MAC 1140C

UCF

Course Overview

Lessons & Practice

I. Welcome

41 sec

1. Functions (Basics)

1.7hr

1.1.1. Interval Notation 4 min

1.1.2. Set Notation3 min

1.1.3. Example4 min

1.1.4. Practice Level 12 min

1.1.5. Practice Level 252 sec

1.2.4. Practice Level 140 sec

1.2.5. Practice Level 23 min

1.2.6. Practice Level 32 min

1.3.1. Basic Functions & Their Graphs14 min

1.4.1. Basic Functions & Graph Properties11 min

1.4.2. Example3 min

1.4.3. Practice Level 14 min

1.4.4. Practice Level 22 min

1.4.5. Practice Level 34 min

1.5.1. Inverse Functions3 min

1.5.2. Example3 min

1.5.3. Practice Level 12 min

1.5.4. Practice Level 21 min

1.5.5. Practice Level 32 min

1.6.1. Piecewise Functions4 min

1.6.2. Example5 min

1.6.3. Practice Level 13 min

1.6.4. Practice Level 24 min

1.6.5. Practice Level 32 min

1.7.1. Operations with Functions3 min

1.7.2. Example2 min

1.7.3. Example

1.7.4. Practice Level 12 min

1.7.5. Practice Level 21 min

1.7.6. Practice Level 33 min

1.Q. Chapter 1 Quiz5 Qns

2. Transformations

1.4hr

2.1.1. Vertical Translations2 min

2.1.2. Horizontal Translations3 min

2.1.3. Example 3 min

2.1.4. Example 4 min

2.1.5. Example3 min

2.1.6. Practice Level 12 min

2.1.7. Practice Level 21 min

2.1.8. Practice Level 32 min

2.2.1. Vertical Reflections1 min

2.2.2. Horizontal Reflections2 min

2.2.3. Example3 min

2.2.4. Example3 min

2.2.5. Example3 min

2.2.6. Practice Level 12 min

2.2.7. Practice Level 22 min

2.2.8. Practice Level 32 min

2.3.1. Vertical Expansions & Compressions3 min

2.3.2. Horizontal Expansions & Compressions2 min

2.3.3. Example7 min

2.3.4. Example3 min

2.3.5. Practice Level 11 min

2.3.6. Practice Level 23 min

2.3.7. Practice Level 3

2.4.1. Combining Transformations4 min

2.4.2. Example1 min

2.4.3. Practice Level 12 min

2.4.4. Practice Level 23 min

2.4.5. Practice Level 34 min

2.5.1. Inverse Functions & Transformations5 min

2.5.2. Example

2.5.3. Practice Level 131 sec

2.5.4. Practice Level 23 min

2.5.5. Practice Level 33 min

2.Q. Checkpoint Quiz5 Qns

3. Polynomial Functions

2.7hr

3.1.1. Basic of Polynomials4 min

3.1.2. Example2 min

3.1.3. Practice Level 13 min

3.2.1. Polynomial Graphs & Characteristics4 min

3.2.2. Example2 min

3.2.3. Practice Level 12 min

3.3.1. Factoring 5 min

3.3.2. Factoring a Difference & Sum of Cubes3 min

3.3.3. Example2 min

3.3.4. Practice Level 146 sec

3.3.5. Practice Level 22 min

3.3.6. Practice Level 32 min

3.4.1. Factoring & Graphing Polynomials4 min

3.4.2. Example3 min

3.4.3. Example

3.4.4. Example2 min

3.4.5. Practice Level 12 min

3.4.6. Practice Level 23 min

3.4.7. Practice Level 3

3.5.1. Transformations of Cubic3 min

3.5.2. Example2 min

3.5.3. Transformations of Quartic Functions3 min

3.5.4. Example3 min

3.5.5. Practice Level 12 min

3.5.6. Practice Level 2

3.5.7. Practice Level 32 min

3.6.1. Dividing Polynomials - Long Division6 min

3.6.2. Example3 min

3.6.3. Dividing Polynomials - Synthetic Division8 min

