Course:MATH110/Archive/2010-2011/003/Groups/Group 14/SkillsAssessment

Basic Skills - Group Plan

As a group, we will contribute to the Basic Skills page on Logarithmic Functions. We have identified this topic to be one which many of us struggle with, but also a topic that will continue to be important as we study derivatives.

Here are some ideas we have come up with to contribute to the basic skills page on this topic:

• Some theory such as definitions, re-written in our own words

  This will help us understand what is happening, and help us to be able to apply the theory

• Examples, followed by suggested practice problems. We can find practice problems in our textbook to work on.

  Provide a brief explanation, so we understand what is going on in the problem

• A list of tricks we found helpful when solving logarithmic functions. In other words, different ways to think about logarithmic functions
• A practice quiz
• A "So what's it all for?" Section on some of the things logarithmic functions can be used for
• Perhaps a video lesson on how to solve logarithmic functions, with a detailed explanation as we work through some problems

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Those that pose no problem to anyone in the group:

absolute-valued functions

logarithmic functions

polynomials

Those that some of you have issues with, but not everyone in the group:

Trigonometry and the Pythagorean theorem to apply the Pythagorean theorem, write down trigonometric relationships involving the sides and angles of a right triangle, and express proportional relations between similar triangles;

Mathematical writing to construct neat, logical, understandable explanations and solutions.

Intersections of functions to find intersections of two or more graphs;

Distances and lines to find the distance between two given points and the slope/equation of the line containing two given points;

Operations on graphs of functions to translate, scale and reflect graphs;

Graphs of functions to relate graphs to simple functions such as linear, quadratic, power, root, reciprocal, absolute-valued, trigonometric, inverse trigonometric, exponential, logarithmic and piecewise functions as well as equations involving circles and ellipses; i.e., plot a graph from a given equation and find the equation from a given graph;

Properties of functions to find the domain, range and intercepts of a basic function (see above), and the behaviour of such a function at/near the endpoints of the domain;

Basic functions to evaluate, simplify and manipulate basic functions which includes:

• polynomials,
• radical functions,
• trigonometric functions,
• inverse trigonometric functions,
• exponential functions,
• logarithmic functions,
• absolute-valued functions,
• functions that are constructed by additions, subtractions, multiplications, divi- sions, exponentiations and/or compositions of the above functions,
• piecewise functions;

trigonometric functions

functions that are constructed by additions, subtractions, multiplications, divi- sions, exponentiations and/or compositions of the above functions

exponential functions

inverse trigonometric functions

piecewise functions

radical functions

Reading graphs of functions

Solving Inequalities

Reading graphs of functions to find a value of a function from its graph and determine whether a point of given coordinates lies on the graph;

Those that no one in the group knows how to handle:

Equations to solve linear, quadratic, rational, radical, trigonometric, exponential, logarithmic, and absolute-valued equations;

Inequalities to solve linear, quadratic, rational, radical, trigonometric, exponential and logarithmic inequalities;

Composition of functions to construct new functions by applying function composition and identify the various functions that make up a composite function;

Polynomial long division to perform long divisons of polynomials and write the result out, whether there is a remainder or not;

Construction of graphs to construct a graph from a given context and extract information related to a given context from a graph;

Areas and volumes to compute the area of basic 2D shapes, and the surface area and the volume of basic 3D shapes;