# Course:MATH110/Archive/2010-2011/002/Learning Objectives

< Course:MATH110 | Archive | 2010-2011 | 002

# Learning Objectives

The learner should have mastery of basic arithmetic, algebra, plane geometry, graphing, and ancillary skills equivalent to curriculum specified the BC grade 12 Principles of Mathematics curriculum documents. We'll break these down into more detail later, for those needing to review and brush up their skills.

The following list of objectives is keyed to lectures from section 002. Each objective will have an associated date, textbook reference, and a tag indicating whether it concerns factual knowledge, procedural knowledge, conceptual knowledge, or meta-cognitive skills. Pre-requisite learning objectives may be indicated.

- Plot points and lines on the Cartesian plane
- Find the equation of a line in several different forms
- Plot lines from a data set, or equation
- Find the coordinates of the intersection of two lines
- Participate in classroom interaction using a Clicker
- Give several descriptions of a parabola
- Describe the relationship between the roots of a quadratic and the intersections of the corresponding parabola with the x-axis.
- Give a criterion to determine if a quadratic has real roots (and if so, how many)
- Explain some tests you would perform to determine what equation corresponds to a given graph
- Describe the possible ways two lines can intersect in the plane, and what the corresponding situation is for systems of 2 linear equations in two unknowns
- Compute a parabola lying on three given points
- Give a definition of function
- Explain in your own words what functions are and what they are good for
- Give examples of functions, and examples of non-functions
- Explain the notation and terminology associated to functions
- Determine when a given English sentence is a logical statement
- Construct logical compound statements with “and” and “or”
- Construct the negation of a statement using “not”
- Describe what a propositional variable is, and give examples
- Complete truth tables for “and”, “or” and “not”
- Perform a case analysis of a promise
- Describe the logical connective of “implication”
- Complete a truth table for “implication”
- Describe why theorems are implications
- Describe how to prove implications
- Give examples of sequences with limits
- Show how to produce “sufficient conditions” to bound error
- Calculate the required constraint we need to set in order to achieve a desired accuracy when approximating a function at a limit point.
- Define what it means for a function f:x to have a limit L as x approaches a point a
- Give examples of functions that don’t have a value at a given point a, but do have a limit as x approaches a
- Explain different ways that a function can fail to have a limit at a particular point.
- Explain what is is meant by “the limit of the function f(x) at infinity is L”
- Define what is meant by one-sided limit; list all of the related terms and give examples of each.
- Give examples of functions which have no limit, but which do have one-sided limits.
- Evaluate the limit as x approaches a of rational functions, as long as the limit is not an indeterminate form
- Explain intuitively the process of taking a limit.
- Compute the limits of functions in simple cases, including the limits of polynomials and rational functions
- Describe a process for reading mathematics
- Read a section from the textbook using the described protocol
- Create summary notes by using the summary template provided
- Edit an existing wiki page
- Create a wiki page
- Explain what it means for a function to be continuous at a point
- Correctly analyze whether a given function is continuous at a given point
- Identify points of discontinuity for a given function
- Describe the way continuous functions behave under basic algebraic operations, and use these results to correctly identify whether or not a given function is continuous at a point
- Describe the way continuous functions behave when they are composed
- Apply the knowledge of continuity properties of composite functions to determine whether a given function is continuous at at a point.
- Identify whether or not a given function is continuous on a given interval. This includes identifying when a function is left- or right-continuous at the endpoints of a closed interval.
- Explain one-sided limits and their relationship to two-sided limits.
- Examine one-sided limits graphically and numerically
- Compute the average rate of change of a function.
- Draw a diagram that illustrates the average rate of change of a function
- Draw a diagram to illustrate the process of computing an instantaneous rate of change of a function
- Explain the relationship between finding average and instantaneous rates of change of a function and appropriate secant and tangent lines on graphs of this function
- Be able to prove the formula for the derivative of a polynomial (in several ways)
- Be able to explain how to apply the sum rule, constant multiple rule, derivative of a constant, and explain geometrically why these are true.
- Explain what an exponential function is
- Give examples of exponential functions
- List the basic properties of an exponential function
- Graph an exponential function
- Solve simple equations involving exponential functions
- Give examples of products of functions
- Explain why the product rule does not behave like the sum rule
- State the product rule for taking the derivative of a product of functions
- Explain when you would want to apply this rule
- Apply the rule to compute derivatives of products of functions
- Explain how angles are measured
- Define sin(x), cos(x) in terms of triangles and circles
- Define tan(x), sec(x), csc(x), cot(x) in terms of sin(x) and cos(x)
- Recall or calculate the value of the six trig functions for special values
- Sketch the graph of the six basic trig functions
- State the important identities for trig functions (Pythagorean, addition identities)
- Calculate with trig identities (example: calculate the value of sine, cosine for multiples of )
- Recognize and describe the set of functions which you can now differentiate
- Recognize that there are certain types of functions that we can not yet differentiate
- Differentiate more complex functions involving multiple applications of the product and quotient rules
- Give several different explanations of function composition
- Give examples of composing functions
- Relate function composition to transformations of graphs of functions
- Write the chain rule in several different formulations
- Express the chain rule in your own words
- Apply the chain rule to differentiate compositions of functions
- Apply the chain rule to differentiate compositions of three or more functions
- Define absolute maximum and absolute minimum of a function
- Explain why some functions do not have absolute extrema
- Give examples of functions have absolute maxima, and functions that don’t
- Give examples of functions have absolute minima, and functions that don’t
- Define what it means for a function to be increasing on an interval
- Find points of the domain of a function f where the graph of f has a horizontal tangent line (i.e., critical points)
- Determine (for suitably simple examples) whether f is increasing or decreasing (or neither) in the intervals between
- Determine whether a critical point represents a local minimum, local maximum, or neither
- Sketch curves of relatively simple functions using information about the derivative of the function