3.6.4. Example2 min

3.6.5. Practice Level 12 min

3.6.6. Practice Level 2

3.6.7. Practice Level 33 min

3.7.1. Remainder Theorem, Factor Theorem, & Rational Root Theorem5 min

3.7.2. Factoring Polynomials (Degree 3+)6 min

3.7.3. Example5 min

3.7.4. Practice Level 154 sec

3.7.5. Practice Level 27 min

3.7.6. Practice Level 34 min

3.8.1. Solving Linear Equations3 min

3.8.2. Example2 min

3.8.3. Solving Quadratic Equations5 min

3.8.4. Example1 min

3.8.5. Practice Level 11 min

3.8.6. Practice Level 23 min

3.8.7. Practice Level 3

3.9.1. Solving General Polynomial Equations6 min

3.9.2. Example5 min

3.9.3. Practice Level 11 min

3.9.4. Practice Level 2

3.9.5. Practice Level 33 min

3.10.1. Example4 min

3.10.2. Example6 min

3.10.3. Practice Level 14 min

3.10.4. Practice Level 24 min

3.Q. Checkpoint Quiz5 Qns

4. Radical Functions

37min

4.1.1. Radical Functions59 sec

4.2.1. Transformations of Radical Functions3 min

4.2.2. Example: Transformations of Radical Functions2 min

4.2.3. Practice Level 11 min

4.2.4. Practice Level 23 min

4.2.5. Practice Level 3

4.3.1. Solving Radical Equations5 min

4.3.2. Example5 min

4.3.3. Practice Level 1

4.3.4. Practice Level 23 min

4.3.5. Practice Level 38 min

4.4.1. Example3 min

4.4.2. Practice Level 11 min

4.4.3. Practice Level 22 min

4.Q. Checkpoint Quiz5 Qns

5. Rational Functions

1.7hr

5.1.1. Reciprocal Functions2 min

5.1.2. Graphing Reciprocal Functions7 min

5.1.3. Example4 min

5.1.4. Example5 min

5.1.5. Example3 min

5.1.6. Practice Level 12 min

5.1.7. Practice Level 23 min

5.1.8. Practice Level 33 min

5.2.1. Rational Functions4 min

5.2.2. Example3 min

5.2.3. Example2 min

5.2.4. Example3 min

5.2.5. Practice Level 12 min

5.2.6. Practice Level 22 min

5.2.7. Practice Level 3

5.3.1. Graphing Rational Functions6 min

5.3.2. Example5 min

5.3.3. Example5 min

5.3.4. Example6 min

5.3.5. Practice Level 12 min

5.3.6. Practice Level 2

5.3.7. Practice Level 22 min

5.3.8. Practice Level 33 min

5.4.1. Solving Rational Equations3 min

5.4.2. Example5 min

5.4.3. Practice Level 152 sec

5.4.4. Practice Level 26 min

5.4.5. Practice Level 3

5.5.1. Example3 min

5.5.2. Practice Level 12 min

5.5.3. Practice Level 23 min

5.5.4. Practice Level 35 min

5.Q. Checkpoint Quiz6 Qns

6. Inequalities

42min

6.1.1. Solving Linear Inequalities Algebraically2 min

6.1.2. Example47 sec

6.1.3. Example51 sec

6.1.4. Practice Level 1

6.1.5. Practice Level 22 min

6.1.6. Practice Level 32 min

6.2.1. Solving Polynomial Inequalities using a Number Line3 min

6.2.2. Example5 min

6.2.3. Practice Level 1

6.2.4. Practice Level 24 min

6.2.5. Practice Level 33 min

6.3.1. Solving Polynomial Inequalities Using a Graph5 min

6.3.2. Example2 min

6.3.3. Practice Level 1

6.3.4. Practice Level 2

6.3.5. Practice Level 32 min

6.4.1. Solving Rational Inequalities 5 min

6.4.2. Example5 min

6.4.3. Practice Level 11 min

6.4.4. Practice Level 2

6.4.5. Practice Level 3

