Be sure to read the Basic Skills Exam Policy

Basic Skills Exam Schedule

Sample Exams: Sample Exam 1, Sample Exam 2, Sample Exam 3, Sample Exam 4

The Math 112 basic skills exam consists of nine problems. They are all worth 10 points except for Problem 9 on testing series for convergence, which has 4 parts and is worth 20 points. You must get at least 90 points to do well. To get full credit, you must show your work, except for Problem 9, which is multiple choice. Computers and calculators will not be used on the basic skills exam.

The problems are of the following types (the integrals may be in any order):

• Simple substitution or "u-substitution", in which you need to decide on the appropriate "u". Section 5.4, problems 23-74 except as noted in the next item.
• More complicated integrals involving either a change of variable (in which the formula relating the variables is given) or a trigonometric identity (which will be given except when sin²u + cos²u = 1 or tan²u + 1 = sec²u will work). Section 5.4, problems 8, 10, 28, 31, 36, 50, 65, 66, 76, 77, and section 8.3, problems 11-16, 19, 21, 27, 29-32, 40, 41, 43-45. See below for the formulas that would be given for these particular problems.
• Integration by parts. Section 8.1, 15-20, 37-54
• Improper integral. Be able to recognize when an integral is improper, and evaluate it by writing it as a limit before finding an antiderivative. Section 10.1, problems 1-4, 7-18, 33-48
• Partial fractions problems will not be on the basic skills exam. For other integration problems for practice, try problems from Section 5.5 (without tables of course!) and Section 8.4.
• Two limits, for which L’Hopital’s rule might or might not be appropriate. Know both how to use L’Hopital’s rule, and when to use it. Indeterminate forms will only be of the form 0/0 or infinity/infinity. Other forms (such as 0 × infinity or 0⁰) may appear on other exams, but not on the basic skills exam. When the limit is undefined, the answer should be given as infinity or -infinity if appropriate. Section 4.2, 25-30, 57-67, 69-72, Section 11.1, 11, 12, 14
• Recognize a numerical series (geometric or a special case of e^x, sin x and cos x) and find its sum or show it diverges. When the series diverges, its should be given as infinity or -infinity if appropriate. Section 11.2, 11-18, some of 48-52.
• Find the interval of convergence of a power series except for the endpoints. Section 11.5, 3-10 and review problems, page 603, 37-48.
• Recognize the power series for 1/(1 - x), e^x, sin x and cos x, and use these series to generate series for other functions via substitution, multiplication by monomials, differentiation, and integration. Express the series in summation notation or give the first four non-zero terms. Section 11.6, 5-11, 17-22, 29-34. (These ask for more than just finding the power series, but finding the series is the only thing that will be on the basic skills exam.)
• Intuitively determine whether a series of numbers converges absolutely, converges conditionally, or diverges. You do not need to justify your answers (you will be expected to do this on other exams, however). Section 11.3, 9-12, 17-24, 31-36, 45-52, Section 11.4, 9-12, 19-26.

On the sample exams (1, 2, 3), the problems appear in the order above.

Problems with substitution or trig identity hints: