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Master Linear-Quadratic Systems: Solve Complex Equations

Grade 11 Math: Master Advanced Concepts & Skills

11F.A1.1

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Introduction to quadratic functions

Domain and range of a function

Identifying functions

Function notation

Absolute value functions

Expressing an Absolute Value Linear Function as a Piecewise Function

Expressing an Absolute Value Quadratic Function as a Piecewise Function

11F.A1.2

Characteristics of quadratic functions

Quadratic function in general form: y = ax^2 + bx + c

Graphing quadratic functions: General form VS. Vertex form

11F.A1.3

Graphing reciprocals of linear functions

Graphing reciprocals of quadratic functions

11F.A1.4

Inverse functions

11F.A1.5

Finding inverse trigonometric function from its graph

11F.A1.6

One to one functions

11F.A1.8

Transformations of functions: Horizontal translations

Transformations of functions: Vertical translations

Transformations of functions: Horizontal stretches

Transformations of functions: Vertical stretches

11F.A1.9

Combining transformations of functions

11F.A2.1

Nature of roots of quadratic equations: The discriminant

11F.A2.2

Shortcut: Vertex formula

Converting general form into vertex form by applying the vertex formula

Vertex Formula Application

11F.A2.3

Applications of quadratic functions

Applications of quadratic equations

11F.A2.4

Transformations of quadratic functions

Finding the quadratic functions for given parabolas

11F.A2.5

System of linear-quadratic equations

11F.A3.1

Factor by taking out the greatest common factor

Factor by taking out GCF

Factoring trinomials

Factoring Trinomials

Multiplying polynomial by polynomial

11F.A3.2

Multiplying radicals

Multiplying Radicals

Operations with radicals

Operations with Radicals

11F.A3.3

Simplifying rational expressions and restrictions

Adding and subtracting rational expressions

Adding and Subtracting Rational Expressions

Multiplying rational expressions

Multiplying Rational Expressions

Multiplying Rational Expressions in Factored Form

Dividing rational expressions

Dividing Rational Expressions

Dividing Rational Expressions in Factored Form

11F.B1.1

Graphing exponential functions

11F.B1.2

Exponents: Rational exponents

11F.B1.3

Convert between radicals and rational exponents

11F.B2.2

Graphing transformations of exponential functions

11F.B2.4

Solving exponential equations using exponent rules

11F.B2.5

Finding an exponential function given its graph

11F.B3.2

Exponential growth and decay by a factor

Exponential decay: Half-life

Exponential growth and decay by percentage

11F.C1.1

Introduction to sequences

11F.C1.5

Pascal's triangle

Pascal's Triangle

Pascal"s Triangle

Pascal"s triangle

11F.C1.6

Binomial theorem

11F.C2.1

Arithmetic sequences

Geometric sequences

11F.C2.3

Arithmetic series

Arithmetic series formula

Geometric series

Geometric Series

11F.C3.1

Simple interest

Simple Interest — Word Problem

Basic Concepts of Simple Interest – Word Problem

Borrowing Money for More Than One Year  – Word Problem

Investigate the Advantages of Borrowing Money  – Word Problem

11F.C3.2

Finance: Compound interest

Finance: Compound Interest

11F.C3.5

Finance: Future value and present value

11F.D1.1

Find the exact value of trigonometric ratios

11F.D1.3

ASTC rule in trigonometry (<b>A</b>ll <b>S</b>tudents <b>T</b>ake <b>C</b>alculus)

