Exam 1 Study and Scoring Guidelines
(Math 107 Sections 1-5)
Exam 1 will contain problems
that address the following topics. For each of the seven topics
listed below, part b will be weighted as much as parts a and c
combined. For example, of the number of points fixed to a given
problem, 50% of the points can be earned by performing well in the
conceptual understanding category, 30% may be earned in the basic
skills category, and 20% may be earned in the communication category.
1. Composition of
functions (3,7,8)
a.) Basic skills
Correct use of substitution
Correctly reading a graph
b.) Conceptual understanding
Demonstrated knowledge of
evaluating a function
Demonstrated knowledge of
composition of functions
Correctly identifies and uses
combinations of functions
Recognizes when functions are
defined
c.) Communication skills
Using correct notation
Clear graphical representations
2.
Domain and Range (1,6,9)
a.) Basic skills
Solving inequalities and equations
Arithmetic skills
b.) Conceptual understanding
Know definitions of domain and
range
What's included
What's not included
Recognizes undefined functions
c.) Communication skills
Using correct notation
Understand different
representations (Numerical, verbal, symbolical, and graphical)
3. Linear functions
(2,4)
a.) Basic skills
Correctly read graphs
Correctly use substitution
Correctly use distribution
property
Correctly use property of
equality
b.) Conceptual understanding
Demonstrate understanding of slope
Demonstrate understanding of
relationship of slope of a line with respect to parallel and/or
perpendicular lines
Using the data (i.e. points) of
functions to find constants of functions
Recognize and use key
characteristics of standard forms of functions
c.) Communication skills
Explanations are given in clear
sentences
Work shown is orderly and clearly
legible
4. Transformations of
graphs (5)
a.) Basic skills
Correctly uses basic math facts
Correctly uses arithmetic
Correctly uses graphing
techniques
b.) Conceptual understanding
Distinguishes an argument from
function value
Demonstrates knowledge and
understanding of all types of graphical transformations
Vertical and horizontal shifts,
reflections in the x and in the y axes, vertical and horizontal
stretches and shrinks.
c.) Communication skills
Demonstrates understanding and
correct usage of notation
5. Graphing
Functions (6)
a.) Basic skills
Correctly plots points on graphs
Correctly uses arithmetic
b.) Conceptual understanding
Understanding of domain and range
Understanding of how to evaluate
a function
c.) Communication skills
Uses correct notation
Correctly labels graphs
Work shown is orderly and clearly
legible
6. Inverse
functions (9)
a.) Basic skills
Reading data on a graph
Plotting data on a graph
b.) Conceptual understanding
Reflection (on the line y=x)
Exchange of domain and range
c.) Communication skills
Correct notation
Clarity of Representations
Work shown is orderly and clearly
legible
7. Modeling with
functions (10)
a.) Basic skills
Correct use of substitution
Correct use of property of
equality
Correct use of distribution
property
b.) Conceptual understanding
Demonstrates knowledge of
developing models from data
Demonstrates understanding of
using models
Demonstrates understanding of
maximum and minimum values of quadratic equations
c.) Communication skills
Uses correct notation
Clarity of Representations
Work shown is orderly and clearly
legible