Intermediate Algebra Course

Download Syllabus - Suggested Syllabus for 2020

Summary Like its predecessor, Introductory Algebra, this course does more than cover a list of concepts or skills. Intermediate Algebra is student-centered and promotes exploration into quantitative methods and how they are useful in life experiences. The course will actively strive to build a community of learners through teamwork and a focus on the day-to-day challenges of reading, writing, conversation, and problem-solving. Key to the format is the concept known as the social construction of knowledge. The course, therefore, addresses critical thinking and problem solving, communication, leadership, team building, conflict management, and technological competence. Finally, students are required to communicate mathematically in verbal and written language enabling them to be globally connected via the universal language of mathematics.

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1 Linear Equations

Vocabulary → 1←

1.1: Solving Linear Equations.

• • SWAT:

    • Check solutions of equations.

    • Solve linear equations in

      • standard form (ax+b=0) and

      • nonstandard form (ax+b=kx+c).

      • Identify Equivalent Equations.

1.2: Linear Equations & Problem Solving.

• • SWAT:

    • Write algebraic equations and solve them.

      • Solve percent problems. (30 Riyals is what percent of 200 Riyals?)

    • Translate word problem to Math. expression or equation. (The length of the room is 4 feet more than its width)

    • Use ratios- compare unit prices - Solve proportions.

1.3: Business & Scientific Problems

• • SWAT:

    • Use mathematical models to solve:

      • Business-related problems. (Cost, Selling Price, Markup, Markdown, MarkupRate, MarkdownRate, Discount, Discount Rate)

      • Mixture problems.

      • Classic work rate problems. If 1 machine finishes 1 job in 4 hours, Hence, in 1 hour it finishes 1/4 of the job)

    • Use formulas to solve.

      • Area or Perimeter

      • Interest (Interest = Principal * Interest Rate)

      • Degree (F=9/5C + 32)

1.4: Linear Inequalities

• SWAT

  • • Sketch the graphs of inequalities.

    • Identify the properties of inequalities that can be used to create equivalent inequalities.

    • Solve linear inequalities.

    • Solve compound inequalities.

    • Solve application problems involving inequalities

1.5: Absolute Value Equations & Inequalities

• SWAT

  • • Solve absolute value equations.

    • Solve inequalities involving absolute value.

• Extra Help!! Watch Below Video

2.5 Solve and graph a one-variable inequality <-- Video

2.5 Solving absolute value inequalities Videos 1 2 3 4 5

2.5 Solving absolute value inequalities when there are infinitely many solutions Videos 1 2 3 4 5

Note:

| X | > -13 Use OR

-2 |x+4| <22 Use OR

| X | > +13 Use AND

2 Graphs and Functions

Vocabulary → 3 ←

2.1: The Rectangular Coordinate System

• SWAT

• Graph points on a rectangular coordinate system. (x, y)

• Determine whether ordered pairs are solutions of equations.

• Use the Distance Formula to find the distance between two points.

• Use the Midpoint Formula to find the midpoints of line segments.

2.2: Graphs of Equations

• SWAT

• Graphs of equations using the point-plotting method.

• Find and use x and y-intercepts as aids to do the graphs.

• Find x-intercept, let y = 0, solve for x.

• Find y-intercept, let x= 0, solve for y.

• Use a pattern to write an equation for an application problem, and graph it.

2.3: Slope and Graphs of Linear Equations

• SWAT

• Find the slope of a line given 2 points.

• Find the slope from the equation of a line.

• Write linear equations in slope-intercept form & graph the equations.

• Use slope to determine whether 2 lines are parallel, perpendicular, or neither.

• Use slopes to describe rates of change in real-life problems.

2.4: Equations of the Line

• SWAT

• Write equations of lines using point-slope form. y – y1 = m(x – x1)

• Result can be written as

  • General form → ax + by + c = 0

  • Standard form → ax + by = c

• Write equations of horizontal, vertical, parallel, and perpendicular lines.

• Use linear models to solve application problems.

2.5: Graphs of Linear Inequalities

• SWAT

• Verify solutions of linear inequalities in two variables.

• Graph linear inequalities in two variables.

2.6: Relations And Functions

• SWAT

• Identify the domains and ranges of relations.

• Determine if relations are functions by inspection.

• Use function notation and evaluate functions.

• Identify the domains and ranges of functions.

2.7: Graphs of Functions

• SWAT

• graphs of functions on rectangular coordinate systems.

• Identify the graphs of basic functions.

• Use the Vertical Line Test to determine if graphs represent functions.

• Use vertical and horizontal shifts and reflections to sketch graphs of functions.

3: Review Exercises

3 Systems of Equations and Inequalities

Vocabulary → 3 ←

• 3.1: Systems of Equations (graphically and Substitution).

  • SWAT

  • Determine if ordered pairs are solutions of systems of equations.

