ORCCA MTH 65

Section B.2 MTH 65

This information is accurate as of August 2019. For the complete, most recent CCOG, visit www.pcc.edu/ccog

www.pcc.edu/ccog/default.cfm?fa=ccog&subject=MTH&course=65

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List B.2.1. MTH 65 Skills

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Polynomial Expressions and Exponents
1. Develop exponent rules including for negative exponents and apply them when helpful in algebraic manipulations.
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2. Add, subtract, multiply and square polynomials.
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3. Divide polynomials by a monomial.
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4. Convert between scientific notation and standard form to demonstrate an understanding of magnitude.
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5. Perform multiplication and division operations in scientific notation in context.
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Radical Expressions
1. Evaluate $n$ th roots numerically with and without technology.
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2. Recognize that an even root of a negative number is not real.
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3. Convert radical expressions to expressions with rational exponents and vice versa.
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4. Simplify, add, subtract, multiply and divide radical expressions.
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5. Use rational exponents to simplify radical expressions. E.g. $\sqrt[3]{x^{7}} = \dots = x^{2} \sqrt[3]{x},$ $\sqrt{x} \cdot \sqrt[3]{x} = \dots = \sqrt[6]{x^{5}} .$
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6. Rationalize denominators with square roots in them. E.g. $\frac{5}{\sqrt{2}},$ $\frac{5}{1 + \sqrt{2}} .$
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7. Use a calculator to approximate radicals using rational exponents.
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Solving Equations in One Variable
1. Solve quadratic equations using the square root property.
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2. Solve quadratic equations using the quadratic formula including complex solutions.
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3. Solve radical equations that have a single radical term.
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4. Verify solutions algebraically and graphically, noting when extraneous solutions may result.
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5. Solve a formula for a specific variable.
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6. Solve linear, quadratic, and radical equations when mixed up in a problem set.
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7. Solve real-world models involving quadratic and radical equations.
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Quadratic Equations in Two Variables
1. Algebraically find the vertex (using the formula $h = - \frac{b}{2 a}$ ), the axis of symmetry, and the vertical and horizontal intercepts.
  1. The vertex and intercept(s) should be written as ordered pairs.
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  2. The axis of symmetry should be written as an equation.
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2. Graph by hand a quadratic equation by finding the vertex, plotting at least two additional points on one side and using symmetry to complete the graph.
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3. Create, use, and interpret quadratic models of real-world situations algebraically and graphically.
  1. Interpret the vertex as a maximum or minimum in context with units.
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  2. Interpret the intercept(s) in context with units.
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4. In a mixed problem set, distinguish between linear and quadratic equations and graph them.
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Geometry Applications and Unit Analysis
1. Know and apply appropriate units for various situations; e.g. perimeter units, area units, volume units, rate units, etc.
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2. Explore, understand, and apply the formulas for perimeter; area formulas for rectangles, circles, and triangles; and volume formulas for a rectangular solid and a right circular cylinder.
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3. Use similar triangles to find missing sides in a triangle.
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4. Use the Pythagorean Theorem to find a missing side in a right triangle.
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5. Use estimation to determine reasonableness of solution.
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6. Use unit fractions to convert time, length, area, volume, mass, density, and speed to other units, including metric/non-metric conversions.
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Solving Equations and Inequalities Graphically
1. Given an equation, solve using a graphing utility by finding points of intersection.
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2. Given an inequality, solve using a graphing utility and express the solution in interval notation.
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