This test gives examples of the types of questions asked
on the Diagnostic test
and Final Exam for MTH 004 (In termediate Algebra ). Click on the chapter
number to see the questions. To check your answers, click on
Back to Math Lab
Chapter 0
1. Given A={2,4,6,8} and B={1,3,5,9}, find
2. Perform the indicated operation: 0.83 - 0.31.
3. Perform the indicated operation: -(-8 + 9) - 17.
4. At the end of July my checking account had a balance of $143.87. During
August I wrote checks for rent of $325.00, for credit card payment of
$276.16, and for cash of $250.00. I made a deposit of $850.00. What is the
balance in my checking account at the end of August?
5. Perform the indicated ope rations using scientific notation and the laws of
exponents . Write the results in scientific notation.
(2.1 x 10-7)(3 x 108)
Chapter 1
1. Combine like terms: 5x + 6x + 7y - 2y.
2. Solve: -(8 + 7f+ 2) - 3f = -5f - (2f + 3).
3. Solve: -3x + 7 > 5x - 3 and write the solution in interval notation.
4. Jack scored 83%, 76%, 79%, and 88% on his first four exams. He needs an
average of at least 80% on his five exams to receive a grade of B. What is the
lowest score he can achieve on the next exam to receive a grade of B?
5. Solve: |3x - 5| = 12 - x
Chapter 2
1. Write the ordered pair solution to y = 3 - x2 + 2x for which x = -1.
2. What is the y-intercept of 
3.
Write, in standard form, the equation of the line containing the point
with a slope of 4.
4. What is the graph of a line with slope 1 and y-intercept 4?
5. The salmon population in Gold River is decreasing at the same rate as the
salmon population in the Columbia River. The equation, 350t + n = 17,000,
represents the number of salmon, n, in the Columbia River in the year, t. If the
count of salmon in the Gold River in year 15 is 66,750, what will be the count
of salmon in the Gold River in the thirtieth year of the study?
Chapter
3
1. Solve by graphing : 2x + 3y = 2 and x - 2y = -6.
2. Solve the system by substitution : 2x + 5y = -1 and x = 10y - 3.
3. Solve by linear combinations: 4x - y = -2 and 10x - 3y = -9.
4. Evaluate the determinant: 
5. Solve using Cramer' s Rule : x + 2y = 5 and 2x + 4y = 5.
Chapter
4
1. Perform the indicated multiplication: (5y + 3z)(5y - 3z).
2. Factor: 6x2 + 25x - 44.
3. Solve: 3x2 +11x - 4 = 0.
4. Factor: 4a2 - 25b2.
5. Factor: 10x2 + 52x + 10.
Chapter
5
1. Find the domain of the variable: 
2. 
3. Use synthetic division: (x3 + 8x2 + 15x - 4) ΒΈ (x + 4)
4. Reduce: 
5. Perform the indicated subtraction: 
Chapter 6
1. Write 
in equivalent exponential form.
2. Find the numerical value : 
.
3. Reduce the index of 
, if y represents only positive numbers .
4. Rationalize the denominator : 
.
5. Perform the indicated subtraction: (4 - 3i) - (16 + 2i)
Chapter 7
1. Solve 3x2 - 8x - 3 = 0 for x by completing the square.
2. Solve 12x2 - 5x - 3 = 0 for x using the quadratic formula .
3. Write a quadratic equation in standard form that has the roots
.
4. Solve the equation: 
.
5. Solve: 
.
Chapter 8
1. Write the equation in standard form of the circle with the center (5,5) and
radius r = 10.
2. Sketch the graph of 16y2 - 9x2 = 144.
3. Solve the system of equations: 2x2 - y2 = 23 and x2 - 2y2 = -2.
4. If x varies inversely as y, and if x = 7.5 when y = 2.4, find x when y = 4.
5. If f(x) = x2 - 2x and g(x) = x - 2, evaluate (f/g) (4).
Chapter 9
1. Find a table and graph for 
.
2. Find the exponential equation that is equivalent to the logarithmic equation
3. Solve 
for w.
4. Write 
as a combination of logarithms of single variables.
5. Solve the equation 
.