6.Q. Checkpoint Quiz6 Qns

7. Trigonometric Ratios (Radians)

53min

7.1.1. Radians vs. Degrees4 min

7.1.2. Converting Between Degrees and Radians2 min

7.1.3. Example1 min

7.1.4. Practice Level 11 min

7.1.5. Practice Level 1

7.1.6. Practice Level 1

7.1.7. Practice Level 22 min

7.1.8. Practice Level 3

7.2.1. Trigonometric Ratios in Radians9 min

7.2.2. Example4 min

7.2.3. Practice Level 13 min

7.2.4. Practice Level 22 min

7.2.5. Practice Level 32 min

7.3.1. Special Angles & Unit Circle in Radians3 min

7.3.2. Reciprocal Trigonometric Ratios: Special Angles & Unit Circle2 min

7.3.3. Example3 min

7.3.4. Practice Level 1

7.3.5. Practice Level 22 min

7.3.6. Practice Level 32 min

7.4.1. Solving Simple Trigonometric Equations3 min

7.4.2. Example2 min

7.4.3. Example 3 min

7.4.4. Practice Level 1

7.4.5. Practice Level 21 min

7.4.6. Practice Level 31 min

7.Q. Checkpoint Quiz5 Qns

8. Trigonometric (Sinusoidal) Graphs

42min

8.1.1. Graphs of Sinusoidal Functions3 min

8.2.1. Transformations of Sinusoidal Functions (Pt 1)5 min

8.2.2. Example3 min

8.2.3. Transformations of Sinusoidal Functions (Pt 2)4 min

8.2.4. Example2 min

8.2.5. Practice Level 13 min

8.2.6. Practice Level 2

8.2.7. Practice Level 32 min

8.3.1. Graphs of Reciprocal Trigonometric Functions3 min

8.3.2. Example2 min

8.3.3. Example 3 min

8.3.4. Practice Level 11 min

8.3.5. Practice Level 2

8.3.6. Practice Level 32 min

8.4.1. Equivalent Sinusoidal Functions (Radians)3 min

8.4.2. Example3 min

8.4.3. Practice Level 1

8.4.4. Practice Level 2

8.4.5. Practice Level 3

8.5.1. Applications of Trigonometric Functions19 sec

8.5.2. Example2 min

8.5.3. Practice Level 1

8.5.4. Practice Level 2

8.5.5. Practice Level 3

8.Q. Checkpoint Quiz5 Qns

9. Trigonometric Identities & Proofs

1hr

9.1.1. Equivalent Trigonometric Expressions2 min

9.1.2. Example1 min

9.1.3. Practice Level 1

9.1.4. Practice Level 2

9.1.5. Practice Level 3

9.2.1. Reciprocal & Quotient Identities2 min

9.2.2. Example57 sec

9.2.3. Practice Level 12 min

9.2.4. Practice Level 23 min

9.2.5. Practice Level 35 min

9.3.1. Pythagorean Identities2 min

9.3.2. Example1 min

9.3.3. Practice Level 13 min

9.3.4. Practice Level 22 min

9.3.5. Practice Level 37 min

9.4.1. Sum & Difference Identities2 min

9.4.2. Example1 min

9.4.3. Practice Level 1

9.4.4. Practice Level 2

9.4.5. Practice Level 2

9.4.6. Practice Level 2

9.4.7. Practice Level 3

9.5.1. Double Angle Identities2 min

9.5.2. Example4 min

9.5.3. Half-Angle Identities3 min

9.5.4. Example2 min

9.5.5. Practice Level 1

9.5.6. Practice Level 2

9.5.7. Practice Level 3

9.6.1. Proofs using Trigonometric Identities2 min

9.6.2. Example2 min

9.6.3. Example4 min

9.6.4. Practice Level 14 min

9.6.5. Practice Level 2

9.6.6. Practice Level 35 min

9.Q. Checkpoint Quiz5 Qns

10. Trigonometric Equations

22min

10.1.1. Solving Linear Trigonometric Equations4 min

10.1.2. Example3 min

10.1.3. Practice Level 1

