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438 lines
21 KiB
HTML
438 lines
21 KiB
HTML
<!DOCTYPE html>
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<title>Algebra 2</title>
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<meta name="Description" content="Math explained in easy language, plus puzzles, games, quizzes, worksheets and a forum. For K-12 kids, teachers and parents.">
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<h1 class="center">Algebra 2</h1>
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<div style="clear:both"></div>
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<p class="center"><i>Also known as "College Algebra"</i></p>
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<div class="center80">
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<p>OK. So what are you going to learn here?</p>
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<p>You will learn about Numbers, Polynomials, Inequalities, Sequences and Sums, many types of Functions, and how to <b>solve</b> them.</p>
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<p>You will also gain a deeper insight into Mathematics, get to practice using your new skills with lots of examples and questions, and generally improve your mind.</p>
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<p>With your new skills you will be able to put together mathematical models so you can find good quality solutions to many tricky real world situations.</p>
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</div>
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<p>Near the end of most pages is a "Your Turn" section ... do these! You need to balance your reading with <b>doing</b>. Answering questions helps you sort things out in your mind. And don't guess the answer: use pen and paper and try your best before seeing the solution.</p>
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<h2>Language</h2>
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<p>So what is this thing called Mathematics? And how do you go about learning it?</p>
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<p style="float:right; margin: 0 0 5px 10px;"><img src="../images/reading-math.svg" alt="Reading Math" height="208" width="429"></p>
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<ul class="large">
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<li><a href="../mathematics.html">Welcome to Mathematics</a></li>
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<li><a href="../mathematics-learning.html">Learning Mathematics</a></li>
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<li><a href="../mathematics-language.html">The Language of Mathematics</a></li>
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<li><a href="symbols.html">Symbols in Algebra</a></li>
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</ul>
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<h2>Sets</h2>
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<p>Next, we need to think about mathematics in terms of <b>sets</b>.</p>
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<p style="float:right; margin: 0 0 5px 10px;"><img src="../sets/images/aa.gif" alt="set" height="80" width="60"></p>
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<ul class="large">
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<li><a href="../sets/sets-introduction.html">Introduction to Sets</a></li>
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</ul>
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<h2>Numbers</h2>
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<p>Now we know what a set is, let us look at different sets of numbers that are useful:</p>
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<ul class="large">
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<li><a href="../numbers/evolution-of-numbers.html">The Evolution of Numbers</a></li>
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<li><a href="../prime-composite-number.html">Prime and Composite Numbers</a></li>
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<li><a href="../numbers/fundamental-theorem-arithmetic.html">Fundamental Theorem of Arithmetic</a></li>
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<li><a href="../whole-numbers.html">Whole Numbers and Integers</a></li>
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</ul><br>
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<p style="float:right; margin: 0 0 5px 10px;"><img src="../numbers/images/pi1.svg" alt="pi symbol" height="100" width="100"></p>
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<ul class="large">
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<li><a href="../rational-numbers.html">Rational Numbers</a></li>
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<li><a href="rational-numbers-operations.html">Using Rational Numbers</a></li>
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<li><a href="../irrational-numbers.html">Irrational Numbers</a></li>
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<li><a href="../9recurring.html">0.999... = 1</a></li>
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<li><a href="../numbers/real-numbers.html">Real Numbers</a></li>
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</ul><br>
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<p style="float:right; margin: 0 0 5px 10px;"><img src="../numbers/images/imaginary-square-root.svg" alt="square root of minus one" height="44" width="135"></p>
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<ul class="large">
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<li><a href="../numbers/imaginary-numbers.html">Imaginary Numbers</a></li>
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<li><a href="../numbers/complex-numbers.html">Complex Numbers</a></li>
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<li><a href="complex-number-multiply.html">Multiplying Complex Numbers</a></li>
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<li><a href="complex-plane.html">The Complex Plane</a></li>
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</ul><br>
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<ul class="large">
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<li><a href="../sets/number-types.html">Common Number Sets</a></li>
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</ul>
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<h2>Inequalities</h2>
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<p>"Equal To" is nice but not always available. Maybe we only know that something is less than, or greater than. So let's learn about <b>in</b>equalities.</p>