  • Solve systems of equations graphically.

  • Solve systems of equations algebraically using the method of substitution.

  • Use systems of equations to model and solve real-life problems.

• 3.2: Linear Systems in Two Variables (Elimination).

  • SWAT

  • Solve systems of linear equations algebraically using the method of elimination.

  • Use systems of linear equations to model and solve real-life problems.

• 3.3

• 3.3: Linear Systems in Three Variables

• 3.4: Matrices Introduction <--- ---> Linear Systems (NEW)

  • SWAT

  • - Determine the orders of matrices.

  • - Make coefficient & augmented matrices from linear systems.

  • - Perform elementary row operations to solve systems of linear equations in matrix form.

  • - Use matrices &Gaussian elimination with back-substitution 2solve systems of linear equations.

• 3.5: Determinants and Linear Systems (Cramer's Rule)

  • SWAT

  • Find DETERMINANTS 2 × 2 of matrices and 3 × 3 matrices.

  • Cramer’s Rule to solve systems of linear equations using DETERMINANTS.

  • Use DETERMINANTS to find areas of triangles, to test for collinear points, and to find equations of lines.

• 3.6: Systems of Linear Inequalities

3: Review Exercises

4 Polynomials and Factoring

Vocabulary → 4 ←

• • 4.1: Integer Exponents and Scientific Notation

    • SWAT

    • Product Rule and Power Rule for Exponents.

    • Quotient Rule.

    • Scientific Rule.

• • 4.2: Adding and Subtracting Polynomials

    • SWAT

    • Identify the degree of a polynomial.

    • Combine like terms.

    • Classify a polynomial.

    • Write a polynomial in standard form.

    • Evaluate polynomials.

    • Tell the leading coefficients and degrees of polynomials.

    • Add polynomials.

    • Subtract polynomials.

      • using a Horizontal format and a Vertical format.

      • Use polynomials to model and solve real-life problems.

• • 4.3: Multiplying Polynomials

    • SWAT

    • Multiply a monomial (1) and a polynomial.

    • Multiply two polynomials by Distributive Property.

    • Multiply binomials by the FOIL method.

    • Use special product formulas to multiply two binomials.

    • Use multiplication of polynomials in application problems.

• • 4.4: Factoring by Grouping and Special Forms

    • SWAT

    • Find the Greatest Common Factor (GCF) of a list of numbers.

    • Find the GCF of a list of variable terms.

    • Factor out the GCF Completely.

    • Factor by grouping (4 terms).

• • 4.5: Factoring Trinomials

    • SWAT

    • Factor the difference of squares.

    • Factor a perfect square trinomial.

• • 4.6: Solving Polynomial Equations by Factoring

    • SWAT

    • Solve quadratic equations by factoring.

    • Solve other equations by factoring.

5: Review Exercises

Midterm Review - Part 1 - Recorded Lecture

5 Rational Expressions, Equations, and Functions

Vocabulary → 5 ←

• • • • • 5.4 Recorded Lecture

        • 5.5 Recorded Lecture

        • 5.6 Recorded Lecture

• • • • • 5.1: Rational Expressions and Functions

    • SWAT

      • • • • Simplify rational expressions.

• • • • • • • Find the domain of a rational function.

• • • • • 5.2: Multiplying and Dividing Rational Expressions

  • SWAT

    • • • • Multiply rational expressions and simplify.

          • Divide rational expressions and simplify.

5.3: Adding and Subtracting Rational Expressions

• • SWAT

  • Add or subtract rational expressions with like denominators, and simplify.

  • Add or subtract rational expressions with unlike denominators, and simplify.

• • • • • 5.4: Complex Fractions

  • SWAT

• • • • • 5.5: Dividing Polynomials and Synthetic Division

  • SWAT

• • • • • 5.6: Solving Rational Equations

  • SWAT

• • • • • 5.7: Applications and Variation

5: Review Exercises

6 Radicals and Complex Numbers

Vocabulary → 6 ←

• 6.1 Recorded Lecture

• 6.2 Recorded Lecture

• 6.3 Recorded Lecture

• 6.4 Recorded Lecture

• Pythagorean theorem

• 6.1: Radicals and Rational Exponents

  • SWAT

  • Determine the nth roots of numbers and evaluate radical expressions

  • Use the rules of exponents to evaluate or simplify expressions with rational exponents.

  • Use a calculator to evaluate radical expressions.

  • Evaluate radical functions and find the domains of radical functions.

• 6.2: Simplifying Radical Expressions

  • SWAT

  • Determine the perfect square number and perfect cube number

  • Find square roots.

  • Decide whether a given root is rational, irrational, or not a real number.

  • Find decimal approximations for irrational square roots.

  • Use the Pythagorean theorem.

  • Find cube, fourth, and other roots. Multiply square root radicals.

