College Algebra/Trigonometry
(Functions and Trigonometry)
Essential Curriculum
Quarter 1
UNIT 1: Equations and Modeling
Goal. The students will demonstrate the ability to solve various types of equations that have both real and
imaginary roots.
Objectives – The student will be able to:
a1. Sketch graphs of equations (1:1 – The Graph of an Equation pp78 – 79. Problems pp. 85: 1 –
8.)
a2. Find x- and y- intercepts of graphs. (1:1 – Intercepts of Graphs p 80. Problems pp. 86: 25 –
52.)
b1. Solve linear equations in one variable. (1:2 – Equations and Solutions of Equations pp 88 - 90.
Problems on pp. 94:1 – 20, 27 – 36.)
c1. Solve equations involving fractional expressions. (1:2 – Equations Involving Fractional
Expressions p. 91 – 93. Problems p. 95: 55 – 70.)
d1. Solve quadratic equations by factoring. (1:4 – Factoring Quadratic Equations pp. 110 – 111.
Problems pp. 119: 7 – 34.)
d2. Solve quadratic equations by quadratic formula. (1:4 – Factoring Quadratic Equations pp. 113
– 114. Problems pp. 119: 67 – 98.)
d3. Solve quadratic equations by graphing. (1:4 – Factoring Quadratic Equations pp. 120.
Problems pp. 119:35 – 58.)
e1. Solve systems of equations. (9:1 – Solving Systems of Equations pp. 642 – 646. Problems pp.
649 – 650: 1 – 42.
f1. Solve polynomial equations. (1:6 – Solving Polynomial Equations pp131 – 132. Problems pp.
139: 1 – 18.)
f2. Solve radical equations. (1:6 – Equations involving Radicals pp133. Problems pp. 139: 29 –
44.)
f3. Solve fractional and absolute value equations. (1:6 – Equations with Fractions or Absolute
Values pp 134 – 135. Problems pp. 140: 57 – 70.)
g1. Use different types of equations to model real-world problems (linear). (1:3 – Introduction to
Problems Solving pp. 98 – 104. Problems page 105: 11 – 40.)
g2. Use different types of equations to solve real-world problems (Linear). (1:3 – Introduction to
Problems Solving pp. 98 – 104. Problems page 106 - 107: 41 – 59.)
g3. Use different types of equations to solve real-world problems (Quadratic) (1:3 – Introduction
to Problems Solving pp. 98 – 104. Problems page 106 - 107: 41 – 59.)
h1. Learn how to use complex numbers. (1:5 – Operations with complex Numbers pp. 125 – 128.
Problems p. 129: 1 – 72.)
1
College Algebra/Trigonometry
(Functions and Trigonometry)
Essential Curriculum
UNIT 2: Function Theory
Goal. The students will demonstrate the ability to identify graphs, domain and range,
intercepts, and maxima and minima of various functions.
Objectives – The student will be able to:
a1. Identify relations as functions. (2:2 – Introduction to Functions pp. 187 – 189. Problems pp.
195 – 196: 1 – 22.)
b1. Use function notation and evaluate functions. (2:2 – Use Function Notation pp. 189 – 190.
Problems p. 196: 25 – 42.)
c1. Find the domain and range of functions. (2:2 & 2:3 – The domain of a Function p. 191, and
The Graph of a Function p. 201 Problems p. 197: 43 – 68.)
d1. Use functions to model and solve real-world problems. (2:2 – Applications pp. 192 – 193.
Problems pp. 197 – 198: 85 – 99.)
e1. Find the zeros of functions. (2:3 – Zeros of a Function p. 203. Problems pp. 209 – 210: 15 –
28.)
f1. Determine where a function is increasing or decreasing and find the maxima and minima. (2:3
– Increasing and Decreasing Functions pp. 204 – 205. Problems p. 210: 29 – 56.
g1. Identify and graph linear, step, and other piecewise-defined functions. (2:3 – Linear Functions,
Step Functions and Piecewise-Defined Functions pp. 206 – 207. Problems pp. 210 – 211: 75 – 90.
h1. Identify even and odd functions. (2:3 – Even and Odd Functions p. 208. Problems p. 211: 93 –
102.)
i1. Recognize graphs of common functions as well as transformations of these graphs. (2:4 –
Summary of Graphs of Common Functions, Shifting Graphs, Reflecting Graphs, Non-Rigid
Transformations pp. 214 – 219. Problems pp. 220 - 222: 9 – 46.)
j1. Add, subtract, multiply, and divide functions. (2:5 – Arithmetic Combinations of Functions pp.
