MATH 1314
FINAL EXAM PREPARATION GUIDE
FALL 2008
Your final exam in MATH 1314 this semester will consist of two parts. The first will be a 40 question, multiple-choice test. Students from all sections of MATH 1314 will take similar versions of the same test. The second part of your exam will consist of several questions written by your instructor. That portion of the exam will allow you to show written work.
Part 1.
The 36 questions will be based on the 36 Student Learning Outcomes (needs link to them here.) you received at the beginning of the semester. You should review your class notes and textbook to make sure that you are familiar with those outcomes and can solve problems related to them.
When you go to your exam, be sure to take a (graphing) calculator and pencils. A formula sheet and scantron will be provided to you. You should not take any notes for use in this exam, nor should you have any cell phones or other electronic devices besides a stand-alone calculator.
The information below is NOT a complete review of the 36 objectives for MATH 1314. Your instructor will provide general review materials from your textbook, MyMathLab or other sources. You should know that any preparation you do that increases your understanding of or performance on the objectives will increase your readiness for ANY test on those objectives.
Below are a couple of sample questions to demonstrate the format of Part 1 of your final exam. The exam has been written to discourage guessing. In most cases, the best method for marking the best answer is to work the problem as you have learned in class and then follow any additional instructions.
Each Sample Question (SQ) is connected to a Student Learning Outcome (SLO).
SLO #1. Solve linear equations in one variable.
SQ: Solve the equation 4(x-4) + 3x = 2x – 6. Find the value of the expression 3x + 1.
A)1
B)3
C)5
D)7
E)None of these.
Solution. Note that first instruction follows directly the SLO. Your solution of that equation probably looks somewhat like the following
4(x-4) + 3x = 2x – 6Given
4x – 16 + 3x = 2x – 6Distributive Law
7x – 16 = 2x – 6Combine like terms
7x – 2x – 16 + 16 = 2x - 2x – 6 + 16Subtract 2x and add 16 to both sides of the equation
5x = 10Combine like terms
x = 2Divide both sides of the equation by 5
Now follow the additional instructions. The value of the expression 3x + 1 if x = 2 is 3(2)+1 = 7. So the best choice in this case is (D).
For the same SLO, there could be an alternate version of the same question:
SQ: Solve the equation 4(x-4) + 3x = 2x – 6. In which interval does the solution lie?
A)[-2, 0)
B)[0, 2)
C)[2, 4)
D)[4, 6)
E)None of these.
Solution. Solving the original equation as above, we know that x = 2. This value of x lies in the interval [2,4). So the best answer is C).
SLO #32: Solve logarithmic equations
SQ: Solve 4 ln(x-5) = 2 for x. If x is in the form ea + b, what is the value of a?
A)2
B)5
C)-5
D)4
E)None of these.
Solution. Your solution following the original directions probably looks something like the following:
4 ln(x – 5) = 2Given
ln(x – 5) = 2/4 = 1/2Divide both sides by 4.
x – 5 = e1/2Change to exponential form
x = e1/2+ 5Add 5 to both sides.
Now respond to the second directions. In the form x = ea + b, a = 1/2 and b = 5. The correct answer is none of A through D. The best answer in this case is E.
SLO #24 Graphs quadratic functions and find vertex
(min/max), axis of symmetry, domain and range. [3.1]
SQ: A quadratic function with domain all real numbers
has graph as on the right. What is the most extreme
value of the function?
A)1
B)2
C)-3
D)-14
E)None of these.
Solution: The graph of a quadratic function with domain all real numbers is a parabola. The most extreme value is the y-coordinate of the vertex. In this case, the vertex appears to be (1,2). The extreme value, a maximum in this case is y = 2. The best answer choice is (B).
SLO #17.Determine values for which a function is increasing, decreasing and/or constant. [2.3]
SQ: The graph of a function is as pictured above. Over what interval is the function increasing?
A)[-14, -2]
B)[-3, 1]
C)[-2, 2]
D)[1,3]
E)None of these.
Solution: From the left hand end of the domain (x = -3) the graph appears to increase, reach a maximum at x = 1 and then decrease. The interval over which the function is increasing ends at 1. The interval over which the function is increasing is [-3, 1]. The best answer choice is (B).
Part 2.
You will get further instruction about the second portion of your exam from your instructor. In short, it will not be multiple choice. You will need to write out your work and explain your work for full credit.