10.1.4. Practice Level 21 min

10.1.5. Practice Level 33 min

10.2.1. Solving Quadratic Trigonometric Equations4 min

10.2.2. Example4 min

10.2.3. Practice Level 1

10.2.4. Practice Level 22 min

10.2.5. Practice Level 32 min

11. Exponential Functions

1.8hr

11.1.1. Investigating Integer Exponents6 min

11.1.2. Integer Exponents1 min

11.1.3. Practice1 min

11.1.4. Practice4 min

11.1.5. Practice3 min

11.2.1. Investigating Rational Exponents5 min

11.2.2. Rational Exponents2 min

11.2.3. Practice Level 19 min

11.2.4. Practice Level 24 min

11.2.5. Practice Level 34 min

11.3.1. Exponent Rules4 min

11.3.2. Example5 min

11.3.3. Practice Level 14 min

11.3.4. Practice Level 25 min

11.3.5. Practice Level 23 min

11.3.6. Practice Level 32 min

11.4.1. Solving Exponential Equations1 min

11.4.2. Example2 min

11.4.3. Practice Level 1

11.4.4. Practice Level 2

11.4.5. Practice Level 3

11.5.1. Characteristics of Exponential Functions2 min

11.5.2. Example53 sec

11.5.3. Practice Level 12 min

11.5.4. Practice Level 22 min

11.6.1. Transformations of Exponential Functions3 min

11.6.2. Example3 min

11.6.3. Practice Level 12 min

11.6.4. Practice Level 23 min

11.6.5. Practice Level 29 min

11.7.1. Applications of Exponential Functions1 min

11.7.2. Example2 min

11.7.3. Practice Level 14 min

11.7.4. Practice Level 25 min

11.7.5. Practice Level 33 min

11.Q. Checkpoint Quiz5 Qns

12. Logarithmic Functions

34min

12.1.1. Basics of Logarithms3 min

12.1.2. Example3 min

12.1.3. Practice Level 1

12.1.4. Practice Level 2

12.1.5. Practice Level 3

12.2.1. Logarithm Laws4 min

12.2.2. Example2 min

12.2.3. Example 2 min

12.2.4. Practice Level 1

12.2.5. Practice Level 2

12.2.6. Practice Level 32 min

12.3.1. Solving Logarithmic Equations2 min

12.3.2. Example2 min

12.3.3. Practice Level 1

12.3.4. Practice Level 22 min

12.3.5. Practice Level 31 min

12.4.1. Using Logarithms to Solve Exponential Equations1 min

12.4.2. Example58 sec

12.4.3. Practice Level 1

12.4.4. Practice Level 2

12.4.5. Practice Level 3

12.5.1. Characteristics of Logarithmic Functions2 min

12.5.2. Example57 sec

12.5.3. Practice Level 1

12.5.4. Practice Level 2

12.5.5. Practice Level 3

12.6.1. Transformations of Logarithmic Functions2 min

12.6.2. Example2 min

12.6.3. Practice Level 1

12.6.4. Practice Level 2

12.6.5. Practice Level 3

12.7.1. Applications of Logarithmic Functions30 sec

12.7.2. Example

12.7.3. Practice Level 1

12.7.4. Practice Level 2

12.7.5. Practice Level 3

12.Q. Checkpoint Quiz5 Qns

13. Combination of Functions

28min

13.1.1. Combining Families of Functions2 min

13.1.2. Example2 min

13.1.3. Practice Level 1

13.1.4. Practice Level 21 min

13.1.5. Practice Level 31 min

13.2.1. Sum & Difference1 min

13.2.2. Example60 sec

13.2.3. Practice Level 13 min

13.2.4. Practice Level 2

13.2.5. Practice Level 3

13.3.1. Product & Quotient of Functions2 min

13.3.2. Example2 min

13.3.3. Practice Level 1