225 – 226. Problems p. 230: 5 – 24.)
k1. Find compositions of one function with another function. (2:5 – Composition of Functions pp.
227 – 228. Problems pp. 231: 37 – 50.)
l1. Find and verify inverses of functions. (2.6 – Finding the Inverse of a Function pp. 237 – 238.
Problems p. 239: 5 – 24.)
2
College Algebra/Trigonometry
(Functions and Trigonometry)
Essential Curriculum
Quarter 2
UNIT 3: Polynomial Functions
Goal. The students will demonstrate the ability to use a problem-solving approach to solve
polynomial equations, both with and without the use of technology, and sketch and
analyze graphs of polynomial functions.
Objectives – The student will be able to:
a1. Analyze and sketch graphs of quadratic functions. (3:1 – The Graph of a quadratic function pp.
254 – 256. Problems p. 260: 1 – 36.)
a2. Identify the Standard form of a quadratic equation. (3:1 – The Standard form of a quadratic
function pp. 257 – 258. Problems p. 261: 37 – 64.)
b1. Sketch graphs of polynomial functions using transformations and end behavior. (3:2 – Graphs
of Polynomial Functions pp 265 – 268. Problems p. 274: 1 – 26.)
b2. Sketch graphs of polynomial functions using zeros. (3:2 – Graphs of Polynomial Functions pp
269 – 271. Problems p. 274: 27 – 66.)
c1. Divide polynomials using long division.(3:3 – Polynomial Long Division pp 278 – 280.
Problems p. 285: 1 – 20.)
c2. Divide polynomials using synthetic division. (3:3 – Polynomial Synthetic Division p. 281.
Problems p. 285 – 286: 21 – 50.)
d1. Apply the Remainder Theorem to polynomial functions. (3:3 – The Remainder and Factor
Theorems pp. 282 – 284. Problems p. 285 - 286: 39 – 50.)
d2. Apply the Factor Theorem to polynomial functions. (3:3 – The Remainder and Factor
Theorems pp. 282 – 284. Problems p. 286: 51 – 66.)
e1. Determine the zeros of polynomial functions algebraically. (3:4 – The Rational Zero test. pp.
289 – 291. Problems p. 298: 1 – 28.)
e2. Determine the zeros of polynomial functions graphically. (3:4 – The Rational Zero test. pp.
289 – 291. Problems p. 298 - 299: 29 – 36.)
f1. Use polynomial functions to model and solve real-world problems. (3:4 – Using a Polynomial
Model pp. 297. Problems p. 301: 109 – 112.)
g1. Use direct variation to model and solve real-world problems. (3:5 – Direct Variation and as an
nth power. Problems p. 304 - 305. Problems p. 309 - 311: 5 – 40.)
g2. Use inverse variation to model and solve real-world problems. (3:5 – Inverse Variation p. 306.
Problems p. 311 – 312: 41 – 63.)
g3. Use joint variation to model and solve real-world problems. (3:5 – Joint Variation p. 307.
Problems p. 312: 64 – 72.)
3
College Algebra/Trigonometry
(Functions and Trigonometry)
Essential Curriculum
UNIT 4: Rational Functions
Goal. The students will demonstrate the ability to describe, interpret, analyze and apply
rational functions to real-world problems.
Objectives – The student will be able to:
a1. Determine the domain of a rational expression. (P: 5 – Introduction, Finding the
domain of a rational function. p. 42. Problems p. 49: 15 – 32.)
b1. Simplifying rational expressions. ( P:5 – Simplifying rational expressions p. 43 - 45.