ASTC rule in trigonometry

11F.D1.4

Inverse reciprocal trigonometric function: finding the exact value

Inverse Reciprocal Trigonometric Function: Finding the Exact Value

11F.D1.5

Quotient identities and reciprocal identities

Pythagorean identities

11F.D1.6

Law of sines

Ambiguous case: SSA triangles

Law of cosines

Applications of the sine law and cosine law

11F.D2.1

Sine graph: y = sin x

Cosine graph: y = cos x

Tangent graph: y = tan x

11F.D2.5

Graphing transformations of trigonometric functions

11F.D2.8

Determining trigonometric functions given their graphs

11F.D3.2

Ferris wheel trig problems

Tides and water depth trig problems

Spring (simple harmonic motion) trig problems

<p>Aligned with your class and textbook, our comprehensive Grade 11 math help covers all topics that you would expect in any typical grade 11 math classes, whether it&apos;s <a href="http://www.edu.gov.on.ca/eng/curriculum/secondary/grade11.html">Ontario math curriculum</a>, <a href="https://curriculum.gov.bc.ca/curriculum/10-12#m">B.C.</a>, <a href="https://education.alberta.ca/mathematics-10-12/programs-of-study/">Alberta</a>, <a href="http://www.edu.gov.mb.ca/k12/cur/math/framework_9-12/index.html">Manitoba</a>, <a href="https://www.curriculum.gov.sk.ca/webapps/moe-curriculum-BBLEARN/index.jsp?lang=en&subj=mathematics&level=precalc20">Saskatchewan</a>, <a href="http://www.ed.gov.nl.ca/edu/k12/curriculum/guides/mathematics/">Newfoundland</a>, or other provinces.</p>

<p>Our video lessons walk you through all topics in trigonometry like Unit circle, Factoring trinomials, Radicals, Rational expressions, Quadratic equations, Sequences and series, and so many more. Learn the concepts with our tutorials that show you step-by-step solutions to even the hardest math problems. Then, reinforce your understanding with tons of grade 11 math practice.</p>

<p>All our lessons are taught by experienced Grade 11 Math teachers. Let&apos;s finish your homework in no time, and ACE that final.</p>

Grade 11 Functions, University Preparation (MCR3U) 

A. Characteristics of Functions

B. Exponential Functions

C. Discrete Functions

D. Trigonometric Functions

math

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<p>Our intention for StudyPug was to create a 24/7, online companion to meet all your Grade 11 math tutoring needs. We&apos;ve carefully designed our website to be intuitive and easy to navigate but we&apos;ve also included this section for those of you that are visiting or trying us out for the first time. Keep in mind that if you are a student that is still unsure about whether StudyPug is for you, you can still sample our product/service by beginning with the free lessons that are accessible immediately without hassle.</p>
<p>As a general guideline, before jumping into any of our topics in grade 11 math, we recommend starting with assessing your prior knowledge. This is simply done by reviewing your familiarity with concepts we believe you should have a relatively strong command of. Almost all of our topics begin with an outline on the basic concepts you should know as well as other related, pertinent concepts.</p>
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<p>Once you have identified the topic you require more work on, our short but informative video lessons wills walk you through examples (from easy to complex problems) to flesh out the concepts you need to learn as well as study tips and strategies. Watch and re-watch these lessons as many times as you need! We also provide a paraphrased transcript on the gist of what was addressed in the video if you prefer to learn and revise this way instead.</p>
<p>Last but certainly not the least of these steps, we encourage you to put your knowledge and skills to the test! We&apos;ve prepared plenty of questions per topic for you to master and perfect! See how well you have learnt and acquire more practice from a wide variety and range (i.e. easy to hard) of questions.</p>
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<p>Remember this &ndash; learning and preparing to pass 11th grade math will not happen overnight! So do not fret if you are finding certain chapters or problems more challenging than others. The key is to first ensure a strong grasp of the underlying concepts and then get into the habit of exercising your knowledge through practice. With over 290 unique practice questions in total for 11th grade math, we readily supplement your classroom learning with the objective of not to merely pass 11th grade math, but to also obtain excellent grades while in the process. Our inventory of practice questions is available to you immediately and should make easy practice out of 11th grade math questions.</p>

https://dmn92m25mtw4z.cloudfront.net/img/textbook/textbook-grade11math.png

Ex.1

Ex.3

Ex.2

Intro

The solutions to a system of equations are the points of intersection of their graphs. There are 3 cases you will come across when trying to solve the system. There can be 2 solutions, 1 solution or even no solutions.