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Math 1080 Final Exam Review
1.7
Solve quadratic and rational inequalities.
# 41, 57 on page 80
2.1
Evaluate functions. Find difference quotient. Find domain of function.
# 17, 35 on pages 149 – 150
2.2
Graph piecewise defined functions. Use vertical line test. Recognize graphs of basic functions.
# 35, 51 on pages 160 – 161
2.3
From graph, identify domain and range, intervals where increasing/ decreasing, local maximum and minimum
values.
# 5, 31 on page 169
2.4
Find average rate of change.
# 9, 25 on pages 177 – 178
2.5
Graph function using transformations. Determine whether function is even or odd.
# 57, 79 on pages 188 – 189
2.6
Combine or find composition of functions. Determine domain of resulting function.
# 23, 37 on pages 196 – 197
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.
# 47, 63 on page 205
3.1
Graph quadratic function and find maximum or minimum value.
# 13, 63 on page230
3.2
Use zeros, their multiplicities, and end behavior of polynomial to graph the function.
# 9, 27 on pages 243 - 244
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.
# 17, 57 on pages 251 - 252
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.
# 9, 15 on page 260
3.5
Add, subtract, multiply and divide complex numbers.
# 37, 51 on pages 268 – 269
3.6
Find all complex zeros of a polynomial. Factor a polynomial completely. Find a polynomial with specified
complex zeros.
# 7, 39 on page 276
3.7
For a rational function, find horizontal, vertical, and slant asymptotes; determine intercepts; graph.
# 37, 49 on pages 289 – 290
4.1
Graph exponential functions. Solve applications such as compound interest.
# 19, 51 on pages 308 – 309
4.2
Graph natural exponential function. Solve applications such as continuously compounded interest.
# 9, 21 on page 313
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.
# 23, 47 on pages 322 – 323
4.4
Know laws of logarithms and use them to expand/combine logarithmic expressions. Know the change of base
formula.
# 49, 57 on pages 329 - 330
4.5
Solve exponential and logarithmic equations.
# 33, 49 on page 338
4.6
Solve applications of exponential growth and decay.
# 13, 23 on pages 351 – 352
5.1
Determine if a point is on the unit circle.
# 3, 17 on pages 375 – 376
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.
# 15, 65 on pages 384 - 385
5.3
Graph the sine and cosine functions, as well as transformations of these two functions.
# 13, 33 on page 396
5.4
Graph the tangent, cotangent, secant and cosecant functions.
# 3, 7 on page 405
5.5
Evaluate expressions containing inverse sine, cosine, and tangent.
# 5, 41 on pages 411 – 412
5.6
Find amplitude, period and frequency and graph functions modeling harmonic motion.
# 3, 15 on page 420
6.1
Convert between radians and degrees. Find coterminal angles. Find circular arc length, area of circular sector,
linear and angular speed.
# 55, 69 on pages 440 - 441
6.2
Use trigonometric ratios to solve a right triangle. Find all trigonometric ratios for a right triangle.
# 23, 51 on pages 448 - 450
6.3
Use reference angle to evaluate trigonometric function. Find trigonometric functions for a given angle. Find
area or a triangle.
# 27, 47 on pages 459 – 460
6.4
Know domains of inverse sine, cosine, and tangent. Evaluate inverse trigonometric functions. Use inverse
trigonometric functions to evaluate angles.
# 5, 15 on page 467
6.5
Use Law of Sines to solve ASA, SAA, and SSA.
# 29, 35 on page 474
6.6
Use Law of Cosines to solve SAS and SSS. Find area of a triangle using Heron’s Formula.
# 33, 39 on page 481
7.1
Know Cofunction Identities. Simplify trigonometric expressions. Prove trigonometric identities.
# 11, 37 on page 498
7.2
Use Addition and Subtraction Formulas for sine and cosine to simplify expressions, prove identities, and find
exact values of trigonometric expressions.
# 15, 33 on pages 505 – 506
7.3
Use Double-Angle and Half-Angle Formulas to simplify expressions, prove identities, and find exact values of
trigonometric expressions.
# 3, 31
7.4
Solve basic trigonometric equations, including equations of quadratic type.
# 17, 49 on page 523
7.5
Solve multiple angle equations (example 5, page 526) and equations that require the use of trigonometric
identities.
# 3, 19 on page 528
8.1
Plot points in polar form. Convert between rectangular and polar coordinates and equations.
# 23, 49 on page 546
8.2
Graph polar equations.
# 17, 25 on page 553
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.
# 55, 71 on page 563
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.
# 7, 13 on page 569
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.
# 51, 53 on page 588
9.2
Find the dot product. Find the angle between two vectors. Solve application problems involving vectors.
# 9, 47 on page 596
10.3 Convert between system of linear equations and augmented matrix. Use elementary row operations to solve a
linear system.
# 13, 19 on page 659
10.4 Perform addition, scalar multiplication and multiplication of matrices. Write a system of equations as a matrix
equation.
# 25, 35 on page 670
10.5
Find the inverse of a matrix. Use an inverse matrix to solve a linear system.
# 9, 25 on page 680
10.6
Find the determinant of a matrix. Use Cramer’s Rule to solve a linear system.
# 23, 33 on page 691
10.7
Decompose a rational expression into partial fractions.
# 15, 27 on page 698
11.1 Given an equation, graph a parabola. Given information about a parabola, find an equation. Solve an
application problem involving a parabola.
# 15, 53 on pages 730 - 731
11.2 Given an equation, graph an ellipse. Given information about an ellipse, find an equation. Solve an application
problem involving an ellipse.
# 11, 35 on page 739
11.3
Given an equation, graph a hyperbola. Given information about a hyperbola, find an equation.
# 15, 31 on page 748
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.
# 17, 65 on pages 792 – 793
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.
# 23, 65 on pages 798 – 799
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.
# 15, 53 on page 806