13.3.4. Practice Level 22 min

13.3.5. Practice Level 31 min

13.4.1. Composition of Functions2 min

13.4.2. Example2 min

13.4.3. Practice Level 1

13.4.4. Practice Level 2

13.4.5. Practice Level 31 min

13.5.1. Solving Equations & Inequalities Graphically2 min

13.5.2. Example54 sec

13.5.3. Practice Level 1

13.5.4. Practice Level 245 sec

13.5.5. Practice Level 341 sec

13.Q. Checkpoint Quiz5 Qns

14. Rates of Change

24min

14.1.1. Average Rate of Change & the Secant Line2 min

14.1.2. Example

14.1.3. Practice Level 12 min

14.1.4. Practice Level 2

14.1.5. Practice Level 3

14.2.1. Instantaneous Rate of Change & the Tangent Line4 min

14.2.2. Example2 min

14.2.3. Practice Level 1

14.2.4. Practice Level 2

14.2.5. Practice Level 3

14.3.1. Graphs & Rates of Change

14.3.2. Example

14.3.3. Practice Level 1

14.3.4. Practice Level 2

14.3.5. Practice Level 3

14.4.1. Rates of Change of Polynomials1 min

14.4.2. Example3 min

14.4.3. Practice Level 1

14.4.4. Practice Level 2

14.4.5. Practice Level 3

14.5.1. Rates of Change of Trigonometric Functions1 min

14.5.2. Example2 min

14.5.3. Practice Level 1

14.5.4. Practice Level 2

14.5.5. Practice Level 3

14.6.1. Rates of Change of Exponential Functions1 min

14.6.2. Example3 min

14.6.3. Practice Level 1

14.6.4. Practice Level 2

14.6.5. Practice Level 3

14.7.1. Rates of Change of Logarithmic Functions2 min

14.7.2. Example2 min

14.7.3. Practice Level 1

14.7.4. Practice Level 2

14.7.5. Practice Level 3

14.Q. Checkpoint Quiz13 Qns

15. Permutations and Combinations [BC/AB]

1.8hr

15.1.1. Fundamental Counting Principle4 min

15.1.2. Example5 min

15.1.3. Example: Fundamental Counting Principle w/ Cases3 min

15.1.4. Example: Fundamental Counting Principle w/ Complements4 min

15.1.5. Counting Elements & Tree Diagrams4 min

15.1.6. Example: Tree Diagrams3 min

15.1.7. Example: Counting Choices w/ Trees3 min

15.1.8. Example: Counting Elements w/ Trees8 min

15.1.9. Practice: Fundamental Counting Principle2 min

15.1.10. Practice: Fundamental Counting Principle w/ Cases5 min

15.1.11. Practice: Counting Outcome w/ Trees6 min

15.1.12. Practice: Counting Elements w/ Trees7 min

15.2.1. Factorial Symbol (!)3 min

15.2.2. Permutations3 min

15.2.3. Example5 min

15.2.4. Example3 min

15.2.5. Example: Permutation w/ Repeated Objects1 min

15.2.6. Practice2 min

15.2.7. Practice: Permutation w/ Repeated Objects4 min

15.3.1. Combinations5 min

15.3.2. Example: Combination Notation3 min

15.3.3. Example: Splitting up a Group w/ Combination2 min

15.3.4. Example: Combinations6 min

15.3.5. Example: Combinations w/ Cards3 min

15.3.6. Practice: Combination Notation3 min

15.3.7. Practice: Combinations5 min

15.3.8. Practice: Combinations w/ Cards2 min

15.3.9. Practice: Combinations3 min

15.4.1. Binomial Theorem

15.4.2. Example

15.4.3. Practice

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Answered

Kunmi O

What does this offer to help improve my math skills?

