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In this lesson, we have four objectives:
1. To define a complex number
2. To plot a complex number in the complex plane
3. To work with complex numbers and their conjugates
4. To perform arithmetic operations on complex numbers

Lesson 1 - Worksheet Review

In this lesson, we talk about the zero product rule and review the process of factoring. We go through examples where we:
1. factor out the common factor
2. use identities such as difference of squares, difference and sum of cubes, perfect squares
3. use grouping
4. convert the given equation into quadratic form.

Lesson 2 - Worksheet Review

In this lesson, we learn about solving radical equations. We also cover situations where we need to check for extraneous solutions.

Lesson 3 - Worksheet Review

In this lesson, we learn how to define and evaluate expressions with integer and rational exponents. We also solve some equations.

Lesson 4 - Worksheet Review

In this lesson, we discuss properties of exponents and radicals and apply these properties to the task of simplifying algebraic expressions.

Lesson 5 - Worksheet Review

In this lesson, we look at problems which can be modelled with systems of inequalities in two variables. We learn to write the inequalities, sketch their graphs and interpret the solution to the system.

Lesson 6 - Worksheet Review

In this lesson, we look at linear systems in three variables and we solve these systems using substitution and/or elimination. We also talk about the geometric interpretation of these solutions.

Lesson 7 - Worksheet Review

In this lesson, we introduce basic vocabulary regarding polynomials, such as degree, coefficient, leading term, and we also perform addition, subtraction, multiplication and division on polynomials.

Lesson 8- Worksheet Review

In this lesson, we examine the method of finite differences to find the expression for a polynomial. We also verify the method of finite differences for a linear, quadratic and cubic polynomial.

Lesson 9 - Worksheet Review

In this lesson, we use polynomial identities to solve equations in complex numbers.

Lesson 10 - Worksheet Review

In this lesson, we add and subtract rational expressions where we expand the rational expressions using a least common denominator.

Lesson 11 - Worksheet Review

In this lesson, we multiply or divide rational expressions and simplify the result through factoring and simplifying common factors between the numerator and the denominator. We also work with compound fractions, fractions where, in the numerator and/or the denominator, we have a sum or a difference of rational expressions.

Lesson 12 - Worksheet Review

In this lesson, we revisit the quadratic equation and use completing the square to solve the equation. Then, we use the quadratic formula to solve some quadratic equations and we learn to use the discriminant to identify the nature of the roots.

Lesson 13 - Worksheet Review

In this lesson, we look at the main features of a parabola, such as its direction, its line of symmetry, vertex and intercepts. We also sketch the graphs of parabolas using these features.

Worksheet Review

In this lesson, we are working on solving systems of linear and quadratic equations. We are also graphing the systems and interpreting the solutions geometrically.

Worksheet Review

This midterm exam covers lesson 1 through 15. The duration is 80 minutes.

In this lesson, we learn about the definition of a logarithm and how to evaluate a logarithmic value. We also talk about the common logarithm and the natural logarithm.

Worksheet Review

In this lesson, we explore the properties of logarithms, including the Change of Base Formula, and we evaluate and simplify logarithmic expression with these properties.

Lesson 17 - Worksheet Review

In this lesson, we apply the properties of logarithms in solving logarithmic equations. We also learn to identify extraneous solutions to these equations.

Worksheet Review

In this lesson, we will solve exponential equations. We will express some of the solutions as logarithmic expressions and use factoring techniques in some of the equations.

Worksheet Review

In this lesson, we take a brief look at when polynomial, linear, trigonometric and exponential models are useful for certain real-life situations. In the second half of the lesson, we derive exponential models for given problems.

Lesson 20 - Worksheet Review

In this lesson, we are introducing functions, function notation, domain, range and building functions.

Lesson 21 - Worksheet Review

In this lesson, we look at operations on functions and transformations of functions.

Lesson 22 - Worksheet Review

In this lesson, we first decide if a given function is odd, even or neither. We also look at the symmetry of odd and even function graphs. Then, we learn to take the inverse of a given function and to graph the inverse function on the coordinate plane.

