Download Q1 Review Precalculus

Precalculus
Quarter One Topic Review and Recommend Problems
Please note that the topics and problems below are intended to prepare you for the exam.
This review sheet is not intended to be all encompassing, i.e. the exam is limited only by
covered material and not by topics and problems outlined here.
Be able to:
 Use all of the mathematics that you’ve learned in previous courses and all of the
mathematics that we have learned up to this point in this course.
 Think.
 Graph relations when given ordered pair, tables, maps, or equations. (1.1)
 Explain the difference between a relation and a function graphically, verbally, and
numerically. (1.1)
 Evaluate a function for a given value. (1.1)
 State the domain of a function. (1.1)
 Perform operations with functions: (addition, subtraction, multiplication,
division, and composition). (1.2)
 Graph linear equations (1.3)
 Write linear equations using slope intercept, point slope, and standard forms.
(1.4)
 Write equations of a line parallel or perpendicular to a given line through a given
point. (1.5)
 Plot data on a coordinate plane, estimate a line of best fit, and give an equation for
that line. (1.6)
 Use a graphing calculator to find the equation of a best fit line and to estimate
data values that are not in the original data set. (1.6)
 Graph piecewise functions including absolute value and the greatest integer
function. (1.7)
 Graph linear inequalities. (1.8)
 Solve systems of equations in two variables by graphing, by elimination (linear
combination), and by substitution. (2.1)
 Explain the terms inconsistent, consistent, dependent, and independent
graphically and verbally. Also be able to identify systems that demonstrate these
terms. (2.1)
 Be able to solve a system of equations in three variables using algebraic methods.
(2.2)
 Represent and interpret data in matrix form. (2.3)
 Find values for which a matrix equation is true (2.3 example 2)
 Identify the dimensions of a matrix and explain what it means for a matrix to be
square(2.3)
 Add, Subtract, Multiply (both scalar and matrix) matrices. (2.3)
 Explain the criteria for matrix addition and multiplication. (2.3)
 Do absolutely nothing from 2.4
 Find the determinant of 2x2 and 3x3 matrices without the aid of a calculator.
(2.5)
 Explain why not all two by two matrices have inverses.
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Find the inverse of a 2x2 matrix if it exists (2.5)
Graph systems of linear inequalities. (2.6)
Use the boundary points of a graph of a linear inequality to determine the
maximum/minimum values of a function of x and y. (2.6 example 3).
 Explain the difference between point symmetry and line symmetry. (3.1)
 Determine if graphs are symmetric to the x-axis, y-axis, y=x, y=-x, and the origin.
 Explain the difference between even and odd functions.
 Graph the “parent” graphs described on p. 137 without the aid of a calculator.
 Interpret the algebraic equation of a function by how the it’s graph is related to
the parent graph: Reflections, translations, stretching, compressing. (p. 139-140)
 Graph nonlinear inequalities. (3.3)
 Represent inverse relations graphically, algebraically, and numerically (in table
form). (3.4)
 Show that two functions are inverses. (3.4 example 5)
 Identify and produce 3 types of discontinuities. (3.5)
 Describe the end behavior of a function (3.5)
 Describe the end behavior of a polynomial using only the value of the highest
exponent and the coefficient of the term with the highest exponent. (p. 163)
 Show that a function is continuous or discontinuous at a given x value by using
the continuity test on p. 160.
 Explain what a critical point is in terms of tangent lines. (3.6)
 Explain the difference between relative and absolute extrema. (3.6)
 Identify extrema of a given function. (3.6)
 Identify intervals on which a function is increasing and decreasing. (3.6)
 Explain what three things can happen at a critical point. (3.6)
 Determine vertical, horizontal, and slant asymptotes of rational functions. (3.7)
 Graph rational functions based on asymptotes. (3.7)
Recommended Problems
 Ch 1
o P. 57-60 #’s 1-10 all, 11-66 odd
 Ch 2
o P. 119-122 #’s 1-10 all, 11-27 odd, 34-38 all, 39-43 odd, 49, 50
 Ch 3
o P. 197-200 #’s 1-9 all, 11-55 odd.