Problems p. 49: 15 - 32.)
b2. Adding and subtracting rational expressions. ( P:5 – Simplifying rational
expressions p. 43 - 45. Problems p. 50: 55 - 66.)
b3. Multiplying and dividing rational expressions. ( P:5 – Simplifying rational
expressions p. 43 - 45. Problems p. 50: 39 - 54.)
c1. Simplify complex fractions. ( P:5 – Complex Fractions p. 46 – 47. Problems p. 50 - 51:
77 – 88.)
d1. Determine the horizontal, vertical asymptotes of rational functions. (4:1 –
Horizontal and Vertical Asymptotes pp 325 – 326. Problems p. 329: 1 – 20.
d2. Determine the slant asymptotes of rational functions. (4:2 – Slant Asymptotes p.
336. Problems pp. 339: 45 - 58.)
e1. Analyze and sketch graphs of rational functions. (4:2 – Analyzing graphs of
Rational Functions. pp 333 – 335. Problems pp. 338 – 339: 1 – 44.)
f1. Use rational functions to model and solve real-world problems. (4:1 –
Applications p 327 – 328, 4:2 – Applications p. 337. Problems pp. 331- 332: 35 – 42, and pp. 340
– 341 : 65 – 75.
4
College Algebra/Trigonometry
(Functions and Trigonometry)
Essential Curriculum
Quarter 3
UNIT 5: Exponential and Logarithmic Functions
Goal. The students will demonstrate the ability to use a problem-solving approach to use the laws of
exponents and logarithms and apply them to real-world situations.
Objectives – The student will be able to:
a. Use properties of integer and rational exponents. (P:2 – Rational Exponents pp. 19 – 20. Problems page
21: 9 – 42.)
b. Use scientific notation. (P:2 – Scientific Notation p. 14. Problems p. 23: 113 – 118.)
c1.Simplify radical expressions. (P:2 – Simplifying Radicals pp. 17 - 18. Problems p. 22: 71 – 76.)
c2.Combine radical expressions. (P:2 – Simplifying Radicals pp. 17 - 18. Problems p. 23: 95 – 100.)
d. Rationalize denominators. (P:2 – Rationalizing Denominators and Numerators pp. 18 – 19. Problems p.
22: 83 – 90.)
e. Recognize and evaluate exponential functions, including base e. (5:1 – The Natural Base e p. 384.
Problems pp. 388: 29 – 36, 49 – 54.)
f. Sketch and analyze the graph of an exponential function. (5:1 – Graphs of Exponential Functions pp. 381
– 383. Problems pp. 388: 15 – 28, 37 – 48.
g1. Recognize and evaluate logarithmic functions. (5:2 – Logarithmic Functions pp. 392 – 393. Problems
pp. 399 - 400: 1 – 6, 9 – 14, 19 – 28, 33 – 36, 51 – 58, 63 – 64.
g2. Recognize and evaluate the natural logarithm. (5:2 – The Natural Logarithmic function pp. 396 – 397.
Problems pp. 399 – 400: 7 – 8, 15 – 18, 29 – 30, 41 – 44.
h1. Sketch and analyze the graph of a common logarithmic function. (5:2 – Graphs of Logarithmic
Functions pp. 394 – 395. problems p 399: 45 – 58, 63 - 68.)
h2. Sketch and analyze the graph of a natural logarithmic function. (5:2 – Graphs of Logarithmic Functions
pp. 396 – 375. problems p 399: 59 – 62, 65 - 68.)
i. Use properties of logarithms to evaluate and rewrite logarithmic expressions. (5:3 – Properties of
Logarithms pp. 403 – 405. Problems pp. 407 – 408: 1 – 84 .)
j1. Solve exponential equations. (5:4 – Solving Exponential Equations pp. 410 – 411. Problems pp. 416 417: 7 – 20, 45 – 64, 73 - 82. )
j2. Solve logarithmic equations. (5:4 – Solving Logarithmic Equations pp. 412 – 413. Problems pp. 416 417: 7 – 20, 83 - 106.)
5
College Algebra/Trigonometry
(Functions and Trigonometry)
Essential Curriculum
k1. Use exponential functions to model and solve real-world problems. (5:1 – Applications pp. 385 – 387.
Problems pp. 389: 63 – 72).
k2. Use logarithmic functions to model and solve real-world problems. (5:1 – Applications pp. 414 – 415.