Lesson 23 - Worksheet Review

In this lesson, we learn to calculate average rates of change for functions over different intervals. Then, we learn to find linear functions whose rate of change is constant over any interval.

Lesson 24 - Worksheet Review

In this lesson, we look at characteristics of quadratic functions, such as vertex and the axis of symmetry of a parabola. We find the vertex of a parabola using the intercepts, the quadratic formula and the method of completing the square. Then, we compare properties of linear and quadratic functions.

Lesson 25 Worksheet Review

In this lesson, we study exponential functions and their graphs. We look at important features such as intercepts, end behavior, asymptotes. We also cover transformations of exponential functions and go over finding the equations for exponential functions.

Lesson 26 - Worksheet Review

This lesson has four objectives: 1. Applying the idea of a function to trigonometric functions 2. Revisiting the unit circle to sketch the parent sine and cosine curves. 3. Establishing features of trigonometric curves such as period and amplitude. 4. Applying transformations towards sketching graphs of sine and cosine curves.

Lesson 27 - Worksheet Review

In this lesson, we look at logarithmic functions and graphs. We define logarithmic functions as the inverse of exponential functions, we identify features of their graphs and cover transformations of parent logarithmic graphs.

Lesson 28 - Worksheet Review

In this lesson, we look at probabilities of simple events and we go over definitions of event, sample space, outcome and complement. We then represent situations with Venn diagrams and calculate probabilities from Venn diagrams.

Lesson 29 - Worksheet Review

In this lesson, we work with the probability rules and learn to display information using tree diagrams. We also calculate conditional probability and learn about independent and mutually exclusive events.

Lesson 30 - Worksheet Review

This midterm exam covers lesson 16 through 30. The duration is 80 minutes.

In this lesson, we learn to calculate the measures of center and spread of distributions. We then interpret the shape of a distribution from its histogram.

Lesson 31 - Worksheet Review

In this lesson, we cover the normal distribution and the standard normal distribution. We calculate probabilities from data values and data values from probabilities. We also find the mean and the standard deviation from given information about percentiles.

Lesson 32 - Worksheet Review

In this lesson, we look at three issues in Statistics. We learn about the three types of statistical studies. we look at how we can estimate a population characteristic from a sample and we examine the sampling variability in considering the sample mean as an estimate of the population mean.

Lesson 33 - Worksheet Review

In this lesson, we cover finding square roots of positive rational numbers and learn to apply proportional reasoning to problems.

Lesson 34 - Worksheet Review

In this lesson, we look at properties of angles in triangles, polygons and on parallel lines.

Lesson 35 - Worksheet Review

In this lesson, we apply theorems about angles and segment lengths related to circles.

Lesson 36 - Worksheet Review

In this lesson, we talk about defining angles and trigonometric ratios of angles in the coordinate plane. Then, we introduce the unit circle and learn to use the unit circle to find trigonometric values.

Lesson 37 - Worksheet Review

In this lesson, we look at how we can model a periodic trend with a trigonometric function. We apply the concepts of amplitude, period, phase shift and vertical translation in devising such models.

Lesson 38 - Worksheet Review

In this lesson, we work with trigonometric identities to prove other trigonometric identities and simplify trigonometric expressions.

Lesson 39 - Worksheet Review

This exam covers the entire course. The duration is 120 minutes. Good luck!

**Course Description**

This course is a gateway to Precalculus and it provides you with all the knowledge and skills you need in Precalculus.

**The course includes:**

The course comprises 10 units and 39 lessons

Over 15 hours of video-lessons!

Each lesson includes a video lecture, a worksheet, a worksheet review video and an online quiz.

