AP Courses

# AP Pre-Calculus

AP Pre-Calculus prepares students for advanced mathematical concepts they will encounter in college-level calculus

#### 90%

of students score

4 and above

#### 78%

students get a top score of

5 in

AP Pre-Calculus

#### 80%

students showed exceptional
performance in their first semester of

AP Pre-Calculus

## Course Concept

AP Pre-Calculus is a high school course designed to prepare students for the study of advanced mathematical concepts and topics. It serves as a bridge between algebra, geometry, and calculus, providing students with a solid foundation in mathematical skills and problem-solving strategies. It is divided in:

• Functions and Graphs: Students learn about different types of functions, including linear, quadratic, polynomial, rational, exponential, and logarithmic functions. They study the behavior and properties of functions, such as domain, range, symmetry, and transformations. Students also explore the graphical representations of functions and analyze their characteristics.
• Trigonometry: The course introduces students to trigonometric functions, identities, and equations. They learn how to solve triangles, apply trigonometric functions to real-world problems, and understand the relationships between angles and trigonometric ratios.
• Algebraic Manipulations: Students develop their algebraic skills and learn techniques for simplifying and manipulating algebraic expressions. They study topics such as factoring, rational expressions, complex numbers, and solving equations and inequalities.
• Sequences and Series: Students explore arithmetic and geometric sequences and series. They learn how to find the terms of a sequence, calculate the sums of series, and apply mathematical formulas to solve related problems.
• Probability and Statistics: The course introduces basic concepts of probability and statistics. Students learn about counting techniques, probability calculations, data analysis, and descriptive statistics.
• Problem Solving: AP Pre-Calculus emphasizes problem-solving skills and strategies. Students engage in solving complex mathematical problems, applying multiple concepts and techniques to find solutions. They develop critical thinking, analytical reasoning, and mathematical modeling skills.

#### Course Details:

Dedicated Test Prep Manager to Oversee Your Program

Test Reports

Personalized Assignments

150000

+ GST

/

\$

1850

## Syllabus

Best-in-class content by leading faculty and industry leaders in the form of videos, cases and projects, assignments and live sessions

1. Basic Algebraic Methods
• Real Numbers , Variables and Exponents
• Solving Linear Equations
• Solving Linear Inequalities
• Operations with Polynomials
• Factoring Polynomials
•  Special Products and Factoring Patterns
10. Graphing Trigonometric Functions
•  Periodic Functions and Their Graphs
•  Graphing Trigonometric Functions
•  Transformation of Trigonometric  Functions
•  Inverse Trigonometric Functions
11. Trigonometric Identities and Equations
•  Pythagorean Trigonometric Identities
•  Solving Trigonometric Equations
•  Sum and Difference Identities
•  Double - Angle Identities
•  Half -Angle Identities
12. Solving Triangles
•  The Area of a Triangle
•  The Law of Sines
•  The Law of  Cosines
13. Polar Coordinates And Parametric Equations
•  Parametric Equations
•  The Polar Coordinate system
•  The Polar form of Complex Numbers
•  Powers and Roots of Complex Numbers
14. Conic Sections and Their Equations
•  The Parabola
•  The Ellipse
•  The Hyperbola
•  General Equations of Conics
•  Polar Equations of Conics
15. Sequence Series and Counting
•  Arithmetic Sequences and Series
•  Geometry Sequences and Series
•  Generalized Sequences
•  Mathematical Induction
•  Permutations and Combinations
•  The Binomial Theorem
16.Calculus Preview
• Limits of Functions
• Slope of a Tangent Line
• Rules for Finding Derivatives
• Finding Antiderivatives
• Integration and Area Under a Curve
2. Rational and Irrational Expressions
• Operations with Rational Expressions
•  Simplifying Complex Fractions
3. Graphing and Systems of Equations
•  Graphing Points and Linear Equations
•  Midpoint and Distance Formulae
•  The Slope of a Line
•  Graphing a Linear Equation
•  Writing Equations of lines
•  Solving Linear Systems Graphically
•  Solving Linear System Algebraically
• Functions Concepts
• Quadratic Functions and Their Graphs
5. Complex Numbers and The Quadratic Formula
•  Functions  Concepts
•  Multiplying  and Dividing Complex Numbers
•  Completing the Square
6. Special Functions and Equations
•  AbsoluteValue Equations and Inequalities
•  Transformation of Graphs
•  Special functions and Their Graphs
•  Graphing Rational Functions
•  Rational Equations and Inequalities
7. Arrays and Array Lists
• One Dimensional Arrays
• Initialization
• Length Of array
• Traversing a One- Dimensional Array
• Arrays as Parameters
• Array Variable Parameters
• Array of Class Objects
• Analyzing Array Algorithms
• Array Lists
• The Arraylist Class
• The Methods Of Arraylist <E>
• Autoboxing And Unboxing
• Using Arraylist <E>
• Two Dimensional Arrays
• Declarations
• Matrix as Array of Row Arrays
• Two - Dimensional Array as parameter
7. Polynomial and Rational Functions
•  Divisions of Polynomial
•  Zeros of Polynomial functions
•  Solving Polynomial Functions
•  Graphing Polynomial Functions
•  Decomposing Rational Expression
8. Exponential And Logarithmic Functions
•  Inverse Functions
•  The Exponential Functions
•  The Logarithmic Functions
•  Logarithmic Laws and Equations
•  Exponential and Logarithmic Models
9. Trigonometry
•  Right- Triangle Trigonometry
•  The General Angle
•  Working with Trigonometric  Functions
•  Trigonometric Functions of Special Functions

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## Our Students have been accepted at

##### Experienced Tutors

Our team of teachers boasts the top 1% scores for the sections they teach.

