# Mathematics Department

## Assessment

You are now able to use the Guided Self-Placement tool in lieu of taking the assessment exams. To use the tool, click the button below.

## Cypress College Math Review Videos

### Arithmetic & Algebra

#### Algebra Review Videos

##### Math 40 Intermediate Algebra Lecture Videos

Each of these links send you to a play list of the videos for that chapter. The videos are listed both by section number and topic.

##### Chapter 1 Videos — This chapter covers:
• simplifying expressions
• order of operations
• subsets of real numbers (Integers, Rationals, etc.)
• properties (commutative, inverse, distributive, etc.)
• translation (English to math)
##### Chapter 2 Videos — This chapter covers:
• solving linear equations
• solving linear and compound inequalities
• solving applications of linear equations and inequalities
• geometric formulas
• unit conversion
• compound interest
• solving absolute value equations and inequalities
##### Chapter 3 Videos — This chapter covers:
• graphing lines
• domain and range
• slope and y-intercept of a line
• definition of a function
• finding the equation of a line
• linear applications
• graphing linear inequalities and systems of linear inequalities
##### Chapter 4 Videos — This chapter covers:
• solving systems of equations by graphing, elimination and by substitution
• solving applications of systems of equations
• distance, rate and time applications
• geometry applications
• mixture applications
##### Chapter 5 Videos — This chapter covers:
• exponent rules
• negative exponents
• rational exponents
• scientific notation
• add, subtract and multiply polynomials
• factoring polynomials
• solving quadratic equations by factoring
• solving applications of quadratic equations
##### Chapter 6 Videos — This chapter covers:
• add, subtract, multiply and divide rational expressions
• simplify complex fractions
• divide polynomials
• solve rational equations
• solve applications of rational equations
• solve direct and indirect variation problems
##### Chapter 7 Videos — This chapter covers:
• simplifying expressions with rational exponents
• add, subtract, multiply and divide radicals
• solve radical equations
• solve applications of radical equations
• complex numbers (working with “i”)
##### Chapter 8 Videos — This chapter covers:
• solving a quadratic equation by completing the square
• solving a quadratic equation by using the quadratic formula
• solving quadratic type equations
• solving nonlinear inequalities
• graph parabolas
##### Chapter 9 Videos — This chapter covers:
• graphing exponential functions
• solving exponential equations
• graphing logarithmic functions
• solving logarithmic equations
• work with the properties of logarithms
##### Chapter 10 Videos — This chapter covers:
• graphing circles
• graphing ellipses
• graphing parabolas
• graphing hyperbolas
• completing the square to put the equation of a circle of parabola in standard form

#### Preparation for Math 110

Here are some videos that will help you prepare to take Math 110.

There are also sample problems with answers that you can try on your own to make sure you understand the concepts.

#### Preparation for Math 115

Here are some videos that will help you prepare to take Math 115.

There are also sample problems with answers that you can try on your own to make sure you understand the concepts.

#### Preparation for Math 120

Here are some videos that will help you prepare to take Math 120.

There are also sample problems with answers that you can try on your own to make sure you understand the concept.

#### Math 120 Probability and Statistics

##### Math 120 Lecture Videos

Each of these links send you to a play list of the videos for that chapter. The videos are listed both by section number and topic.