39 video lectures

39 worksheets

39 worksheet review videos with every question solved step-by step by the instructor

39 online quizzes

2 midterms (on paper)

1 final exam (on paper)

**COURSE GOALS**

Upon course completion, you will learn how to:

- solve quadratic equations, including complex solutions
- solve radical equations
- work with exponents and radicals
- solve systems of inequalities in two variables and linear systems in three variables
- perform operations on polynomials and rational expressions
- define and graph a parabola
- define logarithms and apply properties of logarithms
- solve logarithmic and exponential equations
- choose between models and model with a logarithmic or a trigonometric function
- apply the concept of a function and function notation
- perform operations on functions, including function composition and transformations
- find the inverse of a function and decide if a function is odd, even or neither
- find the average rate of change of a function over a given interval
- work with linear, quadratic, trigonometric, exponential and logarithmic functions
- calculate probabilities and conditional probabilities from probability rules and Venn or tree diagrams
- examine the center, spread and shape of distributions
- work with the normal distribution and the standard normal distribution
- consider types of statistical studies, estimation of a population characteristic and sampling variability in the distribution of sample means
- work with proportional reasoning
- apply theorems about angles in triangles and circles
- use the unit circle in finding trigonometric values
- prove trigonometric identities and simplify trigonometric expressions

**TARGET AUDIENCE **

This video-course is primarily intended for 11th grade students who would like to solidify their mathematical skills and knowledge before they take Precalculus.

**COURSE REQUIREMENTS**

Students taking this course will need to have completed Algebra I, Math for 10th Grade or an equivalent Math course prior to enrolling in this course.

UNIT 1 FACTORING AND SOLVING QUADRATIC EQUATIONS

The Complex Number System

The Zero Product Rule and Factoring

UNIT 2 EXPONENTS AND RADICALS

Radical Equations

Integer and Rational Exponents

Properties of Exponents and Radicals

UNIT 3 SYSTEMS OF EQUATIONS AND INEQUALITIES

Problems with Systems of Inequalities in Two Variables

Linear Systems in Three Variables

UNIT 4 POLYNOMIALS AND RATIONAL EXPRESSIONS

Arithmetic Operations on Polynomials

Successive Differences in Polynomials

Polynomial Identities and Equations

Adding and Subtracting Rational Expressions

Multiplying and Dividing Rational Expressions

UNIT 5 MORE ON SYSTEMS OF EQUATIONS WITH QUADRATIC EQUATIONS

Completing the Square, the Quadratic Formula and Types of Roots of a Quadratic Equation

Defining and Graphing a Parabola

Graphing and Solving Systems of Equations

UNIT 6 EXPONENTS AND LOGARITHMS

Logarithms

Properties of Logarithms

Logarithmic Equations

Exponential Equations

Choosing a Model and Modeling with Exponential Functions

UNIT 7 FUNCTIONS AND TYPES OF FUNCTIONS

Concept of a Function, Function Notation and Building Functions

Creating New Functions from Existing Functions

Even/Odd Functions and Inverse Functions

Rates of Change and Linear Functions

Characteristics of Quadratic Functions and Comparing Properties of Functions

Exponential Functions

Trigonometric Functions

Logarithmic Functions

UNIT 8 PROBABILITY

Probability and Venn Diagrams

Probability Rules, Conditional Probability, Tree Diagrams

UNIT 9 STATISTICS

Center, Spread and Shape of Distributions

The Normal Distribution

Types of Statistical Studies, Estimation of Population Characteristic, Sampling Variability

UNIT 10 GEOMETRY AND CIRCULAR FUNCTIONS

Square Roots and Proportional Reasoning

Properties of Angles in Triangles

Theorems About Circles

The Unit Circle

Modeling Periodic Data with Trigonometric Functions

Proving Trigonometric Identities

- Teacher: Ebru
- Areas of expertise: Mathematics
- Education: Oberlin College, BA in Mathematics and Anthropology 1993 Texas A&M University MSc in Mathematics 2011
- Interests: Epistemology, Acting
- Skills: Learning Languages
- Associations: National Council of Teachers of Mathematics (NCTM)
- Issues I care about: Sustainability, Social Responsibility, Giving Back to the Community

I am happy to start working with Lernsys students as I reach out to you all beyond the physical boundaries of the classroom.

Lesson 1 online quiz answers

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Midterm 1 Solutions

Midterm 2 Solutions

Final Exam Solutions