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<p class="huge" style="float:right; margin: 0 0 5px 10px;">a≥b</p>
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<ul class="large">
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<li><a href="inequality.html">Introduction to Inequalities</a></li>
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<li><a href="inequality-properties.html">Properties of Inequalities</a></li>
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<li><a href="inequality-solving.html">Solving Inequalities</a></li>
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<li><a href="inequality-questions-solving.html">Solving Inequality Word Questions</a></li>
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<li><a href="../sets/intervals.html">Intervals</a></li>
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</ul>
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<p> </p>
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<h2>Exponents</h2>
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<p>We will be using exponents a lot, so let's get to know them well.</p>
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<p style="float:right; margin: 0 0 5px 10px;"><img src="images/exponent-8-2.svg" alt="8 to the Power 2" height="132" width="143"></p>
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<ul class="large">
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<li><a href="../exponent.html">Exponents</a></li>
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<li><a href="variables-exponents-multiply.html">Variables with Exponents</a></li>
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<li><a href="exponents-using.html">Using Exponents in Algebra</a></li>
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<li><a href="../square-root.html">Squares and Square Roots</a></li>
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<li><a href="square-root.html">Squares and Square Roots in Algebra</a></li>
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<li><a href="../numbers/nth-root.html">nth Root</a></li>
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<li><a href="exponent-fractional.html">Fractional Exponents</a></li>
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<li><a href="exponent-laws.html">Laws of Exponents</a></li>
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<li><a href="exponents-squaring-negative.html">Exponents of Negative Numbers</a></li>
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</ul>
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<p> </p>
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<h2>Polynomials</h2>
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<p>Polynomials were some of the first things ever studied in Algebra. They are simple, yet powerful in their ability to model real world situations.</p>
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<p style="float:right; margin: 0 0 5px 10px;"><img src="images/polynomial-example.svg" alt="polynomial example" height="97" width="197"></p>
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<ul class="large">
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<li><a href="polynomials.html">What is a Polynomial?</a></li>
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<li><a href="polynomials-adding-subtracting.html">Adding And Subtracting Polynomials</a></li>
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<li><a href="polynomials-multiplying.html">Multiplying Polynomials</a></li>
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<li><a href="polynomials-multiplication-long.html">Polynomials - Long Multiplication</a></li>
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<li><a href="polynomials-dividing.html">Dividing Polynomials</a></li>
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<li><a href="polynomials-division-long.html">Polynomials - Long Division</a></li>
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</ul><br>
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<ul class="large">
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<li><a href="degree-expression.html">Degree (of an Expression)</a></li>
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<li><a href="special-binomial-products.html">Special Binomial Products</a></li>
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<li><a href="polynomials-difference-two-cubes.html">Difference of Two Cubes</a></li>
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</ul><br>
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<p style="float:right; margin: 0 0 5px 10px;"><img src="images/expand-vs-factor.svg" alt="expand vs factor" height="102" width="203"></p>
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<ul class="large">
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<li><a href="factoring.html">Factoring in Algebra</a></li>
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<li><a href="polynomials-solving.html">Solving Polynomials</a></li>
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<li><a href="polynomials-sums-products-roots.html">Roots of Polynomials: Sums and Products</a></li>
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</ul><br>
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<ul class="large">
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<li><a href="rational-expression.html">Rational Expressions</a></li>
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<li><a href="rational-expression-operations.html">Using Rational Expressions</a></li>
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</ul><br>
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<ul class="large">
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<li><a href="fundamental-theorem-algebra.html">Fundamental Theorem of Algebra</a></li>
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<li><a href="polynomials-remainder-factor.html">Remainder Theorem and Factor Theorem</a></li>
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<li><a href="polynomials-general-form.html">General Form of a Polynomial</a></li>
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</ul>
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<h3>Graphing Polynomials</h3>
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<ul class="large">
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<li><a href="polynomials-behave.html">How Polynomials Behave</a></li>
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<li><a href="polynomials-rule-signs.html">Polynomials: The Rule of Signs</a></li>
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<li><a href="polynomials-bounds-zeros.html">Polynomials: Bounds on Zeros</a></li>