##### Chapter 1 Videos — This chapter covers:
• Define Statistics and statistical thinking
• Explain the process of statistics
• Distinguish between qualitative and quantitative variables
• Distinguish between discrete and continuous variables
• Determine the level of measurement of a variable
• Distinguish between an observational study and an experiment
• Explain the various types of observational studies
• Obtain a simple random sample
• Obtain a stratified sample
• Obtain a systematic sample
• Obtain a cluster sample
• Explain the sources of bias in sampling
• Describe the characteristics of an experiment
##### Chapter 2 Videos — This chapter covers:
• Organize qualitative data in tables
• Construct bar graphs
• Construct pie charts
• Organize discrete data in tables
• Construct histograms of discrete data
• Organize continuous data in tables
• Construct histograms of continuous data
• Draw stem-and-leaf plots
• Identify the shape of a distribution
• Construct frequency polygons
• Create cumulative frequency and relative frequency tables
• Construct frequency and relative frequency ogives
• Draw time-series graphs
• Describe what can make a graph misleading or deceptive
##### Chapter 3 Videos — This chapter covers:
• Determine the arithmetic mean of a variable from raw data
• Determine the median of a variable from raw data
• Explain what it means for a statistic to be resistant
• Determine the mode of a variable from raw data
• Determine the range of a variable from raw data
• Determine the standard deviation of a variable from raw data
• Determine the variance of a variable from raw data
• Use the Empirical Rule to describe data that are bell shaped
• Use Chebyshev’s Inequality to describe any set of data
• Approximate the mean of a variable from grouped data
• Compute the weighted mean
• Approximate the standard deviation of a variable from grouped data
• Determine and interpret z-scores
• Interpret percentiles
• Determine and interpret quartiles
• Determine and interpret the interquartile range
• Check a set of data for outliers
• Compute the five-number summary
• Draw and interpret boxplots
##### Chapter 4 Videos — This chapter covers:
• Draw and interpret scatter diagrams
• Describe the properties of the linear correlation coefficient
• Compute and interpret the linear correlation coefficient
• Determine whether a linear relation exists between two variables
• Explain the difference between correlation and causation
• Find the lest-squares regression line and use the line to make predictions
• Interpret the slope and the y-intercept of the least-squares regression line
• Compute the sum of squared residuals
• Compute and determine the coefficient of determination
• Perform residual analysis on a regression model
• Identify influential observations
##### Chapter 5 Videos — This chapter covers:
• Apply the rules of probabilities
• Compute and interpret probabilities using the empirical method
• Compute and interpret probabilities using the classical method
• Recognize and interpret subjective probabilities
• Use the Addition Rule for disjoint events
• Use the General Addition Rule
• Compute the probability of an event using the
• Complement Rule
• Identify independent events
• Use the Multiplication Rule for independent events
• Compute at-least probabilities
• Compute conditional probabilities
• Compute probabilities using the General Multiplication Rule
• Solve counting problems using the Multiplication Rule
• Solve counting problems using permutations
• Solve counting problems using combinations
• Solve counting problems involving permutations with non-distinct items
• Compute probabilities involving permutations and combinations.
• Determine the appropriate probability rule to use
• Determine the appropriate counting technique to use
##### Chapter 6 Videos — This chapter covers:
• Distinguish between discrete and continuous random variables
• Identify discrete probability distributions
• Construct probability histograms
• Compute and interpret the mean of a discrete random variable
