MATH 111: College Algebra

Gain a solid understanding of college algebra concepts, improve problem-solving skills, and build confidence for future math courses.

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Course curriculum

1. Course Overview and Learning Outcomes
2. Syllabus PDF
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1. 1.1 Real Numbers and Their Properties — number sets, absolute value, order of operations, properties of real numbers
2. Quiz 1.1
3. 1.2 Integer Exponents and Scientific Notation — product, quotient, power, zero, and negative exponent rules; scientific notation
4. Quiz 1.2
5. 1.3 Radicals and Rational Exponents — nth roots, simplifying radicals, rationalizing denominators, converting between radical and rational exponent notation
6. Quiz 1.3
7. 1.4 Simplifying Radical Expressions — product and quotient rules for radicals, adding and subtracting radicals, multiplying radical expressions
8. Quiz 1.4
1. 2.1 Operations on Polynomials — addition, subtraction, multiplication, special products (FOIL, difference of squares, perfect square trinomials)
2. Quiz 2.1
3. 2.2 Factoring: GCF and Grouping — greatest common factor, factoring by grouping
4. Quiz 2.2
5. 2.3 Factoring Trinomials — leading coefficient of 1 and a ≠ 1, trial-and-error and AC methods
6. Quiz 2.3
7. 2.4 Special Factoring Formulas — difference of squares, sum and difference of cubes
8. Quiz 2.4
9. 2.5 Factoring Strategy — choosing the appropriate factoring technique; factoring completely
10. Quiz 2.5
1. 3.1 Simplifying Rational Expressions — identifying excluded values, reducing to lowest terms
2. Quiz 3.1
3. 3.2 Multiplying and Dividing Rational Expressions — factoring to cancel common factors
4. Quiz 3.2
5. 3.3 Adding and Subtracting Rational Expressions — finding the LCD, combining fractions
6. Quiz 3.3
7. 3.4 Complex Fractions — simplifying by LCD method and division method
8. Quiz 3.4
9. 3.5 Radical Expressions — operations: multiplying, dividing, adding, subtracting radical expressions; conjugates
10. Quiz 3.5
1. 4.1 Linear Equations in One Variable — solving, checking solutions, equations with fractions
2. Quiz 4.1
3. 4.2 Formulas and Applications — literal equations, solving for a variable; applied word problems (distance, rate, mixture, geometry)
4. Quiz 4.2
5. 4.3 Linear Inequalities — solving, graphing on a number line, interval notation
6. Quiz 4.3
7. 4.4 Compound Inequalities — AND (intersection) and OR (union) compound inequalities
8. Quiz 4.4
9. 4.5 Absolute Value Equations and Inequalities — solving |ax + b| = c, |ax + b| < c, |ax + b| > c
10. Quiz 4.5
1. 5.1 Systems of Two Linear Equations — graphing method, substitution method, elimination method; consistent, inconsistent, dependent systems
2. Quiz 5.1
3. 5.2 Applications of 2×2 Systems — mixture, rate, investment, and geometry word problems
4. Quiz 5.2
5. 5.3 Systems of Three Linear Equations — solving 3×3 systems by elimination and back-substitution
6. Quiz 5.3
7. 5.4 Systems of Linear Inequalities — graphing feasible regions, identifying vertices
8. Quiz 5.4
1. 6.1 Solving Quadratic Equations by Factoring — zero product property, checking solutions
2. Quiz 6.1
3. 6.2 Square Root Property and Completing the Square — solving equations of the form x² = k; completing the square method
4. Quiz 6.2
5. 6.3 The Quadratic Formula and Discriminant — deriving and applying the quadratic formula; using discriminant to determine number and type of solutions
6. Quiz 6.3
7. 6.4 Quadratic Functions and Parabolas — standard form y = ax² + bx + c; vertex form y = a(x−h)² + k; vertex, axis of symmetry, direction of opening, intercepts
8. Quiz 6.4
9. 6.5 Quadratic Inequalities — solving using sign charts; expressing solutions in interval notation
10. Quiz 6.5
1. 7.1 Relations, Functions, and Function Notation — definition, vertical line test, evaluating f(x), difference quotient
2. Quiz 7.1
3. 7.2 Domain and Range — finding algebraically and from graphs; interval notation
4. Quiz 7.2
5. 7.3 Graphs of Basic Functions — linear, absolute value, square root, cube root, quadratic; identifying and sketching
6. Quiz 7.3
7. 7.4 Piecewise-Defined Functions — evaluating and graphing
8. Quiz 7.4
9. 7.5 Transformations of Functions — vertical/horizontal shifts, reflections, stretches, and compressions
10. Quiz 7.5
11. 7.6 Combining Functions — sum, difference, product, quotient of functions; composite functions (f ∘ g)(x); domain of combined functions
12. Quiz 7.6
13. 7.7 Inverse Functions — one-to-one functions, horizontal line test, finding f¹(x), verifying via ⁻composition
14. Quiz 7.7
1. 8.1 Polynomial Functions and End Behavior — degree, leading coefficient, end behavior, turning points
2. Quiz 8.1
3. 8.2 Zeros of Polynomial Functions — real zeros, multiplicity, graphs touching vs. crossing the x-axis
4. Quiz 8.2
5. 8.3 Polynomial Division and the Remainder Theorem — long division, synthetic division, Remainder and Factor Theorems
6. Quiz 8.3
7. 8.4 Rational Functions and Their Graphs — vertical asymptotes, horizontal asymptotes, oblique asymptotes, holes, graphing strategy
8. Quiz 8.4
9. 8.5 Polynomial and Rational Inequalities — sign chart method; interval notation solutions.
10. Quiz 8.5
1. 9.1 Exponential Functions — definition, base restrictions, graphs and transformations, natural base e, compound interest formula
2. Quiz 9.1
3. 9.2 Logarithmic Functions — definition as inverse of exponential, converting between forms, evaluating log and ln
4. Quiz 9.2
5. 9.3 Properties of Logarithms — product, quotient, power rules; change-of-base formula; expanding and condensing
6. Quiz 9.3
7. 9.4 Solving Exponential and Logarithmic Equations — algebraic methods, checking extraneous solutions
8. Quiz 9.4
9. 9.5 Applications — exponential growth and decay, half-life, population models, compound and continuous interest
10. Quiz 9.5
1. 10.1 Sequences and Recursive Definitions — explicit and recursive formulas, generating terms
2. Quiz 10.1
3. 10.2 Arithmetic Sequences and Series — common difference, nth term, sum of first n terms
4. Quiz 10.2
5. 10.3 Geometric Sequences and Series — common ratio, nth term, sum of finite geometric series
6. Quiz 10.3
7. 10.4 Infinite Geometric Series — condition for convergence (|r| < 1), sum formula, applications
8. Quiz 10.4
9. 10.5 Sigma Notation — writing and evaluating series using sigma notation
10. Quiz 10.5
1. Assignment
2. Grading Rubric (Total: 160 Marks)
1. Final Exam: Instructions (Important)
2. Final Exam

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$250.00
106 lessons
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MATH 111: College Algebra

Course curriculum

College Algebra

Chapter 1 : Algebraic Foundations

Chapter 2 : Polynomials & Factoring

Chapter 3 : Rational & Radical Expressions

Chapter 4 : Linear Equations & Inequalities

Chapter 5 : Systems of Linear Equations

Chapter 6 : Quadratic Equations & Functions

Chapter 7 : Functions & Their Graphs

Chapter 8 : Polynomial & Rational Functions

Chapter 9 : Exponential & Logarithmic Functions

Chapter 10 : Sequences & Series

Assignment

Final exam

About this course

Discover your potential, starting today