High School
SAT
ACT
University
MCAT
LSAT
DAT
MATH 115

UA

Course Overview

Lessons & Practice

I. Welcome

41 sec
1. Quadratic Functions
5hr
2. Complex Numbers [Coming Soon!]
    3. Linear Equations and Inequalities
    2.4hr
    4. Functions
    1.5hr
    5. Transformations of Functions
    1.3hr
    6. Operations with Functions
    11min
    7. Polynomial Functions
    2.7hr
    8. Rational Functions
    1.7hr
    9. Exponential Functions
    1.8hr
    10. Logarithmic Functions
    34min
    11. Factoring Polynomials
    4hr
    12. Trigonometry
    1.3hr
    13. Trigonometric Ratios (Radians)
    53min
    14. Trigonometric (Sinusoidal) Graphs
    42min
    15. Trigonometric Identities & Proofs
    1hr
    16. Trigonometric Equations
    22min
    17. Vectors
    2.6hr
    18. Polar Coordinates
    25min
    Leave Feedback

    I Welcome

    Next
    Free Activity
    0:00 / 0:41
    Ask a Question

    Upgrade to Wizeprep Plus and get unlimited questions answered.

    Learn More
    Answered
    K
    Kunmi O
    What does this offer to help improve my math skills?
    J
    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
    J
    Jessica Y
    Instructor
    Equations represent relationships between variables. For example:
    • 2A=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+1 could represent the linear relationship between the variables x and y
    • x2+y2=4x^2+y^2=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+1 -- if you give this function any specific time input tt, it will output a number that represents the height of the tree at that specific time
    • For example, when t=3t=3 years, h=2(3)+1=7h=2\left(3\right)+1=7 meters.
    • Technically we can just write this function as h=2t+1h=2t+1, but the function notation h(t)=2t+1h\left(t\right)=2t+1 makes it very clear that the name of the function is hh (representing height of the tree), and the independent variable that this function takes in is tt (representing time in years)
    • The equation x2+y2=4x^2+y^2=4 is not a function because for the input value x=1x=1, the yy value can be either 3\sqrt{3} or βˆ’3-\sqrt{3}

    Let me know if you have any questions about this.
    Answered
    Sumayya N
    How to find zeros of a equation
    J
    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+6 We move everything to one side of the equation: xβˆ’1=0x-1=0 Then we solve for xx: x=1x=1
    • Quadratic equation: Solve x2=βˆ’5xβˆ’6x^2=-5x-6 We move everything to one side of the equation: x2+5x+6=0x^2+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, meaning that x=βˆ’2x=-2 or x=βˆ’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?
    J
    Jessica Y
    Instructor
    Great question! It's all about the practice πŸ˜„ 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?

    J
    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 πŸ˜„
    Answered
    J
    Johanna T
    Is this accessible to students across the globe or just Canada?
    J
    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?
    J
    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
    J
    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!
    J
    Jessica Y
    Instructor
    Awesome, glad to hear that! Let me know if you have any questions 😊
    Answered
    A
    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?
    J
    Jessica Y
    Instructor
    The most important/common functions are the following:
    • y=xy=x and its transformations
    • y=x2y=x^2 and its transformations
    • y=x3y=x^3 and its transformations
    • y=∣x∣y=\left|x\right| and its transformations
    • y=xy=\sqrt{x} and its transformations
    • y=1xy=\frac{1}{x} and its transformations
    • y=exy=e^x and its transformations
    • y=ln⁑ xy=\ln\ x and its transformations
    • y=sin⁑xy=\sin x and its transformations
    • y=cos⁑xy=\cos x and its transformations
    • y=tan⁑xy=\tan x and its transfromations
    Here's a tiktok that we made that covers some of these graphs πŸ˜„ 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?
    J
    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?
    J
    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?
    J
    Jessica Y
    Instructor
    Depends on the student :)
    Answered
    Melody T
    What classes are best for someone who is good at trigonometry?
    J
    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?
    J
    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 βˆ’βˆž-\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=a --> if the y value approaches ∞\infty or βˆ’βˆž-\infty, then we have a vertical asymptote
    Answered
    N
    Nikolaos T
    Is advanced functions or calculus more important to know?
    J
    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
    N
    Nikolaos T
    Career oppourtunites in math after high school
    J
    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
    N
    Nikolaos T
    Is calculus or advanced functions harder
    J
    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
    N
    Nikolaos T
    What’s a simple way to find the finite difference of degree 5
    J
    Jessica Y
    Instructor
    There is a formula for this, a5βˆ’b5=(aβˆ’b)(a4+a3b+a2b2+ab3+b4)a^5 - b^5 = (a - b)(a^4 + a^3b + a^2b^2 + ab^3 + b^4)
    Answered
    N
    Nikolaos T
    What is a easy way to remember end behaviours?
    J
    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?
    B
    Brian H
    They get easier with practice!
    Answered
    Sara M
    How do you find the horizontal asymptote?

    B
    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?
    B
    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?
    J
    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 πŸ˜„
    Answered
    Anonymous
    what if your line passes through the horizontal asymptote at 1 component?
    B
    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?
    B
    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
    T
    Taylor S
    How do I factor complex equations with variables.
    B
    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?
    S
    Sidrah S
    Depends on how you found advanced functions!
    Answered
    Anonymous
    How do you do an interval chart
    B
    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 πŸ“ƒ on the left to skip to parts you need help with
    • Watch the video β–Ά or read the written lessons πŸ“–
    • Speed up ⏩ or slow down βͺ the videos
    • Use the "Ask a question"❓ feature below each lesson/question any time!