• Interpret the mean of a discrete random variable as an expected value
• Compute the standard deviation of a discrete random variable
• Determine whether a probability experiment is a binomial experiment
• Compute probabilities of binomial experiments
• Compute the mean and standard deviation of a binomial random variable
• Construct binomial probability histograms
##### Chapter 7 Videos — This chapter covers:
• Use the uniform probability distribution
• Graph a normal curve
• State the properties of the normal curve
• Explain the role of area in the normal density function
• Find and interpret the area under a normal curve
• Find the value of a normal random variable
##### Chapter 8 Videos — This chapter covers:
• Describe the distribution of the sample mean: normal population
• Describe the distribution of the sample mean: non-normal population
• Describe the sampling distribution of a sample proportion
• Compute probabilities of a sample proportion
##### Chapter 9 Videos — This chapter covers:
• Obtain a point estimate for the population proportion
• Construct and interpret a confidence interval for the population proportion
• Determine the sample size necessary for estimating a population proportion within a specified margin of error
• Obtain a point estimate for the population mean
• State properties of Student’s t-distribution
• Determine t-values
• Construct and interpret a confidence interval for a population mean
• Find the sample size needed to estimate the population mean within a given margin of error
• Find critical values for the chi-square distribution
• Construct and interpret confidence intervals for the population variance and standard deviation
• Determine the appropriate confidence interval to construct
##### Chapter 10 Videos — This chapter covers:
• Determine the null and alternative hypotheses
• Explain Type I and Type II errors
• State conclusions to hypothesis tests
• Explain the logic of hypothesis testing
• Test hypotheses about a population proportion
• Test hypotheses about a population proportion using the binomial probability distribution
• Test hypotheses about a mean
• Understand the difference between statistical significance and practical significance
• Test hypotheses about a population standard deviation
• Determine the appropriate hypothesis test to perform
##### Chapter 11 Videos — This chapter covers:
• Distinguish between independent and dependent sampling
• Test hypotheses regarding two proportions from independent samples
• Construct and interpret confidence intervals for the difference between two population proportions.
• Determine the sample size necessary for estimating the difference between two population Proportions
• Test hypotheses regarding matched-pairs data
• Construct and interpret confidence intervals about the population mean difference of matched-pairs data
• Test hypotheses regarding the difference of two independent means
• Construct and interpret confidence intervals regarding the difference of two independent means
• Find critical values of the F-distribution
• Test hypotheses regarding two population standard deviations
• Determine the appropriate hypothesis test to perform
##### Chapter 12 Videos — This chapter covers:
• Perform a goodness-of-fit test
• Perform a test for independence
• Perform a test for homogeneity of proportions
##### Chapter 13 Videos — This chapter covers:
• Verify the requirements to perform a one-way ANOVA
• Test a hypothesis regarding three or more means using one-way ANOVA
##### Chapter 14 Videos — This chapter covers:
• State the requirements of the least-squares regression model
• Compute the standard error of the estimate
• Verify that the residuals are normally distributed
• Conduct inference on the slope
• Construct a confidence interval about the slope of the least-squares regression model
• Construct confidence intervals for a mean response
##### Chapter 15 Videos — This chapter covers:
• Distinguish between parametric and non parametric statistical procedures
• Inference about measures of central tendency