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</ul>
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<p> </p>
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<h2>Equations</h2>
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<p>And, of course, we need to know about equations ... and how to solve them.</p>
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<ul class="large">
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<li><a href="equation-formula.html">Equations and Formulas</a></li>
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<li><a href="equations-solving.html">Solving Equations</a></li>
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<li><a href="simplify.html">Simplify</a></li>
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<li><a href="word-questions-solving.html">Solving Word Questions</a></li>
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<li><a href="zero-product-property.html">Zero Product Property</a></li>
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<li><a href="implication-iff.html">Implication and Iff</a></li>
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<li><a href="theorems-lemmas.html">Theorems, Corollaries, Lemmas</a></li>
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</ul>
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<p> </p>
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<h2>Graphs</h2>
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<p>Graphs can save us! They are a great way to see what is going on and can help us solve many things. But we need to be careful, as they sometimes don't give the full story.</p>
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<p style="float:right; margin: 0 0 5px 10px;"><img src="images/graph-intercepts.svg" alt="Intercepts" height="183" width="276"></p>
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<ul class="large">
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<li><a href="../data/cartesian-coordinates.html">Cartesian Coordinates</a></li>
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<li><a href="../pythagoras.html">Pythagoras' Theorem</a></li>
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<li><a href="distance-2-points.html">Distance Between 2 Points</a></li>
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<li><a href="../sets/graph-equation.html">Graph of an Equation</a></li>
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<li><a href="finding-intercepts-equation.html">Finding Intercepts From an Equation</a></li>
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<li><a href="equation-symmetry.html">Symmetry in Equations</a></li>
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</ul>
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<p> </p>
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<h2>Linear Equations</h2>
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<p>They are just equations for lines. But they come in many forms.</p>
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<p style="float:right; margin: 0 0 5px 10px;"><img src="images/y-mxpb-graph.svg" alt="Slope-Intercept Form" height="241" width="183"></p>
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<ul class="large">
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<li><a href="../equation_of_line.html">Equation of a Straight Line</a></li>
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<li><a href="linear-equations.html">Linear Equations</a></li>
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<li><a href="line-equation-point-slope.html">Point-Slope Equation of a Line</a></li>
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<li><a href="line-equation-general-form.html">General Form of Equation of a Line</a></li>
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<li><a href="line-equation-2points.html">Equation of a Line from 2 Points</a></li>
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<li><a href="line-midpoint.html">Midpoint of a Line Segment</a></li>
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<li><a href="line-parallel-perpendicular.html">Parallel and Perpendicular Lines</a></li>
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</ul>
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<p> </p>
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<h2>Functions</h2>
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<p>A function relates an input to an output. But from that simple foundation many useful things can be built.</p>
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<p style="float:right; margin: 0 0 5px 10px;"><img src="../sets/images/range-domain-graph.svg" alt="doman and range" height="167" width="298"></p>
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<ul class="large">
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<li><a href="../sets/function.html">What is a Function?</a></li>
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<li><a href="../sets/domain-range-codomain.html">Domain, Range and Codomain</a></li>
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</ul><br>
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<ul class="large">
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<li><a href="functions-evaluating.html">Evaluating Functions</a></li>
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</ul><br>
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<ul class="large">
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<li><a href="../sets/functions-increasing.html">Increasing and Decreasing Functions</a></li>
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<li><a href="functions-maxima-minima.html">Maxima and Minima of Functions</a></li>
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<li><a href="functions-odd-even.html">Even and Odd Functions</a></li>
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<li><a href="../sets/set-builder-notation.html">Set-Builder Notation</a></li>
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<li>
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<p><a href="../sets/functions-common.html">Common Functions Reference</a>:</p>
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<ul>
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<li><a href="../sets/function-square.html">Square Function</a></li>
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<li><a href="../sets/function-square-root.html">Square Root Function</a></li>
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<li><a href="../sets/function-cube.html">Cube Function</a></li>
