# English, Math, Statistics

Crash Courses

## PREPARATION COURSE FOR STUDENTS ENTERING COLLEGE ENGLISH 101

### ARE YOU READY?

#### Description:

This crash course is designed to offer a foundation for students who want to enter college English 101 classes.

As you may know, the pre-requisite classes, which traditionally taught the basics for English 101 have been eliminated. We believe this failure by curricula administrators unnecessarily sets students up for failure.

Our goal is to offer courses that will prepare you for English 101 and beyond.

Topics include Listening, Reading, and Writing.

The course is designed so new students can join at any given time and consists of 6 Sessions, each lasting 1.5 hours for a total of 9 hours of instruction.

Offering a workshop environment, in addition to lectures, problemsolving, and quizzes, each session emphasizes a practical approach, wherein students are encouraged to gain hands-on skills by participating in discussion and role-play.

#### Course Objective:

### Skills to be learned during this course:

Session | Topic | Duration |
---|---|---|

Session 1 | LISTENING / READING SKILLS | 1.5 Hours |

Basic exercises for better comprehension | ||

Session 2 | WRITING SKILLS | 1.5 Hours |

Basic sentence structure | ||

Punctuation | ||

Contractions | ||

Upper case vs. Lower-case letter usage | ||

Proper use of tense | ||

Singular v. Plural | ||

Gender distinction | ||

Session 3 | PARAGRAPH STRUCTURE | 1.5 Hours |

Maintaining your focus / Consistency | ||

Using appropriate content | ||

How to avoid slang usage | ||

Delivering the information to the reader | ||

Session 4 | 1.5 Hours | |

Proper usage skills | ||

Internet / Social Media | ||

Benefits | ||

Dangers | ||

Session 5 | FINAL EXAM PREPARATION | 1.5 Hours |

During this module, students will be presented with several challenges to test student strengths and weaknesses. As a result, students will be able to “fine tune” their skills and will be ready for the final exam. | ||

Session 6 | FINAL EXAM | 1.5 Hours |

## COLLEGE PREP COURSE FOR STEM MAJORS

#### Description:

This crash course is designed for students who want to take Calculus or Precalculus in the upcoming school year.

Topics include algebraic, exponential, logarithmic, and trigonometric functions and their inverses and identities.

The course is designed so new students can join at any given time and consists of 12 sessions, each lasting 1.5 hours for a total of 18 hours.

#### Course Objective:

### Skills to be learned during this course:

- Determine whether a relation represents a function. If it is a function, determine its domain and range; determine whether it is odd or even or neither based on its formula or its graph; and determine whether it is one-to-one, and if it is, assess its inverse function and its domain and range
- Analyze and graph a given function, including but not limited to piecewise-defined, polynomial, rational, exponential, logarithmic, trigonometric, and inverse trigonometric functions, without the aid of graphing devices.
- Determine intercepts, coordinates of holes, and equations of asymptotes. Determine intervals on which polynomial and rational functions are positive and negative.
- Use transformation techniques, including vertical and horizontal shifts, compression, stretching, and reflection over the x- or y-axis to sketch the graph of a function.
- Use transformation techniques, including vertical and horizontal shifts, compression, stretching, and reflection over the x- or y-axis to sketch the graph of a function.
- Use the language and standard mathematical notation of the algebra of functions.
- Determine algebraic combinations and compositions of functions and state their domains. Write a given function as a composition of two non-identity functions.
- Use techniques and facts, including synthetic division, long division, the Fundamental Theorem of Algebra, and the Rational Zeros Theorem, to find all complex zeros of a polynomial function of degree three or higher and write the function in a completely factored form.
- From memory, state and apply the definitions of the six trigonometric ratios of sides of right triangles; the definitions of the six trigonometric functions of real numbers using the unit circle; and the definitions, domains, and ranges of the inverse sine, inverse cosine, and inverse tangent functions.
- Evaluate trigonometric functions at integer multiples of pi over six and pi over 4, including values outside zero to two pi, without using notes or calculators. Evaluate compositions of trigonometric and inverse trigonometric functions, including ones for which cancellation equations do not apply.
- From memory, state and apply the fundamental reciprocal, quotient, and Pythagorean trigonometric identities and the sum, difference, double-angle, and half-angle identities for sine and cosine.
- Prove trigonometric identities, including those that require sum, difference, double-angle, and half-angle identities.
- Solve polynomial, rational, exponential, logarithmic, and trigonometric equations.
- Evaluate, manipulate, and interpret summation notation.

#### Tentative Course Schedule:

Session | Topic | Duration |
---|---|---|

Session 1 | Functions: | 1.5 Hours |

Their properties and graphs | ||

Session 2 | Polynomials: | 1.5 Hours |

Rules of exponents | ||

Expanding and factoring | ||

Session 3 | Polynomials: | 1.5 Hours |

(Continued) | ||

Session 4 | Rational Functions | 1.5 Hours |

Session 5 | Rational Functions | 1.5 Hours |

(Continued) | ||

Session 6 | Rational Expressions | 1.5 Hours |

(Continued) | ||

Session 7 | Exponential and Logarithmic Functions and Expressions | 1.5 Hours |

Session 8 | Exponential and Logarithmic Functions and Expressions | 1.5 Hours |

(Continued) | ||

Session 9 | Trigonometric Functions and Identities | 1.5 Hours |

Session 10 | Trigonometric Functions and Identities | 1.5 Hours |

(Continued) | ||

Session 11 | Trigonometric Functions and Identities | 1.5 Hours |

(Continued) |

#### Note:

The course is designed so new students can join at any given time.

## COLLEGE PREP COURSE STATISTICS

#### Description:

This crash course is designed for students who want to take Statistics in the upcoming school year.

The course introduces the mathematical and statistical concepts necessary for understanding and applying statistics. Topics include fundamental arithmetic, algebra, and graphical representation of data. Emphasis is placed on building a solid mathematical foundation and developing critical thinking skills essential for success in further statistical studies.

The course is designed so new students can join at any given time and consists of 12 sessions, each lasting 1.5 hours for a total of 18 hours.

#### Tentative Course Schedule:

Session | Topic | Duration |
---|---|---|

Session 1 | Review of basic arithmetic | 1.5 Hours |

The number line, addition, subtraction, multiplication, division, and order of operations | ||

Session 2 | Solving equations and inequalities. | 1.5 Hours |

Session 3 | Graphing linear equations. | 1.5 Hours |

Session 4 | Laws of exponents | 1.5 Hours |

Session 5 | Data Analysis: | 1.5 Hours |

Measure of central tendency: Mean, median, mode | ||

Session 6 | Data Analysis: | 1.5 Hours |

(Continued) Measure of Variability: range, variance, standard deviation | ||

Session 7 | Data Analysis | 1.5 Hours |

(Continued) Graphical representation of data. | ||

Session 8 | Probability: | 1.5 Hours |

Basic concepts. | ||

Session 9 | Probability Distributions and the binomial probability distribution | 1.5 Hours |

Session 10 | The normal probability distribution. | 1.5 Hours |

Session 11 | Estimation: | 1.5 Hours |

Point estimates and interval estimation | ||

Session 12 | An Introduction to hypothesis testing | 1.5 Hours |