#### Preparation for Math 130

Here are some videos that will help you prepare to take Math 130.

There are also sample problems with answers that you can try on your own to make sure you understand the concept.

#### Preparation for Math 141

Here are some videos that will help you prepare to take Math 141.

There are also sample problems with answers that you can try on your own to make sure you understand the concept.

#### Math 141 College Algebra

##### Math 141 Lecture Videos

Each of these links send you to a play list of the videos for that chapter. The videos are listed both by section number and topic.

##### Chapter R Videos — This chapter covers:
• union, intersection, complement of sets
• subsets of the real numbers
• properties of the real numbers
• domain
• laws of exponents
• geometry formulas
• add, subtract, multiply and divide polynomials
• synthetic division
• special products
• factoring difference between squares and trinomials
• factor by grouping
• factor by factoring out binomial factors
• completing the square
• add, subtract, multiply and divide rational expressions
• simplify complex rational expressions
• simplify expressions with rational exponents
##### Chapter 1 Videos — This chapter covers:
• solve linear and rational equations
• solve quadratic equations
• use the discriminant to determine the number and type of solutions
• solve radical equations
• learn about extraneous solutions
• learn how to write the solution to an inequality in interval notation
• solve linear inequalities
• solve absolute value equations and inequalities
• mixture word problems
• distance, rate, time word problems
• investment word problems
• perimeter, area and other geometry word problems
• work rate word problems
##### Chapter 2 Videos — This chapter covers:
• distance and midpoint formulas
• graphing techniques
• intercepts of a graph
• graphing a line
• finding the equation of a line
• parallel and perpendicular lines
• find the equation of a circle
• graph a circle
• complete the square to put the equation of a circle in standard form
• solve variation problems – direct, inverse and joint
##### Chapter 3 Videos — This chapter covers:
• definition of a function
• domain
• difference quotient
• graph basic functions
• determine if a function is even, odd or neither
• locate local minima and maxima of a graph
• determine when a graph is increasing, decreasing or  constant
• find average rate of change
• find the equation of the secant line
• graph a function using transformations:
• graph parent function
• multiply or divide x or y coordinates (if needed) then move up, down, right or left (if needed)
• come up with an equation that models a real life situation
• write one variable as a function of another variable
##### Chapter 4 Videos — This chapter covers:
• determine the average rate of change (slope) of a line
• solve linear application problems
• complete the square to put a quadratic function in standard form – often called vertex form
• determine the vertex of a quadratic function using x= -b/(2a)
• determine the maximum or minimum of a quadratic function without graphing
• use quadratic models to solve real life situations
• solve quadratic inequalities
##### Chapter 5 Videos — This chapter covers:
• graph a monomial function
• find zeros and multiplicities of a polynomial
• use the leading term to determine the end behavior of the graph of a polynomial function
• graph a polynomial using it’s leading term, zeros and their multiplicities
• determine where a rational function will have hole, x-intercepts, and vertical asymptotes
• determine the horizontal or slant asymptote of a rational function
• use a sign graph as an aid in graphing a function
• domain of a function
• graphing rational functions near different types of asymptotes
• solve polynomial and rational inequalities
• use of the Remainder Theorem to determine other zeros of a function
• use of the Intermediate Value Theorem to help in determining zeros of a function
• use of the Rational Zero Test to find the possible rational zeros of a function
• find the real zeros of a polynomial function
• find the complex zeros of a polynomial function
• find a function with known zeros
##### Chapter 6 Videos — This chapter covers:
• find the composition of functions
• find the inverse of a function
• graph an exponential function
• graph a logarithmic function
• work with properties of logarithms
• solve exponential and logarithmic equations
• find the domain of a logarithmic function
##### Chapter 7 Videos — This chapter covers:
• graph a parabola
• find the directrix, focus and latus rectum of a parabola
• graph an ellipse
• find the foci of an ellipse
• graph a hyperbola
• find the foci, and equations of the asymptotes of a hyperbola
• complete the square to change the equation of a conic section from general form to standard form
• derive the equation of a conic section
##### Chapter 8 Videos — This chapter covers:
• solve a system of linear equations
• find the partial fraction decomposition for a rational expression
• solve a system of nonlinear equations
##### Chapter 9 Videos — This chapter covers:
• find the terms of a sequence
• determine the formula for a sequence or series
• find the value of a series
• recognize arithmetic and geometric sequences and series
• prove statements using mathematical induction
• use the binomial theorem to expand a power of a binomial
• use the binomial theorem to find a specific term in the expansion of the power of a binomial

#### Math 142 Trigonometry

Each of these links send you to a play list of the videos for that chapter. The videos are listed both by section number and topic.