Problems pp. 417 – 418: 111 - 119).
UNIT 6: Introduction to Trigonometry
Goal. The students will demonstrate the ability to define trigonometric ratios and apply
trigonometry to solve real-world problems.
Objectives – The student will be able to:
a1. Describe Angles using Degree measure. (6:1 – Angles & Degree Measure pp. 444 –
446. Problems pp. 451: 1 – 8, 17 – 24 ).
a2. Describe Angles using Radian measure. (6:1 – Radian Measure. 447. Problems pp.
451: 29 – 34 ).
b1. Convert between Degree and Radian measures. (6:1 – Conversion of Angles from
Degrees to Radians and vice versa. pp. 448. Problems pp. 452: 51 – 74).
c1. Model and solve real-world problems involving arc length and speed. (6:1 –
Applications pp. 449 – 450. Problems pp. 453: 91 – 96 ).
d1. Evaluate the six trigonometric functions. (6:2 – The Six Trigonometric Functions pp.
455 – 456. Problems pp. 462: 9 – 50 ).
e1. Use reference angles to evaluate trigonometric functions. (6:3 – Reference Angles
p. 468 - 470. Problems pp. 474 – 475: 15 – 36, 45 – 74 ).
f1. Use trigonometric functions and right triangle relations to model and solve
real-world problems. (6:2 – Applications Involving Right Triangles. 460 – 461. Problems pp.
463 - 464: 61 – 66 ).
g1. Use the Fundamental Trigonometric Identities to Evaluate Trigonometric
Functions. (7:1 – Using Fundamental Identities pp. 531 - 533. Problems pp.535: 1 – 14 ).
g2. Use the Fundamental Trigonometric Identities to Simplify Trigonometric
Expressions. (7:1 – Using Fundamental Identities pp. 531 – 533. Problems pp. 535 – 536: 15 –
56 ).
g3. Use the Fundamental Trigonometric Identities to Rewrite Trigonometric
Expressions. (7:1 – Using Fundamental Identities pp. 531 – 533. Problems pp. 536: 57 – 68 ).
6
College Algebra/Trigonometry
(Functions and Trigonometry)
Essential Curriculum
h. Verify trigonometric identities. (7:2 – Verifying Trigonometric Identities pp. 539 – 541.
Problems pp. 543: 1 – 44).
Quarter 4
UNIT 7: Trigonometric Graphs and Equations
Goal. The students will demonstrate the ability to sketch and analyze trigonometric
graphs, solve trigonometric equations and apply trigonometry to solve real-world
problems.
Objectives – The student will be able to:
a1. Sketch the graph of the sine function, including its amplitude, period and
phase shift. ( )
a2. Analyze the graph of the sine function, including its amplitude, period and
phase shift. ( )
a3. Sketch the graph of the cosine function, including its amplitude, period and
phase shift. ( )
a4. Analyze the graph of the cosine function, including its amplitude, period and
phase shift. ( )
b1. Sketch the graph of the tangent function, including its period and phase shift. (
)
b2. Analyze the graph of the tangent function, including its period and phase shift.
( )
c. Solve trigonometric equations (limited to sine, cosine, and tangent) in basic
algebraic and quadratic form. ( )
d. Use the Law of Sines to solve triangles (AAS, ASA, or SSA). ( )
e. Use the Law of Sines to model and solve real-world problems. ( )
UNIT 8: Sequences and Series
Goal. The students will demonstrate the ability to identify and evaluate arithmetic
and geometric sequences and series.
Objectives – The student will be able to:
a. Use sequence notation to write the terms of a sequence. ( )
b. Use factorial notation. ( )
c. Use summation notation. ( )
d. Recognize and write arithmetic sequences. ( )
7
College Algebra/Trigonometry
(Functions and Trigonometry)
Essential Curriculum
e. Find an nth partial sum of an arithmetic sequence. ( )
f. Recognize and write geometric sequences. ( )
g. Find the nth partial sum of a geometric sequence. ( )
h. Find the sum of an infinite series. ( )
i. Use arithmetic and geometric sequences and series to model and solve realworld problems. ( )
8