December 2011 Exam Review
PreCalculus
Chapter One
Arithmetic Sequences
 Know the formula for finding any term of an arithmetic sequence
 Know the formula for finding the sum of an arithmetic series.
 Write an arithmetic series given the rule for the sequence.
 Give the nth term of an arithmetic sequence, using the formula.
 Give the first five or six terms of an arithmetic sequence given the first term and
common difference.
 Given any term of an arithmetic sequence and the common difference, be able to
calculate the first term of the sequence.
 Given any two terms of an arithmetic sequence, find the common difference and the
first term.
 Rewrite an arithmetic series with summation notation.
 Use summation notation to evaluate an arithmetic series.
 Write the explicit form of an arithmetic sequence. an = a1 + (n - 1)*d
Geometric Sequences
 Know the formula for finding any term of a geometric sequence.
 Know the formula for finding the sum of a finite geometric series.
 Know the formula for finding the sum of an infinite geometric series.
 Give the nth term of a geometric sequence, using the formula.
 Give the first five or six terms of a geometric sequence given the first term and the
common ratio.
 Given any term of a geometric sequence and the common ratio, be able to calculate
the first term of the sequence.
 Given any two terms of a geometric sequence, find the common ratio and the first
term.
 Rewrite a geometric series (finite or infinite) with summation notation.
 Use summation notation to evaluate a geometric series (finite or infinite).
 Determine if the infinite geometric converges or diverges.
 Write the explicit form of a geometric sequence an = a1*rn-1
Least-Squares Regression Line
 Given data for x and y, find the regression line using a graphing calculator.
 Using the linear regression model, predict values for x or y.
Chapter Two
Polynomials
 Given a polynomial determine the degree, the leading coefficient, possible number of
zeros, possible number of turning points (extrema), and end behavior without a
calculator.
 Using a calculator, determine the x-intercepts (zeros), y-intercepts, maximum or
minimum (extrema), and end behavior of a polynomial.
 Factor polynomials to determine the zeros the function.
 Using the Rational Root Theorem, determine the possible rational roots.
 Using the Factor Theorem or synthetic division, find the real zeros.
 Using the Descartes’ Rule of Signs, determine the number of positive and negative roots.
 Given the degree and zeros (real and complex), write a polynomial of lowest degree
with real coefficients.
 Rewrite a polynomial function as the product of complex factors and find the zeros.
Rational Functions
 Determine horizontal, vertical, and slant asymptotes, if any, of a rational function.
 Give the domain and range of a polynomial function.
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Identify the parent functions of y = x, y = x2, y = x3, y = 𝑥, y = ІxІ, and y = √𝑥.
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Determine how the graph of a function changes when a constant is added (or
subtracted) to x or added (or subtracted) to y.
Determine how the graph of a function changes when a constant is multiplied by x or y.
Determine whether undefined values for the rational function are vertical asymptotes
or holes on the graph.
Create a rational function from its asymptotes.
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Exponential Functions
 Write an exponential function for growth or decay problems.
 Determine the balance of an account with compound interest.