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Master Systems of Quadratic Equations: Techniques & Solutions

Grade 11 Math: Master Advanced Concepts & Skills

Demonstrate an understanding of the absolute value of real numbers

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Upper and lower bound

Upper and Lower Bound

Absolute value functions

Expressing an Absolute Value Linear Function as a Piecewise Function

Expressing an Absolute Value Quadratic Function as a Piecewise Function

Solving absolute value equations

Solving absolute value inequalities

Solving Absolute Value Inequalities Involving "less than"

Solving Absolute Value Inequalities Involving "greater than"

Recognizing Absolute Value Inequalities with "No Solution" or "All Real Numbers"

Factor polynomial expressions of various forms

Factoring difference of cubes

Factoring sum of cubes

Factor by taking out the greatest common factor

Factor by taking out GCF

Factor by grouping

Factoring difference of squares: \(x^2 - y^2\)

Factoring difference of squares: <katex>x^2 - y^2</katex>

Factoring difference of squares: x^2 - y^2

Factoring trinomials

Factoring Trinomials

Analyze quadratic functions of the form y = a(x - p)² + q and determine their characteristics

Introduction to quadratic functions

Transformations of quadratic functions

Converting from general to vertex form by completing the square

Shortcut: Vertex formula

Converting general form into vertex form by applying the vertex formula

Vertex Formula Application

Finding the quadratic functions for given parabolas

Quadratic function in vertex form: y = a(x-p)^2 + q

Analyze quadratic functions of the form y = ax² + bx + c to identify characteristics of the corresponding graph

Solving polynomial equations by iteration

Characteristics of quadratic functions

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

Graphing quadratic functions: General form VS. Vertex form

Applications of quadratic functions

Completing the square

Completing the Square

Solve problems that involve quadratic equations

Solving 3 variable systems of equations by substitution

Solving 3 variable systems of equations by elimination

Solving quadratic equations by factoring

Solving quadratic equations by completing the square

Using quadratic formula to solve quadratic equations

Solving a quadratic equation with TWO REAL SOLUTIONS

Solving a quadratic equation with TWO COMPLEX SOLUTIONS

Nature of roots of quadratic equations: The discriminant

Applications of quadratic equations

System of linear equations

Solve, algebraically and graphically, problems that involve systems of linear-quadratic and quadratic-quadratic equations in two variables

What is linear programming?

Finding Optimal Values Given Constraints In Slope-Intercept Form

Finding Optimal Values Given Constraints In Standard Form

Linear programming word problems

System of linear-quadratic equations

System of quadratic-quadratic equations

Solve problems that involve linear and quadratic inequalities in two variables

Graphing linear inequalities in two variables

Graphing quadratic inequalities in two variables

Graphing systems of quadratic inequalities

Graphing systems of linear inequalities

Applications of inequalities

Solve problems that involve quadratic inequalities in one variable

Solving quadratic inequalities

Sigma notation

Analyze arithmetic sequences and series to solve problems

Arithmetic sequences

Arithmetic series

Arithmetic series formula

Arithmetic mean vs. Geometric mean

Analyze geometric sequences and series to solve problems

What is a rational function?

Point of discontinuity

Geometric sequences

Geometric series

Geometric Series

Infinite geometric series

Vertical asymptote

Horizontal asymptote

Horizontal Asymptote

Solve problems that involve operations on radicals and radical expressions with numerical and variable radicands

Conversion between entire radicals and mixed radicals

Adding and subtracting radicals

Combining Like Radicals

Adding and Subtracting Radicals

Multiplying radicals

Multiplying Radicals

Operations with radicals

Operations with Radicals

Adding radicals

Subtracting radicals

Multiplying and dividing radicals

Dividing radicals

Rationalize the denominator

Graph and analyze reciprocal functions (limited to the reciprocal of linear and quadratic functions)

Graphing reciprocals of linear functions

Graphing reciprocals of quadratic functions

Solve problems that involve radical equations (limited to square roots)

Solving radical equations

Solving Radical Equations Involving One Square Root Term

Solving Radical Equations Involving More than One Square Root Term

Determine equivalent forms of rational expressions (limited to numerators and denominators that are monomials, binomials or trinomials)

Partial fraction decomposition

Simplifying rational expressions and restrictions

Perform operations on rational expressions (limited to numerators and denominators that are monomials, binomials or trinomials)

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

Simplifying complex fractions

Solve problems that involve rational equations (limited to numerators and denominators that are monomials, binomials or trinomials)

Solving rational equations

Applications of rational equations

Demonstrate an understanding of angles in standard position 0° to 360°

Angle in standard position

Coterminal angles

Coterminal Angles

Reference angle

Solve problems, using the three primary trigonometric ratios for angles from 0° to 360° in standard position

Unit circle

Find the exact value of trigonometric ratios

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

ASTC rule in trigonometry

Solve problems, using the cosine law and sine law, including the ambiguous case

Law of sines

Ambiguous case: SSA triangles

Law of cosines

Applications of the sine law and cosine law

<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>

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<h2>Is grade 11 math hard?</h2>
<p>Grade 11 math can be a struggle and will definitely put your math skills to the test. This can make it seem like grade 11 math is hard and overwhelming. But fear not &ndash; here at StudyPug we&apos;ve made sure to address all your questions and concerns! From topics such as quadratic functions to Sigma notation, down to unraveling the Vertex formula, (and even more!) we&apos;re here to provide you help with grade 11 math. Our carefully crafted Grade 11 math tutorials are well suited for all &ndash; so whether you are a student that requires a refresher on fundamentals or a keener looking to get ahead of the game, we have content covering Grade 11 math for dummies as well as more advanced, challenging content. Regardless of the level of difficulty, we&apos;re here to help you every step of the way with step-by-step examples and lots of practice questions. Grade 11 Math does not have to be hard folks! With help from our review lessons and methodical-disciplined practice, you&apos;ll find yourself powering through the difficult questions with ease and confidence in no time!</p>

<h2>How to prepare for grade 11 math?</h2>
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<h2>How do I use StudyPug to study Grade 11 Math?</h2>
<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>
<p>If you know exactly what you are looking for, we recommend jumping straight to using our search engine tool. Use this to hone in on the concepts, topics, or questions you are finding the most difficult. Remember; don&apos;t be afraid if you feel like you need to begin with some of the rudimentary foundations you covered previously in grade 10 math or elsewhere.</p>
<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>

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Ex.1

Ex.2

Ex.4

Intro

Ex.3

The solutions to a system of equations are the points of intersection of the lines. For a system with two quadratic equations, there are 4 cases to consider: 2 solutions, 1 solution, no solutions, and infinite solutions.

Simultaneous quadratic-quadratic equations

How to solve quadratic-quadratic equations

Solving quadratic equations using the quadratic formula