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Math 1080 Final Exam Objectives
1.7
Solve quadratic and rational inequalities.
2.1
Evaluate functions. Find difference quotient. Find domain of function.
2.2
Graph piecewise defined functions. Use vertical line test. Recognize graphs of basic functions.
2.3
From graph, identify domain and range, intervals where increasing/ decreasing, local maximum and
minimum values.
2.4
Find average rate of change.
2.5
Graph function using transformations. Determine whether function is even or odd.
2.6
Combine or find composition of functions. Determine domain of resulting function.
2.7
Determine whether function is one-to-one. Use horizontal line test. Find and graph inverse of function.
Find domain and range of function and its inverse.
3.1
Graph quadratic function and find maximum or minimum value.
3.2
Use zeros, their multiplicities, and end behavior of polynomial to graph the function.
3.3
Divide polynomials using long division and synthetic division. Use Remainder Theorem and Factor
Theorem to find remainders/zeros and to factor polynomials. Find polynomial with specified zeros.
3.4
Use Rational Zeros Theorem to find possible rational zeros of a polynomial. Use Descartes’ Rule of Signs
to determine number of positive and negative real zeros. Find rational and real zeros of a polynomial and
use these zeros to factor the polynomial.
3.5
Add, subtract, multiply and divide complex numbers.
3.6
Find all complex zeros of a polynomial. Factor a polynomial completely. Find a polynomial with specified
complex zeros.
3.7
For a rational function, find horizontal, vertical, and slant asymptotes; determine intercepts; graph.
4.1
Graph exponential functions. Solve applications such as compound interest.
4.2
Graph natural exponential function. Solve applications such as continuously compounded interest.
4.3
Switch between logarithmic form and exponential form. Evaluate logarithms. Graph logarithmic
functions. Use the common logarithm and the natural logarithm. Find the domain of a logarithmic
function.
4.4
Know laws of logarithms and use them to expand/combine logarithmic expressions. Know the change of
base formula.
4.5
Solve exponential and logarithmic equations.
4.6
Solve applications of exponential growth and decay.
Math 1080 Final Exam Objectives (continued)
5.1
Determine if a point is on the unit circle.
5.2
Know special values of the trigonometric functions (page 378) and signs of the trigonometric functions in
each of the four quadrants. Use these to evaluate trigonometric functions. Know the even-odd
properties of the trigonometric functions. Know the Reciprocal and Pythagorean Identities.
5.3
Graph the sine and cosine functions, as well as transformations of these two functions.
5.4
Graph the tangent, cotangent, secant and cosecant functions.
5.5
Evaluate expressions containing inverse sine, cosine, and tangent.
5.6
Find amplitude, period and frequency and graph functions modeling harmonic motion.
6.1
Convert between radians and degrees. Find coterminal angles. Find circular arc length, area of circular
sector, linear and angular speed.
6.2
Use trigonometric ratios to solve a right triangle. Find all trigonometric ratios for a right triangle.
6.3
Use reference angle to evaluate trigonometric function. Find trigonometric functions for a given angle.
Find area or a triangle.
6.4
Know domains of inverse sine, cosine, and tangent. Evaluate inverse trigonometric functions. Use inverse
trigonometric functions to evaluate angles.
6.5
Use Law of Sines to solve ASA, SAA, and SSA.
6.6
Use Law of Cosines to solve SAS and SSS. Find area of a triangle using Heron’s Formula.
7.1
Know Cofunction Identities. Simplify trigonometric expressions. Prove trigonometric identities.
7.2
Use Addition and Subtraction Formulas for sine and cosine to simplify expressions, prove identities, and
find exact values of trigonometric expressions.
7.3
Use Double-Angle and Half-Angle Formulas to simplify expressions, prove identities, and find exact values
of trigonometric expressions.
7.4
Solve basic trigonometric equations, including equations of quadratic type.
7.5
Solve multiple angle equations (example 5, page 526) and equations that require the use of trigonometric
identities.
8.1
Plot points in polar form. Convert between rectangular and polar coordinates and equations.
8.2
Graph polar equations.
8.3
Graph complex numbers. Find the modulus of a complex number. Convert between standard form, a+bi,
and polar (trigonometric) form for complex numbers. Multiply and divide complex numbers. Use
DeMoivre’s Theorem to find powers of complex numbers. Find nth roots of complex numbers.
Math 1080 Final Exam Objectives (continued)
8.4
Complete a t-x-y table and graph a curve defined parametrically. Eliminate the parameter in a pair of
parametric equations. Find a pair of parametric equations for a line segment given the endpoints, or a
portion of a circle centered at the origin given the radius.
9.1
Find scalar multiple, sum, and difference of vectors algebraically and geometrically. Find horizontal and
vertical components of a vector. Find magnitude and direction of a vector.
9.2
Find the dot product. Find the angle between two vectors. Solve application problems involving vectors.
10.3
Convert between system of linear equations and augmented matrix. Use elementary row operations to
solve a linear system.
10.4
Perform addition, scalar multiplication and multiplication of matrices. Write a system of equations as a
matrix equation.
10.5
Find the inverse of a matrix. Use an inverse matrix to solve a linear system.
10.6
Find the determinant of a matrix. Use Cramer’s Rule to solve a linear system.
10.7
Decompose a rational expression into partial fractions.
10.8
Solve a system of nonlinear equations using substitution or elimination.
11.1
Given an equation, graph a parabola. Given information about a parabola, find an equation. Solve an
application problem involving a parabola.
11.2
Given an equation, graph an ellipse. Given information about an ellipse, find an equation. Solve an
application problem involving an ellipse.
11.3
Given an equation, graph a hyperbola. Given information about a hyperbola, find an equation.
12.1
Find the terms of a sequence, including a recursively defined sequence. Find the partial sums of a
sequence. Find the sum of a sequence defined using sigma notation. Write a sum using sigma notation.
12.2
Find the terms and common difference of an arithmetic sequence. Determine whether a sequence is
arithmetic. Find the partial sums of an arithmetic sequence. Find the sum of an arithmetic sequence.
Solve an application problem involving an arithmetic sequence.
12.3
Find the terms and common ratio of a geometric sequence. Determine whether a sequence is geometric.
Find the partial sums of a geometric sequence. Determine whether an infinite geometric series is
convergent or divergent. For a convergent geometric series, find the sum.