Math Competitions

CEMC Grade 12 Advanced Functions and Pre-Calculus

The CEMC Grade 12 Advanced Functions and Pre-Calculus course is designed to challenge and inspire students in their math skills.

78%

of students score

90%

students get a top score of

CEMC Grade 12 Advanced Functions and Pre-Calculus

80%

students showed exceptional
performance in their first semester of

CEMC Grade 12 Advanced Functions and Pre-Calculus

Course Concept

The CEMC (Centre for Education in Mathematics and Computing) Grade 12 Advanced Functions and Pre-Calculus course is a comprehensive educational program designed to provide high school students with a solid foundation in advanced mathematical concepts and skills. This course focuses on preparing students for post-secondary studies in mathematics, engineering, science, and other related fields. It covers a wide range of topics, from advanced algebra and trigonometry to functions and calculus, equipping students with the knowledge and problem-solving abilities necessary for success in higher education. Here's a detailed overview of the CEMC Grade 12 Advanced Functions and Pre-Calculus course:

  • Purpose and Scope: The primary purpose of this course is to deepen students' understanding of mathematical concepts and to prepare them for advanced studies in mathematics-related fields. The course emphasizes the development of critical thinking, problem-solving skills, and mathematical reasoning.
  • Target Audience: The Grade 12 Advanced Functions and Pre-Calculus course is intended for high school students in their final year who are pursuing careers or further education in mathematics, engineering, science, computer science, and related disciplines.
  • Advanced Topics: The course covers a wide range of advanced topics, including but not limited to functions, trigonometry, polynomial and rational functions, exponential and logarithmic functions, and calculus.
  • Problem-Solving Emphasis: The course places a strong emphasis on problem-solving, requiring students to apply their mathematical knowledge to complex and real-world problems.
  • Calculus Introduction: The course introduces students to calculus concepts, including limits, derivatives, and applications of derivatives, providing a solid foundation for higher-level calculus courses.

CEMC Grade 12 Advanced Functions and Pre-Calculus

Course Details:

Dedicated Test Prep Manager to Oversee Your Program

Test Reports

Personalized Assignments

150000

+ GST

/

$

1850

SET UP A TRIAL

Syllabus

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

COURSE SYLLABUS PDF
1. Functions: Transformations and Properties
  • Relations and Functions
  • Interval Notation and Definitions
  • Solving Linear Inequalities
  • Graphing Five Base Functions
  • Translations
  • Reflections
  • Stretches
  • Combining Transformations
  • Inverses
2. Polynomial Functions
  • Introduction to Polynomial Functions
  • Transformations of Simple Polynomial Functions
  • Characteristics of Polynomial Functions
  • Graphs of Polynomial Functions in Factored Form
  • Equations of Polynomial Functions in Factored Form
  • Finite Differences of Polynomial Functions
  • Even and Odd Polynomial Functions
3. Polynomial Equations and Inequalities
  • Division of Polynomials
  • The Remainder and Factor Theorems
  • Factoring Polynomials Using the Factor Theorem
  • Methods of Factoring Polynomials
  • Solving Polynomial Equations
  • Solving Polynomial Inequalities
  • Solving Polynomial Equations and Inequalities Using Technology
4. Rational Functions
  • The Reciprocal of a Polynomial Function
  • Vertical Asymptotes and Discontinuity
  • End Behaviour Asymptotes
  • Rational Functions of the Form  y=ax+b/cx+d
  • Analyzing and Comparing Rational Functions
  • Solving Rational Equations
  • Solving Rational Inequalities
5. Exponential and Logarithmic Functions
  • Exponential Functions
  • Solving Exponential Equations
  • Modelling Exponential Behaviour
  • Logarithmic Functions
  • Properties and Laws of Logarithms
  • Solving Exponential and Logarithmic Equations
6. Trigonometric Functions
  • Radian Measure
  • The Unit Circle
  • Trigonometric Ratios and Special Triangles
  • Graphs of Primary Trigonometric Functions
  • Graphs of Reciprocal Trigonometric Functions
  • Transformations of the Sine and Cosine Functions
  • Working with Sinusoidal Functions
  • Applications with the Sine and Cosine Functions
7. Trigonometric Identities and Equations
  • Equivalent Trigonometric Expressions
  • Proving Trigonometric Identities
  • Compound Angle Formulas
  • Double Angle Formulas
  • Solving Trigonometric Equations
8. Operations on Functions
  • Sums and Differences of Functions
  • Products and Quotients of Functions
  • Composition of Functions
  • Solving Equations and Inequalities
9. Rates of Change
  • Determining Average and Approximating Instantaneous Rates of Change for Linear, Polynomial, and Rational Functions
  • Determining Average and Approximating Instantaneous Rates of Change with Exponential and Trigonometric Functions
  • Moving from Secants to Tangents
  • Using Limits to Find Slopes and Equations of Tangents

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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.

The AP Guru Advantage

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

Graded Assessments

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...
  • a Program Manager to help you at every step
  • 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

Grade Improvement: Exam Ready

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

Exam Ready
  • 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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FAQs

Frequently Asked Questions

Read some of the most commonly asked questions by parents and students
  • Who are the AP Guru 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.

  • Where are your Programs held?
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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.

  • Is this a live class? Will it be a group or private class?
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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.

  • Do you only help students who want to go to top schools?
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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.