• 6.3: Adding and Subtracting Radical Expressions

  • SWAT

  • Add and subtract radicals.

  • Simplify radical sums and differences.

  • Simplify more complicated radical expressions.

  • Use the Distributive Property to add and subtract like radicals.

  • Use radical expressions in application problems.

• 6.4: Multiplying and Dividing Radical Expressions

  • SWAT

  • Simplify radicals by using the product rule.

  • Simplify radicals by using the quotient rule.

  • Simplify radicals involving variables.

  • Simplify other roots.

  • Rationalize denominators with square roots.

  • Write radicals in simplified form.

  • Rationalize denominators with cube roots.

  • Simplify products of radical expressions.

  • Use conjugates to rationalize denominators of radical expressions.

  • Write radical expressions with quotients in lowest terms.

• 6.5: Radical Equations and Applications

  • SWAT

  • Solve radical equations having square root radicals.

  • Identify equations with no solutions.

  • Solve equations by squaring a binomial.

  • Solve problems using formulas that involve radicals.

  • Solve a radical equation by raising each side to the nth power.

  • Solve application problems involving radical equations.

• 6.6: Complex Numbers

  • SWAT

  • Write square roots of negative numbers in i-form and perform operations on numbers in i-form.

  • Determine the equality of two complex numbers.

  • Add, subtract, and multiply complex numbers.

  • Use complex conjugates to write the quotient of two complex numbers in standard form.

7: Review Exercises

7 Quadratic Equations, Functions, and Inequalities

Vocabulary → 7 ←

• 7.1 Recorded Lecture

• 7.3 Recorded Lecture

• 7.4 Recorded Lecture

• 7.1: Solving Quadratic Equations: Factoring and Special Forms

  • SWAT

    • Familiarize with Concepts and Vocabulary

    • Solve quadratic equations by factoring.

    • Solve quadratic equations by the Square Root Property.

    • Solve quadratic equations with complex solutions by the Square Root Property.

    • Use substitution to solve equations of a quadratic form.

• 7.2: Completing the Square

• 7.3: The Quadratic Formula

  • SWAT

  • Familiarize with Concepts and Vocabulary

    • Derive the Quadratic Formula by completing the square for a general quadratic equation.

    • Use the Quadratic Formula to solve quadratic equations.

• 7.4: Graphs of Quadratic Functions

  • SWAT

  • Familiarize with Concepts and Vocabulary

  • Determine the vertices (singular virtex; means highest or lowest point) of parabolas by completing the square.

  • Sketch (means graph) parabolas.

  • Write the equation of a parabola given the vertex and a point on the graph.

  • Use parabolas to solve application problems.

• 7.5: Applications of Quadratic Equations

  • SWAT

  • Familiarize with Concepts and Vocabulary

  • Use quadratic equations to solve application problems.

• 7.6: Quadratic and Rational Inequalities

8: Review Exercises

8 Exponential and Logarithmic Functions

Vocabulary → 8←

8.1 Recorded Lecture

• • • • • • • 8.2 Recorded Lecture

• • • • • • • 8.1: Exponential Functions (NEW)

  • SWAT

  • Familiarize with Concepts and Vocabulary

  • Evaluate exponential functions.

  • Graph exponential functions.

  • Evaluate the natural base e and graph natural exponential functions.

  • Use exponential functions to solve application problems.

• • • • • • • 8.2: Composite and Inverse Functions (NEW)

  • SWAT

  • Familiarize with Concepts and Vocabulary

  • Form (means create) composite functions and find the domains of composite functions.

  • Find inverse functions algebraically.

  • Compare the graph of a function with the graph of its inverse.

• • • • • • • 8.3: Logarithmic Functions (NEW)

  • SWAT

  • Familiarize with Concepts and Vocabulary

  • Recognize and evaluate logarithmic functions with base “a”.

  • Graph logarithmic functions.

  • Recognize, evaluate, and graph natural logarithmic functions.

  • Use logarithmic functions to model and solve real-life problems.

• • • • • • • 8.4: Properties of Logarithms (NEW)

  • SWAT

  • Familiarize with Concepts and Vocabulary

  • Use the change-of-base formula to rewrite and evaluate logarithmic expressions.

  • Use properties of logarithms to evaluate or rewrite logarithmic expressions.

  • Use properties of logarithms to expand or condense logarithmic expressions.

  • Use logarithmic functions to model and solve real-life problems.

• • • • • • • 8.5: Solving Exponential and Logarithmic Equations (NEW)

  • SWAT

  • Familiarize with Concepts and Vocabulary

  • Solve simple exponential and logarithmic equations.

  • Solve more complicated exponential equations.

  • Solve more complicated logarithmic equations.

  • Use exponential and logarithmic equations to model and solve real-life problems

• • • • • • • 8.6: Applications

8: Review Exercises