Section B.2 MTH 65
This information is accurate as of August 2019. For the complete, most recent CCOG, visit www.pcc.edu/ccog.
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www.pcc.edu/ccog/default.cfm?fa=ccog&subject=MTH&course=65
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Polynomial Expressions and Exponents
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Develop exponent rules including for negative exponents and apply them when helpful in algebraic manipulations.
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Add, subtract, multiply and square polynomials.
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Divide polynomials by a monomial.
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Convert between scientific notation and standard form to demonstrate an understanding of magnitude.
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Perform multiplication and division operations in scientific notation in context.
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Radical Expressions
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Evaluate
th roots numerically with and without technology. -
Recognize that an even root of a negative number is not real.
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Convert radical expressions to expressions with rational exponents and vice versa.
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Simplify, add, subtract, multiply and divide radical expressions.
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Use a calculator to approximate radicals using rational exponents.
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Solving Equations in One Variable
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Solve quadratic equations using the square root property.
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Solve quadratic equations using the quadratic formula including complex solutions.
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Solve radical equations that have a single radical term.
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Verify solutions algebraically and graphically, noting when extraneous solutions may result.
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Solve a formula for a specific variable.
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Solve linear, quadratic, and radical equations when mixed up in a problem set.
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Solve real-world models involving quadratic and radical equations.
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Quadratic Equations in Two Variables
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Algebraically find the vertex (using the formula
), the axis of symmetry, and the vertical and horizontal intercepts.-
The vertex and intercept(s) should be written as ordered pairs.
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The axis of symmetry should be written as an equation.
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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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Create, use, and interpret quadratic models of real-world situations algebraically and graphically.
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Interpret the vertex as a maximum or minimum in context with units.
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Interpret the intercept(s) in context with units.
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In a mixed problem set, distinguish between linear and quadratic equations and graph them.
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Geometry Applications and Unit Analysis
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Know and apply appropriate units for various situations; e.g. perimeter units, area units, volume units, rate units, etc.
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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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Use similar triangles to find missing sides in a triangle.
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Use the Pythagorean Theorem to find a missing side in a right triangle.
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Use estimation to determine reasonableness of solution.
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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
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Given an equation, solve using a graphing utility by finding points of intersection.
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Given an inequality, solve using a graphing utility and express the solution in interval notation.
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