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Basic Skills Exam Schedule

Sample Exams: Sample Exam 1 , Sample Exam 2, Sample Exam 3, Sample Exam 4 , Sample Exam 5, Sample Exam 6

The Math 111 basic skills exam consists of basic computational problems involving derivatives, antiderivatives, and limits. The problems will not be difficult, but you must get at least 90 out of 100 points to do well. Calculators and computers are not allowed.

Mastering this material is a bit like learning your addition and multiplication tables when you were in grade school. The problems are not all that important by themselves, but they represent basic skills needed by anyone who is studying or using calculus.

The types of problems covered on the Math 111 basic skills exam are listed below. The problems will not necessarily appear in the order given here. Page numbers refer to OZ.

• State the definition of the derivative at a point x = a. See page 85.
• Use the definition of the derivative to differentiate a given function. This is illustrated in examples on pages 84, 85, 91-93, and in #29, 31 on page 88. For additional problems, see page 89 (#41-44), 100 (#68-71).
• Two limit problems, one of which is a limit at infinity. The limits may or may not exist. If a limit is infinite, you should be able to say whether it is positive or negative. See page 221, example 2 for a similar problem, page 231 (#9-16) as well as these additional problems. You may not use l'Hopital's Rule.
• Find an equation for the line tangent to the graph of a function at a given x-value. Similar problems: page 87 (# 6), page 99 (# 37-43, 49), page 138 (# 31, 32) and these additional problems.
• Compute the derivatives of three functions using the power, product, quotient and chain rules. These may contain exponential, logarithmic, trigonometric, and arctangent functions. For derivative problems using the power rule, see page 99 (#15-36, 45-48). For derivative problems using the product and quotient rules, see page 166 (#9-36). For problems using the chain rule, see page 175 (#1-20). For exponential and logarithm functions, see page 138 (#15-26). For trigonometric functions, see page 147 (#17-28), and for for arctangent, see page 191 (#13,14,18,19,23,24). Have memorized derivatives of the six trigonometric functions and arctangent. For additional problems, see page 195 (#1-61).
• There will be one problem calling for implicit differentiation. The problem will potentially use any of the derivative rules listed above. See page 181 (#4a, 5a, 6c, 7c, 9, 15b, 16b, 17b, 18b).
• Compute the antiderivatives of two functions using the antiderivative rules we have learned in class. Again, these include rules about trigonometric functions, exponents and logarithms and you should be able to combine rules you know. For power functions see Example 4 on page 116; for exponential and logarithm problems, see page 139 (27-30); for trigonometric functions, see page 147 (7-9, 29-34); and for arctangent, see page 196 (66-71). See also page 151 (27-29) Memorize all derivative formulas both ways, for derivatives and antiderivatives.