All of our teachers have demonstrated an exceptional ability to convey material in a fun, personalized, and results-driven way.

##### One-on-One Learning

AP Guru offers highly customised and personalised SAT Prep delivered live online.

Our programs are one-on-one to ensure each student receives personalized attention.

##### Amazing Curriculum

Our curriculum includes strategy guides, classroom books, homework sets, and full-length tests.

Our curriculum is written by our tutors and founders based on their years of teaching experience.

##### Mentoring & Support

All of our students are paired with an experienced mentor to guide a student through his or her prep.

Our mentors are someone students can always talk to about anything related to their SAT Prep.

## Private Tutoring

AP Guru specializes in one-on-one teaching, empowering students with online personalized exam prep

##### With AP Guru, each student gets...
• their instructor’s undivided attention and a guided exploration of their subject with both theory and applications taught live in class.
• expert guidance at every step that involves interactive sessions, class notes, worksheets, class recordings, and access to past papers.
• specialist subject tutors who have graduated from top universities with a passion for teaching and a dedicated program manager to track your progress.

## Experienced Tutors

Our team of teachers boast top 1% scores for the subjects they teach. All of our teachers have demonstrated an exceptional ability to convey material in a fun, personalized, and results-driven way.

##### With AP Guru, each student gets...
• an experienced and certified online tutor
• a subject specialist that will convey essential concepts in a clear and easily understandable manner
• a teacher who is 99th percentile scorer in the subject he or she teaches

Between each class, you'll get personalized assignments so you master what you learned

##### With AP Guru, you will get...
• Topic-wise worksheets and graded assessments (with marking schemes) to ensure mastery of each topic tested on the school exams
• Doubt sessions after every couple of classes to review incorrect questions
• Additional worksheets on topic areas of concern

## Practice Papers

Practice for the exam with our library of Topic-wise Tests and Past Papers.

##### With AP Guru, you will get...
• detailed progress reports
• study materials for easy revision
• full-length mock papers, graded as per the grade boundaries and marking schemes.

## Mentoring & Support

At AP Guru, we pair you with an experienced mentor to guide you through the exam prep process.

##### With AP Guru, you will get...
• dedicated support to resolve doubts, convenient class schedules and reminders for important sessions
• Parents Teacher Meetings - We set up monthly parent teacher meetings for your to interact with the tutors

The AP Guru course ensures that each student is exam ready regardless of the initial academic level at which they stand.

• Track your progress including topic, class and homework discussion
• 10 Months of exhaustive exam prep to get you ready
• Last 2 months of Exam Improvement Pointers and Strategies for writing high-scoring answers.
##### One-to-One Classes

AP Guru offers highly customised and personalised SAT Prep delivered live online

##### Experienced Tutor

You will be paired with an experienced English and an experienced Math Tutor

##### Targeted Assessments

Between each class, you'll get personalized assignments so you master what you learned

##### Test Prep Manager

All of our students are paired with an experienced mentor to guide the student through his or her prep

##### Doubt Classes

We will conduct regular one-on-one feedback and doubt classes to go through your errors in mock tests and weekly assessments

##### Mock Tests

We offer more than 30 full length tests for our programs to our students with detailed explanations.

##### Test Analytics

For each test you take, you will receive detailed reports of your performance as well as question explanations

##### Study Plan

The program manager will set test schedules, create reminders, set up doubt sessions, etc.

##### Strategy Guides

Our AP Guru SAT Strategy Guides cover every concept and strategy tested on the SAT

##### Weekly Progress Reports

Our curriculum is written by our tutors and founders based on their years of teaching experience.

##### Web Portal

The AP Guru online portal contain 100+ hours of SAT content - detailed lesson notes, and additional practice

##### Parent Teacher Meetings

Parents Teacher Meeting - We set up monthly parent teacher meetings for your to interact with the tutors

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We have hand-selected a small group of highly qualified tutors who have mastery over teaching and helping students in the programs they teach. Our tutors also need to have significant previous teaching experience and be very gifted, dynamic teachers.

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We conduct our programs online.

Is this a live class? Will it be a group or private class?
All our classes are live instructor lead classes. All our academic tutoring are only one-on-one.

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All our classes are live instructor lead classes. All our academic tutoring are only one-on-one.

• When is the best time to get started?
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The earlier the better! When students come to us right before it is time to apply to college, there is only so much we can do. We can certainly help these students with score improvements and craft as compelling an application as possible, but we are given experiences and data points that cannot be altered.

When students come to us early in their educational careers, we pair them with a counselor to help them develop as applicants, students, and people early on. We help students strategize early, build their profiles, and stand out from their peers. We help students explore and develop their academic interests, engage in unique and meaningful extracurricular activities, strengthen their personal qualities and leadership skills, and ultimately, position them to get into the best schools possible.

It takes A LOT of hard work, strategy, determination, and self-reflection to get into the school of your dreams. At AP Guru, we are here, every step of the way, to help you get there.

• Do test prep courses work?
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Yes! Standardized tests focus on a small, unique set of skills and topics. By knowing exactly what types of questions are on the test, a student gains a distinct advantage. Furthermore, a great tutoring company can build on this advantage by providing a highly individualized learning experience and a wealth of fantastic strategies for all types of students.  We have the evidence from thousands of students across 10+ years that great improvement is possible for nearly everyone.

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No. We know that each student is different and has unique goals and aspirations. Our focus is to help each student excel in the tests and exams they are preparing towards.

• What kind of results should I expect?
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In terms of academic scores, for students not already at the top of the range, we typically want to see at least a 20 percentile rank improvement (the actual raw score this translates to varies across the scale). Going from the 50th to 70th percentile or from the 70th to 90th typically opens up a whole new range of schools for students.