Jessica Y

Instructor

Hello! This course covers all the math concepts that students typically learn in a grade 12 math class (advanced functions or pre-calculus class). By going over the activities in this course, you will also be more prepared to take any first year calculus class at the university or college level.

Answered

Sumayya N

The difference between functions and equations 

Jessica Y

Instructor

Equations represent relationships between variables. For example:
2A=3B+12A=3B+12A=3B+1 could mean that twice the age of Adam is the same as one more than triple the age of Betty

y=2x+1y=2x+1y=2x+1 could represent the linear relationship between the variables x and y

x2+y2=4x^2+y^2=4x2+y2=4 is the equation of a circle

Functions are like equations, but for every input value it takes it, it can only return one output. For example:
The height of a tree (in meters) at time t (in years) could be given by the function h(t)=2t+1h\left(t\right)=2t+1h(t)=2t+1 -- if you give this function any specific time input ttt, it will output a number that represents the height of the tree at that specific time
For example, when t=3t=3t=3 years, h=2(3)+1=7h=2\left(3\right)+1=7h=2(3)+1=7 meters.
Technically we can just write this function as h=2t+1h=2t+1h=2t+1, but the function notation h(t)=2t+1h\left(t\right)=2t+1h(t)=2t+1 makes it very clear that the name of the function is hhh (representing height of the tree), and the independent variable that this function takes in is ttt (representing time in years)

The equation x2+y2=4x^2+y^2=4x2+y2=4 is not a function because for the input value x=1x=1x=1, the yyy value can be either 3\sqrt{3}3​ or −3-\sqrt{3}−3​

Let me know if you have any questions about this.

Answered

Sumayya N

How to find zeros of a equation  

Jessica Y

Instructor

We rearrange the equation so that everything is on one side of the equation, and the other side just has a zero, then there are many techniques we can use to solve for the solutions (i.e. zeros) of that equation.

For example:
Linear equations: Solve 5+2x=x+65+2x=x+65+2x=x+6
We move everything to one side of the equation: x−1=0x-1=0x−1=0
Then we solve for xxx: x=1x=1x=1

Quadratic equation: Solve x2=−5x−6x^2=-5x-6x2=−5x−6
We move everything to one side of the equation: x2+5x+6=0x^2+5x+6=0x2+5x+6=0
Then we can factor, complete the square, use quadratic formula, or graph this equation to find the solutions: (x+2)(x+3)=0\left(x+2\right)\left(x+3\right)=0(x+2)(x+3)=0, meaning that x=−2x=-2x=−2 or x=−3x=-3x=−3

Higher degree polynomial equations (like cubics, quartics, etc.)
We still move everything to one side of the equation, then we use factor theorem or graphing to find the solutions

In this course, you will learn how to find the zeros (solutions) of polynomial equations that have degree 3+.

Let me know if you have any questions.

Answered

Anonymous

How can I go from being bad at math to really good at it, almost at a genius level?

Jessica Y

Instructor

Great question! It's all about the practice 😄 Math is like a language, if you want to be fluent at speaking Italian, you have to practice it a lot, same goes for math.

This course has short and concise videos that explains each of the important pre-calculus/advanced functions concepts, but you have to try the practice questions on your own so that you can get great at it!

Let me know if you have any questions. You can do this!

Answered

Anonymous

Do we ask our math questions here? And how long until we get an answer?

Jessica Y

Instructor

There's a Q&A box within each activity, so if you have a question pertaining to any specific activity or concept, you can ask there and then. We usually get back to you within 24 hours or shorter 😄

Answered

Johanna T

Is this accessible to students across the globe or just Canada?

Jessica Y

Instructor

Anyone can access and benefit from our content and resources, but we are curently focusing on aligning our materials with the curricula in North America. Let me know if you have any other questions :)

Answered

Daniel M

What level of math is typical for a college freshman?