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<li><a href="../sets/function-reciprocal.html">Reciprocal Function</a></li>
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<li><a href="../sets/function-absolute-value.html">Absolute Value Function</a></li>
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<li><a href="../sets/function-floor-ceiling.html">Floor and Ceiling Function</a></li>
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</ul></li>
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</ul><br>
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<ul class="large">
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<li><a href="../sets/function-transformations.html">Function Transformations</a></li>
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<li><a href="../data/grapher-equation.html">Equation Grapher</a></li>
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<li><a href="../sets/functions-operations.html">Operations with Functions</a></li>
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<li><a href="../sets/functions-composition.html">Composition of Functions</a></li>
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<li><a href="../sets/function-inverse.html">Inverse Functions</a></li>
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</ul>
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<p> </p>
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<h2>Equations of Second Degree</h2>
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<p>"Second degree" just means the variable has an exponent of 2, like x<sup>2</sup>. It is the next major step after linear equations (where the exponent is 1, like x).</p>
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<p style="float:right; margin: 0 0 5px 10px;"><img src="images/quadratic-graph.svg" alt="Quadratic Graph" height="140" width="175"></p>
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<ul class="large">
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<li><a href="quadratic-equation.html">Quadratic Equations</a> <a href="quadratic-equation-graph.html"></a></li>
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<li><a href="factoring-quadratics.html">Factoring Quadratics</a></li>
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<li><a href="completing-square.html">Completing the Square</a></li>
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<li><a href="quadratic-equation-derivation.html">Derivation of Quadratic Formula</a></li>
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<li><a href="quadratic-equation-graphing.html">Graphing Quadratic Equations</a></li>
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<li><a href="quadratic-equation-real-world.html">Quadratic Equations in the Real World</a></li>
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<li><a href="circle-equations.html">Circle Equations</a></li>
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</ul>
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<h2>Solving</h2>
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<p>We already have experience in solving, but now we can learn more!</p>
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<p style="float:right; margin: 0 0 5px 10px;"><img src="images/3d-square-box.svg" alt="3d Box" height="90" width="167"></p>
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<ul class="large">
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<li><a href="mathematical-models.html">Mathematical Models</a> and <a href="mathematical-models-2.html">Mathematical Models 2</a></li>
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<li><a href="approximate-solutions.html">Approximate Solutions</a></li>
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<li><a href="intermediate-value-theorem.html">Intermediate Value Theorem</a></li>
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<li><a href="radical-equations-solving.html">Solving Radical Equations</a></li>
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<li><a href="change-of-variables.html">Change of Variables</a></li>
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<li><a href="algebra-mistakes.html">Algebra Mistakes</a></li>
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</ul>
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<p> </p>
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<h2>Solving Inequalities</h2>
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<p>We learned about inequalities above, now let's learn how to solve them.</p>
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<ul class="large">
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<li><a href="inequality-solving.html">Solving Inequalities</a></li>
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<li><a href="graphing-linear-inequalities.html">Graphing Linear Inequalities</a></li>
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<li><a href="../data/inequality-grapher.html">Inequality Graphing Tool</a></li>
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<li><a href="inequality-quadratic-solving.html">Solving Quadratic Inequalities</a></li>
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<li><a href="inequality-rational-solving.html">Solving Rational Inequalities</a></li>
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<li><a href="absolute-value-solving.html">Absolute Value in Algebra</a></li>
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</ul>
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<p> </p>
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<h2>Exponents and Logarithms</h2>
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<p>We already know about exponents ... well <b>logarithms</b> just go the other way. And together they can be very powerful.</p>
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<p style="float:right; margin: 0 0 5px 10px;"><img src="images/exponent-vs-logarithm.gif" alt="Exponent vs Logarithm" height="127" width="175"></p>
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<ul class="large">
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<li><a href="logarithms.html">Introduction to Logarithms</a></li>
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<li><a href="exponents-roots-logarithms.html">Exponents, Roots and Logarithms</a></li>
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<li><a href="exponents-logarithms.html">Working with Exponents and Logarithms</a></li>
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<li><a href="../sets/function-exponential.html">Exponential Function</a></li>
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<li><a href="../sets/function-logarithmic.html">Logarithmic Function</a></li>