##### Pre-Trig Review Videos – In this section you will learn how to:
• Add or Subtract Fractions with Pi
• Review Factoring
• Work with Special Products and Powers of Binomials
• Simplify Fractions with Pi
• Domain and Range
• Transformations of Graphs
• Even and Odd Functions, Symmetry
• Solve Equations involving Pie that have Infinite Answers
• Find Common Denominators for Algebraic Expressions
• Solve Equations and use the Quadratic Formula
##### Chapter 1 Videos — In this chapter you will learn how to:
• Identify Acute, Obtuse, Right and Straight Angles
• Evaluate Complementary and Supplementary Angles
• Convert between Degree Measure and Revolutions
• Classify Triangles by their Sides and Angles
• Solve problems involving Similar Triangles
• Draw an Angle in Standard Position
• Identify Quadrantal Angles and find their Trig Function values
• Learn and Use the Definitions of the Trigonometric Functions
• Determine the Ranges of the Trig Functions
• Derive and Use the Reciprocal and Quotient Trig Identities
##### Chapter 2 Videos — In this chapter you will learn how to:
• Learn the Right Triangle Trig definitions using SohCahToa
• Write a Trig Function in terms of its Cofuntion
• Solve Trig Equations using Cofunctions
• Evaluate Trig Function Values of Acute Angles
• Determine a Reference Angle
• Evaluate Trig Function Values of Non-Acute Angles
• Find Trig Function Values using a Calculator
• Find Angle Measures using a Calculator
• Solve problems involving Angle of Elevation and Angle of Depression
• Solve problems involving Right Triangles
##### Chapter 3 Videos — In this chapter you will learn how to:
• Define Radian Measure and show its relationship to a circle
• Apply Radian Measure to a circle’s physical attributes of Arc Length and Area of a Sector
• Use the Unit Circle to Define the Circular Functions
• Solve problems involving Linear and Angular Speed as an object moves in a circular path
##### Chapter 4 Videos — In this chapter you will learn how to:
• Derive the basic graphs of Sine, Cosine, Tangent, Cotangent, Secant and Cosecant
• Construct and analyze graphs involving translations of the Trig Function graphs
• Apply the Trig Function graphs to solve application problems involving Harmonic Motion
##### Chapter 5 Videos — In this chapter you will learn how to:
• Derive and memorize all the Identities: Fundamental, Sum and Difference, Cofunction, Double Angle and Half Angle
• Verify Trigonmetric Identities using two different methods
• Solve application problems using the Identities and algebra techniques
##### Chapter 6 Videos — In this chapter you will learn how to:
• Graph the Inverse Sine, Inverse Cosine and Inverse Tangent Functions
• Give exact values of all six Inverse Trig Functions by applying their ranges
• Solve equations involving the Inverse Trig Functions
• Solve Trigonometric Equations by factoring, using the Quadratic Formula, and substituting Trig Identities
• Solve Trigonometric Equations for all possible solutions
• Solve Trigonometric Equations with Multiple Angles
##### Chapter 7 Videos — In this chapter you will learn how to:
• Set up and solve triangle application problems using Law of Sines
• Set up and solve triangle application problems using the Ambiguous Case of the Law of Sines
• Set up and solve triangle application problems using Law of Cosines
• Perform Vector Operations
• Set up and solve application problems using vectors involving bearing, navigation, forces on an incline
##### Chapter 8 Videos — In this chapter you will learn how to:
• Solve equations with Complex Numbers by factoring and using the Quadratic Formula
• Convert between Rectangular Form and Complex Trigonometric Form
• Apply the Product and Quotient rules to the Trig Form of Complex Numbers
• Apply De Moivre’s Theorem to evaluate powers of Complex Numbers in Trig Form
• Apply the nth Root Theorem to evaluate roots of Complex Numbers in Trig Form

#### Math 250B Linear Algebra and Differential Equations

##### AB 705

State law AB 705 changed the way that students are placed into their Math courses. Some prerequisite courses have been eliminated. Other courses now have a support component to help students review the prerequisite material. The video below will guide you in choosing which Math class is right for you.

##### Placement
• Starting fall 2019, all incoming students will be placed into transfer-level math regardless of their preparation. There will be no more placement tests.
• Students will save money and time since they will be able to go straight into a transfer level course.
• In order to support our students in these difficult classes we have developed co-requisite classes that will be linked to many of our beginning transfer level math courses (Math 110, 115, 120, 130 and 141). These courses are designed to supplement the material of the course with review material that students need in order to be successful in the course.
• Students will be placed either into the stand-alone course or the course with the linked co-requisite based on their high school GPA. · Students may use our new online Guided Self Placement Tool in order to get placed into a math course. They can also see a counselor to help determine their placement.
• If a student is placed into the stand-alone course, but would prefer to have the support of the paired course they can always opt to take that course instead.

The Mathematics Department is dedicated to providing each student with an education that stresses high quality instruction. Our dynamic, knowledgeable faculty provides a supportive atmosphere which includes mentoring students through a “hands-on” approach to instruction. Students will gain the skills they need, whether they are working to meet professional goals, earn an AA or AS degree, or plan on transferring to a 4-year university.

##### What we offer:
• a full range of mathematics courses
• Supplemental Instruction in numerous courses
• courses taught using free Open Educational Resources
• the provision of a Math Learning Center where students may receive additional assistance
• the sponsoring of an on-campus Math Club which competes twice a year in a competition hosted by the American Mathematical Association of Two-Year Colleges Student Mathematics League

##### About the Department

Our department offers classes both throughout the day, and in the evenings. Classes are typically no more than 35 students, providing a low teacher-to-student ratio and increasing direct access to instructors. We offer Trigonometry, Finite Math, Statistics, College Algebra and Intermediate Algebra in online and/or hybrid formats. Our students have an exceptional rate of transfer to and success in U.C. system schools and other 4-year universities and colleges.