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