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Master Simplifying Rational Expressions: Step-by-Step Guide

Grade 11 Math: Master Advanced Concepts & Skills

Real number system

Understanding the number systems

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Prime factorization

Number properties: Prime or Composite

Number properties: Prime?

Prime factors – Word Problem

Greatest common factors (GCF)

Greatest Common Factor 2 Numbers

Greatest Common Factor 2 Numbers – Word Problem

Least common multiple (LCM)

Lowest Common Multiple - 2 Numbers – Word Problem

Lowest Common Multiple 2 Numbers

Rational vs. Irrational numbers

Converting repeating decimals to fractions

Powers with rational exponents

Product rule of exponents

Quotient rule of exponents

Power of a product rule

Power of a quotient rule

Power of a power rule

Simplify the power

Negative exponent rule

Combining the exponent rules

Scientific notation

Convert between radicals and rational exponents

Solving for exponents

Radical operations and equations

Radical functions and transformations

Square root of a function

Solving radical equations

Solving Radical Equations Involving One Square Root Term

Solving Radical Equations Involving More than One Square Root Term

Evaluating and simplifying radicals

Basic radical functions

Basic Radical Function

Basic Radical Functions

Converting radicals to mixed radicals

Converting radicals to entire radicals

Adding and subtracting radicals

Adding radicals

Subtracting radicals

Multiplying and dividing radicals

Dividing radicals

Multiplying radicals

Rationalize the denominator

Polynomial factoring

Factoring polynomials: ax^2 + bx + c

Factoring Polynomials: ax^2 + bx + c

Factoring difference of cubes

Factoring sum of cubes

Factoring perfect square trinomials: (a + b)^2 = a^2 + 2ab + b^2 or (a - b)^2 = a^2 - 2ab + b^2

Factoring perfect square trinomials

Find the difference of squares: (a - b)(a + b) = (a^2 - b^2)

Find the difference of squares

Evaluating polynomials

Using algebra tiles to factor polynomials

Solving polynomial equations

Word problems of polynomials

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

Common factors of polynomials

Factoring polynomials by grouping

Solving polynomials with unknown coefficients

Solving polynomials with unknown constant terms

Factoring polynomials: x^2 + bx + c

Applications of polynomials: x^2 + bx + c

Rational expressions and equations

Partial fraction decomposition

What is a rational function?

Point of discontinuity

Slant asymptote

Determining the Equation of a Slant Asymptote Using Long Division

Determining the Equation of a Slant Asymptote Using Synthetic Division

Solving rational equations

Solving rational inequalities

Solving Rational Inequalities With Two Fractions

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

Applications of rational equations

Vertical asymptote

Horizontal asymptote

Horizontal Asymptote

Graphs of rational functions

Simplifying complex fractions

Quadratic functions and equations

Characteristics of quadratic functions

Transformations of quadratic functions

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

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

Graphing quadratic functions: General form VS. Vertex form

Finding the quadratic functions for given parabolas

Applications of quadratic functions

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

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

Completing the square

Completing the Square

Linear and quadratic inequalities

Compound inequalities

Analyze the Alternate Form of Compound Inequalities: AND

Compound linear inequalities

Evaluate Compound Inequalities: And

Express linear inequalities graphically and algebraically

Graph the Inequality

Linear Inequalities – Word Problem 

Linear inequalities

Solving one-step linear inequalities

One-step Linear Inequalities

One-step linear inequalities

One-step Linear Inequalities Decimal

One-step Linear Inequalities Decimal with Fraction

One-step Linear Inequalities Fraction

Solve One Step Linear Inequalities Find Solution– Word Problem

One-step Linear Inequalities — Word Problem

Solving multi-step linear inequalities

Multi-step Linear Inequalities

Two-step Linear Inequalities

Multi-step linear inequalities

Two-step linear inequalities

Solve Multi-step Linear Inequalities – Word Problem 

Solve Multi Step Linear Inequalities Solve Equation – Word Problem

Solve Multi Step Linear Inequalities Equation – Word Problem

Solving quadratic inequalities

Graphing linear inequalities in two variables

Graphing quadratic inequalities in two variables

Graphing systems of quadratic inequalities

Solving polynomial inequalities

Applications of inequalities

Trigonometry: non-right triangles and angles in standard position

Unit circle

Quotient identities and reciprocal identities

Pythagorean identities

Sum and difference identities

Sum and Difference Identities

Double-angle identities

Solving first degree trigonometric equations

Solving second degree trigonometric equations

Solving trigonometric equations involving multiple angles

Law of sines

Ambiguous case: SSA triangles

Law of cosines

Applications of the sine law and cosine law

Angle in standard position

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<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>

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Pre-Calculus 11

math

<h2>Is grade 11 math hard?</h2>
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<h2>How to prepare for grade 11 math?</h2>
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<p>Understanding grade 11 math will take time and that can be difficult if you only see your tutor once a week or feel like you need a refresher on topics previously covered in class. Here at StudyPug our Grade 11 math tutors and all of our content are readily at your disposal whenever you need them. With 24/7 help and 1000&apos;s of lessons at your fingertips, we are here to help you exercise your understanding of grade 11 math topics and prepare for your upcoming Grade 11 math test and/or Grade 11 math exam preparation. Still feeling like you need more support and background information on some of the topics covered in grade 11 math? Some of the topics you are learning in Grade 11 math (e.g. Quadratic relations, completing the square) we started introducing in <a href='[[region_textbook.html|{"textbook_key":"grade10"}]]'>Grade 10 math</a>. <a href='[[region_textbook.html|{"textbook_key":"grade10"}]]'>Grade 10 math</a> is a prerequisite course for Grade 11 math and we strongly recommend a strong command of the knowledge and skills learned in Grade 10 to help you succeed in Grade 11 math. Head over to our <a href='[[region_textbook.html|{"textbook_key":"grade10"}]]'>Grade 10 math page</a> to begin your revision now!</p>

<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>
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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>

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