Calculus A – Practice Problems for Exam I
The upcoming exam on Friday, September 19 will cover the
material in appendices A and B. Some of the problems will, however, cover some
extra pre-calculus material ( mainly algebra ).
The following problems do not represent all of the
possible types of problems that could appear on the exam. Problems chosen for
the exam will be similar to homework problems, previous quizzes , examples done
in class, and the basic problems from the workshops. You would be best prepared
by studying your class notes, previous quizzes, this practice exam, and all
homework problems. Also note that the number of problems presented in this
practice exam may not represent the actual length of the exam you see on the
exam day. It is likely that the exam will be shorter than the practice exam
here, but you should be prepared for a lengthy exam anyway.
IMPORTANT! First try these problems as if it were the real
exam ; work by yourself without the text or your
notes. This is supposed to be a gauge on what you need to work on to prepare for
the exam. Answering these problems as you might handle homework problems won’t
necessarily give you much of a clue on what you need to work on.
Instructions: Provide all steps necessary to solve the
problem. Unless otherwise stated, your answer should be exact and reasonably
simplified. Additionally, clearly indicate the value or expression that is your
final answer! Calculators are not allowed.
1. Simplify the following expressions by writing each as a
single fraction in lowest terms (for (a) and (b)) or without absolute value
signs (for (c)).
2. Simplify and evaluate each number by eliminating
radicals and/or exponents.
3. Simplify each expression and eliminate all negative
exponents
4. Expand and simplify .
5. Factor the expression completely.
6. Simplify the expression as much as possible. (Your
answer must be written as a SINGLE fraction . It cannot be written as fractions
within fractions or as two fractions added or subtracted together.)
7. Solve each equation .
8. Solve each inequality and graph each solution on the
real line.
9. Find the equation ( in slope -intercept form) of the line
that has the following properties.
(a) Passes through (10,-4) and (-3,7).
(b) Passes through (8,7) and is parallel to the line 5x + 4y = 3.
(c) Passes through (9,5) and is perpendicular to the line 4x – 3y = 2.
Calculus A – Answers to Practice Problems for Exam I
5. Factor the expression completely.
7.
(a) x = −2,0,4
(b) no solutions (note that x = 1 cannot be substituted into the original
equation)
(c) x = −1
(d) x = 3 (note that x = 0 cannot be substituted into the original equation
8.
