Important Concepts for This Unit

We will review the real numbers, equations, and the coordinate plane. you are probably already familiar with these concepts but it is helpful to get a fresh look at how these ideas work together to solve problems and model real-world situations. The standards that will be assessed in this chapter are

1.2 Can simplify expressions using properties of exponents
1.3 Can simplify expressions involving factoring and expanding
1.4 Can combine and simplify rational expressions
1.5 Can solve equations involving exponents, algebraic expressions, and rational expressions.

 Topic, Focus, and Exercises Khan Academy Videos Khan Academy Homework (KHW) u1.1 - Real Numbers   ·   The various subsets of the real number line. ·   The algebraic properties of real numbers. ·   Closed and open intervals of real numbers, and their unions and intersections. ·   Absolute value and distance.   Core Exercises: 1, 28, 31, 41, 44, 55, 64, 70, 76   Recommended: 1, 13, 18, 22, 28, 31, 32, 33, 40, 41, 44, 45, 48, 55, 59, 64, 70, 76, 87 Algebraic expressions with fractions. Absolute value equations. u1.2 - Exponent and Radicals The definition of an in the case where n is rational, and where n negative. Algebraic properties of exponents. Rationalizing denominators. Scientific notation and significant figures.  Core Exercises: 3, 44, 67, 70, 76, 86, 88, 100   Recommended: 1, 3, 6, 15, 40, 44, 45, 48, 62, 67, 70, 74, 76, 83, 86, 88, 89, 90, 95, 100 Properties of exponents Exponent properties examples with variables Fractional exponents Simplifying radical expressions Solving equations with radicals u1.3 - Algebraic Expressions Definition of and algebraic operations with polynomials. Special product formulas. Factoring expressions by finding common factors and recognition of special cases. Factoring quadratics by trial and error. Core Exercises: 2, 18, 27, 42, 51, 60, 72, 94, 136 Recommended: 2, 4, 13, 18, 20, 24, 27, 29, 33, 42, 46, 51, 55, 60, 68, 72, 78, 85, 94, 124, 136 Adding and multiplying polynomials Factoring quadratics u1.4  Rational Expressions Finding the domain of an algebraic expression. Simplifying, adding, and subtracting rational expressions, including compound fractions. Rationalizing numerators and denominators. Core Exercises: 4, 6, 15, 24, 48, 65, 83, 98 Recommended: 1, 4, 6, 10, 12, 15, 18, 24, 25, 31, 39, 48, 54, 65, 83, 86, 98, 99, 25 Rational Expressions Domain and range Simplifying rational expressions Adding and subtracting rational expressions Multiplying and dividing rational expressions Solving rational equations u1.5 - Equations Solving equations using the techniques of adding constants to both sides of the equation, multiplying both sides of the equation by a constant, and raising both sides of the equation to the same nonzero power. Avoiding the pitfalls of accidentally multiplying or dividing by zero, or introducing extraneous solutions. Solving quadratic equations using the techniques of factoring, completing the square, and the quadratic formula, and the use of the discriminant to determine the nature of the solutions to a quadratic equation. Solving generalized quadratic equations. Solving equations involving fractional expressions. Core Exercises: 1, 13, 32, 45, 58, 70, 80, 90, 123, 129 Recommended: 1, 5, 10, 12, 13, 20, 30, 32, 41, 45, 51, 58, 64, 70, 73, 80, 81, 87, 90, 123, 129, 139 u1.7 - Modeling with equations Solving applied problems described verbally (word problems) Presenting the solution process in a clear, organized way. Core Exercises: 3, 7, 20, 37, 42, 46, 56, 70, 85 Recommended: 3, 6, 7, 15, 18, 20, 23, 29, 37, 42, 46, 48, 51, 56, 61, 66, 70, 77, 82, 85 u1.9 - The Coordinate Plane  The distance and midpoint formulas.      The relationship between a two-variable equation and its graph. (This is the most crucial concept.) Sketching graphs by plotting points, using intercepts and symmetry. Equations of circles and their graphs, including the technique of completing the square.              Core Exercises: 2, 10, 25, 35, 50, 60, 71, 92, 98, 115  Recommended : 2, 6, 8, 10, 14, 17, 25, 35, 38, 45, 50, 56, 60, 65, 71, 76, 87, 92, 98, 106, 115, 127 u1.12 - Modeling Variation Direct variation and proportionality inverse variation Combinations of direct and inverse variation   Core Exercises: 3, 7, 34, 39, 47, 49, 74, 79, 96      Recommended: 3, 4, 7, 13, 18, 24, 31, 34, 39, 46, 47, 49, 50, 62, 71, 74, 79, 86, 92, 96

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Nikhil Joshi,
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