Jessica Y

Instructor

It depends on what college program you are enrolled in. For example, if you are in engineering, physical science, or life science, you will typically need calculus in your freshman year. So this pre-calc course will be very helpful in building the foundations you need. On the other hand, if you are enrolled in for example, businesss, economics, or english lit, you probably won't need calculus, in which case you likely won't need to know all of the concepts covered in this pre-calc course.

Let me know if you have any other questions :)

Answered

Brynn H

How often should I practice 

Jessica Y

Instructor

Learning math is like learning a new language, all the concepts build on one another, and you should practice as much as you can. If you are currently taking a math course, I recommend doing at least 20-30 minutes of review and practice every day on top of the lessons in school.

Answered

Anonymous

This looks like an awesome platform that can help me study!

Jessica Y

Instructor

Awesome, glad to hear that! Let me know if you have any questions 😊

Answered

Aidan W

Are there any patters, acronyms, or just easy ways I can use to help me remember the 12 basic functions and their shapes?

Jessica Y

Instructor

The most important/common functions are the following:
y=xy=xy=x and its transformations
y=x2y=x^2y=x2 and its transformations
y=x3y=x^3y=x3 and its transformations
y=∣x∣y=\left|x\right|y=∣x∣ and its transformations
y=xy=\sqrt{x}y=x​ and its transformations
y=1xy=\frac{1}{x}y=x1​ and its transformations
y=exy=e^xy=ex and its transformations
y=ln⁡ xy=\ln\ xy=ln x and its transformations
y=sin⁡xy=\sin xy=sinx and its transformations
y=cos⁡xy=\cos xy=cosx and its transformations
y=tan⁡xy=\tan xy=tanx and its transfromations
Here's a tiktok that we made that covers some of these graphs 😄
https://www.tiktok.com/@wizeprep/video/6880349335243083009?is_copy_url=1&is_from_webapp=v1

Answered

Melody T

Are end behaviors really important to memorize?

Jessica Y

Instructor

End behaviours help us determine the shape of the graph, which is very important when you take calculus courses at the university or college level.

Answered

Melody T

How often should I practice?

Jessica Y

Instructor

Learning math is like learning a language, you can to continuously use it and practice with it to get good at it. I recommend doing at least 15-30 minutes of math practice each day if you are taking a math course.

Answered

Melody T

What is the hardest part to learn?

Jessica Y

Instructor

Depends on the student :)

Answered

Melody T

What classes are best for someone who is good at trigonometry?

Jessica Y

Instructor

There's no specific course that is only trigonometry focused, but if you take pre-calculus (a.k.a advanced functions), you will need trigonometry.

Answered

Melody T

What did you do with your graph when it was an infinite answer?

Jessica Y

Instructor

When it comes to graphing, there are two "types" of infinities
You can look at the graph as x goes to ∞\infty∞ or −∞-\infty−∞ --> if the y value approaches a certain value, then we have a horizontal asymptote
You can look at the graph as x approaches a certain point x=ax=ax=a --> if the y value approaches ∞\infty∞ or −∞-\infty−∞, then we have a vertical asymptote

Answered

Nikolaos T

Is advanced functions or calculus more important to know?

Jessica Y

Instructor

They are both necessary if you plan on taking a college or university program that requires an intro to calculus (or calculus I) course. In Ontario, students usually take advanced functions before they could even take Calculus because the topics in Calculus depends on the topics in Advanced Functions.

Here's a quick breakdown of what you will learn in both courses:
Advanced functions: 
You'll learn important functions such as polynomials, reciprocals, trigonometric functions, exponential functions, and log functions
You'll learn how to graph these functions and their transformations
You'll learn how to work with these functions in application problems
You'll learn how to combine these functions
This course will introduce you to "rates of change", which is the big part of calculus
Calculus and Vectors:
You'll learn the meaning of "rates of change" of functions
You'll learn how to find the rates of change of the functions you learned in Advanced functions
You'll learn how to work with rates of change application problems
You'll learn about vectors in 2D and 3D space
You'll learn about application problems with 2D and 3D vectors

I hope this helps :)

Answered

Nikolaos T

Career oppourtunites in math after high school

Jessica Y

Instructor

There are lots of opportunities for careers that require math! For example, if you want to go into engineering, architecture, health care, data analysis & computers, construction, etc.

