ORCCA MTH 65

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Section B.2 MTH 65

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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

Polynomial Expressions and Exponents
1. Develop exponent rules including for negative exponents and apply them when helpful in algebraic manipulations.
2. Add, subtract, multiply and square polynomials.
3. Divide polynomials by a monomial.
4. Convert between scientific notation and standard form to demonstrate an understanding of magnitude.
5. Perform multiplication and division operations in scientific notation in context.
Radical Expressions
1. Evaluate $n$ th roots numerically with and without technology.
2. Recognize that an even root of a negative number is not real.
3. Convert radical expressions to expressions with rational exponents and vice versa.
4. Simplify, add, subtract, multiply and divide radical expressions.
5. Use rational exponents to simplify radical expressions. E.g. $\sqrt[3]{x^{7}} = \dots = x^{2} \sqrt[3]{x},$ $\sqrt{x} \cdot \sqrt[3]{x} = \dots = \sqrt[6]{x^{5}} .$
6. Rationalize denominators with square roots in them. E.g. $\frac{5}{\sqrt{2}},$ $\frac{5}{1 + \sqrt{2}} .$
7. Use a calculator to approximate radicals using rational exponents.
Solving Equations in One Variable
1. Solve quadratic equations using the square root property.
2. Solve quadratic equations using the quadratic formula including complex solutions.
3. Solve radical equations that have a single radical term.
4. Verify solutions algebraically and graphically, noting when extraneous solutions may result.
5. Solve a formula for a specific variable.
6. Solve linear, quadratic, and radical equations when mixed up in a problem set.
7. Solve real-world models involving quadratic and radical equations.
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.
  2. The axis of symmetry should be written as an equation.
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.
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.
  2. Interpret the intercept(s) in context with units.
4. In a mixed problem set, distinguish between linear and quadratic equations and graph them.
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.
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.
3. Use similar triangles to find missing sides in a triangle.
4. Use the Pythagorean Theorem to find a missing side in a right triangle.
5. Use estimation to determine reasonableness of solution.
6. 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
1. Given an equation, solve using a graphing utility by finding points of intersection.
2. Given an inequality, solve using a graphing utility and express the solution in interval notation.

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