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<li><a href="exponential-growth.html">Exponential Growth and Decay</a></li>
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</ul>
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<h2>Systems of Linear Equations</h2>
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<p>What happens when we have two or more linear equations that work together? They can often be solved! It isn't very hard but can take a lot of calculations.</p>
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<p style="float:right; margin: 0 0 5px 10px;"><img src="images/matrix-example.svg" alt="A Matrix" height="71" width="153"></p>
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<ul class="large">
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<li><a href="systems-linear-equations.html">Systems of Linear Equations</a></li>
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</ul><br>
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<ul class="large">
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<li><a href="matrix-introduction.html">Matrices</a></li>
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<li><a href="matrix-types.html">Types of Matrix</a></li>
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<li><a href="matrix-multiplying.html">How to Multiply Matrices</a></li>
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<li><a href="matrix-determinant.html">Determinant of a Matrix</a></li>
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<li><a href="matrix-inverse.html">Inverse of a Matrix:</a></li>
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<li>
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<ul>
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<li><a href="matrix-inverse-row-operations-gauss-jordan.html">Using Elementary Row Operations (Gauss-Jordan)</a></li>
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|
<li><a href="matrix-inverse-minors-cofactors-adjugate.html">Using Minors, Cofactors and Adjugate</a></li>
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</ul></li>
|
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<li><a href="scalar-vector-matrix.html">Scalar, Vector, Matrix</a>and <a href="vectors.html">Vectors</a></li>
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|
<li><a href="matrix-calculator.html">Matrix Calculator</a></li>
|
|
<li>More at <a href="matrix-index.html">Matrix Index</a></li>
|
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</ul><br>
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<ul class="large">
|
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<li><a href="systems-linear-equations-matrices.html">Solving Systems of Linear Equations Using Matrices</a></li>
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</ul><br>
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<ul class="large">
|
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<li><a href="systems-linear-quadratic-equations.html">Systems of Linear and Quadratic Equations</a></li>
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</ul>
|
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<h2>Probability</h2>
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<p style="float:right; margin: 0 0 5px 10px;"><img src="../combinatorics/images/permutation-lock.jpg" alt="lock" height="121" width="150"></p>
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<p>Is it likely? You be the judge!</p>
|
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<ul class="large">
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<li><a href="../data/probability.html">Probability</a></li>
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<li><a href="../data/basic-counting-principle.html">The Basic Counting Principle</a></li>
|
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<li><a href="../combinatorics/combinations-permutations.html">Combinations and Permutations</a></li>
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</ul>
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|
|
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<h2>Sequences, Series and Partial Sums</h2>
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<p>A Sequence is a set of things (usually numbers) that are in order. We can also sum up a series, where Sigma Notation is very useful.</p>
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|
<p style="float:right; margin: 0 0 5px 10px;"><img src="images/sequence-term.svg" alt="sequence term" height="85" width="218"></p>
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<ul class="large">
|
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<li><a href="sequences-series.html">Sequences</a></li>
|
|
<li><a href="sequences-finding-rule.html">Sequences - Finding A Rule</a></li>
|
|
<li><a href="sigma-notation.html">Sigma Notation</a></li>
|
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<li><a href="partial-sums.html">Partial Sums</a></li>
|
|
<li><a href="sequences-sums-arithmetic.html">Arithmetic Sequences and Sums</a></li>
|
|
<li><a href="sequences-sums-geometric.html">Geometric Sequences and Sums</a></li>
|
|
</ul>
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<p> </p>
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<h2>Finally</h2>
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<p>These last few subjects use what we have learned above.</p>
|
|
<ul class="large">
|
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<li><a href="partial-fractions.html">Partial Fractions</a></li>
|
|
<li><a href="mathematical-induction.html">Mathematical Induction</a></li>
|
|
<li><a href="../pascals-triangle.html">Pascal's Triangle</a></li>
|
|
<li><a href="binomial-theorem.html">Binomial Theorem</a></li>
|
|
</ul>
|
|
<p> </p>
|
|
<p class="center"><i>And that is all!</i></p>
|
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<p class="center"> </p>
|
|
<p>But there are many other interesting algebra topics such as:</p>
|
|
<ul class="large">
|
|
<li><a href="eulers-formula.html">Euler's Formula for Complex Numbers</a></li>
|
|
<li><a href="taylor-series.html">Taylor Series</a> (needs a basic understanding of <a href="../calculus/derivatives-introduction.html">derivatives</a>)</li>
|
|
</ul>
|
|
<p> </p>
|
|
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<div class="related">
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<a href="index.html">Algebra 1</a>
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<a href="../calculus/index.html">Calculus</a>
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<a href="../fractions-menu.html">Fractions Index</a>
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