Exponents+and+Radicals+10

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**Exponents and Radicals**
 * = ==**Unit Questions**== ||= ==**Significant Concepts**== ||= ==**Area of Interaction**== ||

Vocabulary

 * = ===English=== ||= ===**Bahasa** === ||
 * exponent, index, radical, radicand, rational, root || eksponen, indeks, radikal, radicand, rasional, ||

** Key Links **

 * [|Purple Math] || A website that can help you to improve your exponent skills. Student friendly explanations ||
 * Using exponents || Basic laws of exponents ||
 * Zero and negative exponents || Extra practice simplifying expressions using the laws of exponents for zero and negative indices ||
 * Indices practice 1 || A remedial worksheet for students who need to practice some of the basic laws of indices ||
 * Indices practice 2 || An extension worksheet for students who can apply the laws of indices with confidence ||
 * [|Rational exponents] || Web link to Purple math with an easy to understand explanation and examples ||
 * Rational exponents || A challenging worksheet using rational exponents to simplify expressions and solve equations ||

Content and skills

 * **Content:** || **Extended content:** ||
 * * real number system
 * exponent laws
 * radical expressions
 * radical equations
 * rational exponents
 * exponential equations || * numerical logarithms
 * complex number algebra ||
 * **Outcomes/Skills:** || **Extended outcomes/skills:** ||
 * # simplify and evaluate expressions containing positive integral exponents.
 * 1) simplify and evaluate expressions containing zero and negative exponents.
 * 2) simplify and evaluate expressions containing rational exponents.
 * 3) convert radical expressions to expressions with rational exponents and vice versa.
 * 4) use the properties of surds to simplify square root expressions.
 * 5) simplify radical expressions up to and including index 5.
 * 6) add, subtract and multiply radical expressions.
 * 7) rationalize the denominator of a radical expression.
 * 8) solve exponential equations by making the bases the same.
 * 9) solve simple radical equations. || # define a logarithm and convert, with ease, between the logarithmic and the exponential form of a number
 * 10) evaluate logarithms to any base
 * 11) investigate the laws of logarithms
 * 12) use the laws of logarithms to simplify expressions
 * 13) define the number //i// as the square root of negative one.
 * 14) state the real and imaginary parts of a complex number
 * 15) perform operations with complex numbers in rectangular form (a + b//i//) ||

Standards and Benchmarks
[|Math10 - Exponents and Radicals - Properties involving Rational Exponents Worksheet.pdf] || [|Math10 - Exponents and Radicals - Multiplying Square Roots Worksheet.pdf] [|Math10 - Exponents and Radicals - Multiplying nth Roots Worksheet.pdf] [|Math10 - Exponents and Radicals - Quotients of Square Roots Worksheet.pdf] ||
 * **Master understanding of the laws of exponents including positive and negative integer exponents and apply the laws of exponents to simplify expressions containing both integer and simple rational exponents. ** ||
 * [|Math10 - Exponents and Radicals - Investigating Positive Exponents.pdf] || Use GSP and the Kock curve to investigate expressions which involve exponents || [|Math10 - Exponents and Radicals - Properties of exponents.pdf] ||
 * [|Math10 - Exponents and Radicals - Zero and Negative Exponents.pdf] || Use the rules developed in the first lesson to investigate the laws of exponents for zero and negative indices || [|Math10 - Exponents and Radicals - Positive, Negative and Zero Exponents Worksheet.pdf] ||
 * **Investigate and develop understanding of rational exponents **
 * Evaluate powers with simple rational exponents and assess reasonableness of answers **
 * Convert radical expressions to expressions with rational exponents and vice versa ** ||
 * [|Math10 - Exponents and Radicals - Rational Exponents.pdf] || Use the properties of exponents developed above to give meaning to a rational exponent. || [|Math10 - Exponents and Radicals - Evaluating Expressions with Rational Exponents Worksheet.pdf]
 * **<span style="font-family: Verdana,Geneva,sans-serif;">Simplify, add, subtract, multiply and divide real numbers written in any form with emphasis on square root radicals, simple cube root and fourth root radicals and numbers written in exponential form ** ||
 * [|Math10 - Exponents and Radicals - Surds.pdf] ||  || [|Math10 - Exponents and Radicals - Simplifying Square Roots Worksheet.pdf] ||
 * [|Math10 - Exponents and Radicals - Simplifying Expressions involving nth Roots.pdf] ||  || [|Math10 - Exponents and Radicals - Simplifying nth Roots Worksheet.pdf] ||
 * [|Math10 - Exponents and Radicals - Operations with Radicals.pdf] || Focus on the properties of radicals (surds) to [|add/subtract] radicals, [|multiply] and divide by [|rationalizing] numerators and denominators. || [|Math10 - Exponents and Radicals - Combining Radicals Worksheet.pdf]
 * **<span style="font-family: Verdana,Geneva,sans-serif;">Solve simple radical equations and check the validity of the solution by substituting the solution back into the original equation **
 * <span style="font-family: Verdana,Geneva,sans-serif;">Solve exponential equations by making the bases the same ** ||
 * **<span style="font-family: Verdana,Geneva,sans-serif;">Recognize and classify numbers in different number systems including the set of positive integers and zero (N), integers (Z), rational numbers (Q), irrational numbers (Q’) and real numbers (R) and understand the relationships amongst the different sets ** ||
 * **<span style="font-family: Verdana,Geneva,sans-serif;">Recognize and classify numbers in different number systems including the set of positive integers and zero (N), integers (Z), rational numbers (Q), irrational numbers (Q’) and real numbers (R) and understand the relationships amongst the different sets ** ||
 * **<span style="font-family: Verdana,Geneva,sans-serif;">Recognize and classify numbers in different number systems including the set of positive integers and zero (N), integers (Z), rational numbers (Q), irrational numbers (Q’) and real numbers (R) and understand the relationships amongst the different sets ** ||
 * **<span style="font-family: Verdana,Geneva,sans-serif;">Recognize and classify numbers in different number systems including the set of positive integers and zero (N), integers (Z), rational numbers (Q), irrational numbers (Q’) and real numbers (R) and understand the relationships amongst the different sets ** ||
 * **<span style="font-family: Verdana,Geneva,sans-serif;">Recognize and classify numbers in different number systems including the set of positive integers and zero (N), integers (Z), rational numbers (Q), irrational numbers (Q’) and real numbers (R) and understand the relationships amongst the different sets ** ||
 * **<span style="font-family: Verdana,Geneva,sans-serif;">Recognize and classify numbers in different number systems including the set of positive integers and zero (N), integers (Z), rational numbers (Q), irrational numbers (Q’) and real numbers (R) and understand the relationships amongst the different sets ** ||
 * **<span style="font-family: Verdana,Geneva,sans-serif;">Recognize and classify numbers in different number systems including the set of positive integers and zero (N), integers (Z), rational numbers (Q), irrational numbers (Q’) and real numbers (R) and understand the relationships amongst the different sets ** ||
 * **<span style="font-family: Verdana,Geneva,sans-serif;">Recognize and classify numbers in different number systems including the set of positive integers and zero (N), integers (Z), rational numbers (Q), irrational numbers (Q’) and real numbers (R) and understand the relationships amongst the different sets ** ||