the line passing through (-3, -1) and has slope 6.
9. Find the equation of the line passing through (-1, -2) is
a. perpendicular to the line 
b. parallel to the line 
10. Write the equation 
in standard form
using only integers and a positive coefficient for x.
11. Determine whether each pair of lines is parallel, perpendicular or neither.
a. 
b. 
12. Graph each inequality in a rectangular coordinate system.
a. 
b. 
13. Identify the graph of 
. .
a. b.
c. d.
14. Which of the following relations are functions?
a. 
15. Determine whether each equation specifies y as a function of x.
a. 
b. 
c. 
16. Determine the Domain of:
a. 
b. 
c. 
d. 
e. 
17. Given 
, 
and 
, find the following:
a. 
b. 
c. 
d. 
e. 
f. 
g. 
h. 
i. 
j. 
18. Solve by substitution or elimination method and determine whether the equations are dependent, or inconsistent.
a. 
b. 
c. 
d. 
19. Solve
20. Jim can drive 600 miles in the same time as it takes Chris to drive 500 miles. If Jim drives 10mph faster than Chris, then how fast does Jim drive?
21. A boater drove a motorboat upstream a distance of 46 miles and then immediately drove back to the starting point. The total line of the trip was 3.5 hours. If the rate of the current was 4mph, how fast would the boat have traveled in still water?
22. A picture is 4 inches taller than it is wide and is an area of 192 square inches. What are the dimensions of the picture?
23. The product of two consecutive integers is 80 more than 15 times the larger integer.
24. The base of a triangle is four times its height. The area of the triangle is 98 square centimeters. Find the dimensions of the triangle.
25. A nurse has a 20% alcohol solution and a 45% alcohol solution. How many liters of each should be used to make 5 liters of a 30% alcohol solution!
26. A caterer made 30 pounds of a party mix to sell for $4.05 a pound. Peanuts selling for $2.95 a pound, cashews selling for $6.25 a pound, and coated chocolates selling for $3.50 a pound were all used in the party mix. If two more pounds of peanuts than cashews were used, how many pounds of each item were in the party mix?
27. You invested $12,000 at 10.5% and 13% simple interest. During 1 year, the two accounts earned $1447.50. How much did you invest in each account?
28. Determine the number of gallons of a 20% alcohol solution and the number of gallons of 60% alcohol solution that are required to make 100 gallons of a 40% alcohol solution.
Find the solution set.
29. Graph each inequality in a rectangular coordinate system
a. b.
c. 
and 
30. Simplify
a. 
b. 
c. 
d. 
e. 
f. 
g. 
h. 
i. 
j. 
k. 
l. 
m. 
n. 
31. Simplify.
a. 
b 
c. 
d. 
e. 
f. 
g. 
h. 
i. 
j. 
k. 
l. 
32. Perform the indicated operation. Give exact answers.
a. 
b. 
c. 
d. 
m. 
e. 
n. 
f. 
o. 
g. 
p. 
h. 
q. 
i. 
r. 
j. 
s. 
k. 
t. 
l. 
u. 
33. Solve the equation and check the solution.
a. 
b. 
c. 
d. 
34. Perform the indicated operation. Give exact
answers and write solution in the form of 
.
a. 
b. 
c. 
d. 
e. 
35. Solve by square root method:
a. 
b. 
c. 
36. Solve the quadratic equation by completing the square.
a. 
b. 
c. 
37. Write the equations in quadratic standard form and solve.
a. 
b. 
38. Solve each equation using the Quadratic formula.
a. 
b. 
39. Use the discriminant to determine the number of real solutions to each Quadratic
equation.
a. 
b. 
c.
40.
Show that the given number is a solution to the given
equation: 
41. Solve for y in terms of x.
42. Solve:
a. 
b. 
c. 
43. Given:
.
a. Determine whether the parabola opens upward or downward. Give your reason.
b. Find the axis of symmetry.
c. Find the vertex as an ordered pair.
d. Find the x and y intercepts as ordered pairs.
e. Find the domain and the range.
f. Sketch the graph.
44 Given:
.
a. Determine whether the parabola opens upward or downward. Give your reason.
b. Find the axis of symmetry.
c. Find the vertex as an ordered pair.
d. Find the x and y intercepts as ordered pairs.
e. Find the domain and the range.
f. Sketch the graph.
45. Solve and graph each solution on a real number line.
a. 
b. 
c. 
d. 
e. 
46. Solve graphically. Find the coordinates of all corner points in the solution set.
a.