Answered

Nikolaos T

Is calculus or advanced functions harder

Jessica Y

Instructor

It depends on what you like and how strong your existing math background is. Our Wize courses are designed for students at all levels, so you can learn at your own pace. But students in Ontario are typically required to take advanced functions before they can take calculus.

Answered

Nikolaos T

What’s a simple way to find the finite difference of degree 5 

Jessica Y

Instructor

There is a formula for this, a5−b5=(a−b)(a4+a3b+a2b2+ab3+b4)a^5 - b^5 = (a - b)(a^4 + a^3b + a^2b^2 + ab^3 + b^4)a5−b5=(a−b)(a4+a3b+a2b2+ab3+b4)

Answered

Nikolaos T

What is a easy way to remember end behaviours?

Jessica Y

Instructor

The end behaviour of each graph and function could look different, I don't recommend memorizing or remembering the end behaviours of different graphs, I recommend learning the process for finding end behaviours. Take a look at the examples and questions in this section to learn more: https://www.wizeprep.com/online-courses/16857/chapter/4/core/1/1

Answered

Parneet S

Why are logarithm so hard?

Brian H

They get easier with practice!

Answered

Sara M

How do you find the horizontal asymptote?

Brian H

Please take a look at the lesson talking about this topic :)

Answered

Sara M

what if your line passes through the horizontal asymptote at 1 component?

Brian H

This is okay and happens sometimes. We only really worry about asymptotes at the very "ends" of our graph. Typically far to the left or right.

Answered

Anonymous

I passed pre-calc 11, is calculus 12 a lot harder then pre-calc 11?

Jessica Y

Instructor

Pre-Calc 12 extends a lot of the concepts in pre-calc 11, and introduces some new ones as well. This course goes over all the concepts in pre-calc 12, so if you're having trouble with any of the concepts, just find the corresponding chapter and we should be able to help 😄

Answered

Anonymous

what if your line passes through the horizontal asymptote at 1 component?

Brian H

Typically we think of asymptotes very far out. (the asymptote might be crossed closer to the origin for example)

Answered

Anonymous

I barely passed any high school math, how hard is it going to be for me?

Brian H

This is a tough question for anyone to answer. I'm confident if you put in the time you will succeed - and Wize is here to help! :)

Answered

Taylor S

How do I factor complex equations with variables.

Brian H

Take a look at the Polynomial Functions chapter and factoring sections!

Answered

Emma R

I haven’t had calc yet, is it hard?

Sidrah S

Depends on how you found advanced functions!

Answered

Anonymous

How do you do an interval chart 

Brian H

Take a look at the Inequalities section!

Welcome to Grade 12 Math!
My name is Brian and I'm the instructor for this course. Feel free to go through this course at your own pace
Use the table of contents 📃 on the left to skip to parts you need help with
Watch the video ▶ or read the written lessons 📖
Speed up ⏩ or slow down ⏪ the videos
Use the "Ask a question"❓ feature below each lesson/question any time!

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MAC 1140C

Course Overview

1. Functions (Basics)

2. Transformations

3. Polynomial Functions

4. Radical Functions

5. Rational Functions

6. Inequalities

7. Trigonometric Ratios (Radians)

8. Trigonometric (Sinusoidal) Graphs

9. Trigonometric Identities & Proofs

10. Trigonometric Equations

11. Exponential Functions

12. Logarithmic Functions

13. Combination of Functions

14. Rates of Change

15. Permutations and Combinations [BC/AB]

16. Conics [BC/AB]

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