MAT 1033 Final Review Packet offers comprehensive explanations for key mathematical concepts covered in the course. It includes detailed objectives for each section, such as identifying domain and range, calculating slope, and understanding function notation. This resource is essential for students preparing for exams in college-level mathematics. The packet covers topics like linear equations, inequalities, and quadratic functions, providing examples and practice problems to enhance understanding. Ideal for students seeking to solidify their grasp on algebraic principles and improve their problem-solving skills.

Key Points

  • Explains domain and range concepts with examples from tables and ordered pairs.
  • Covers slope-intercept form, including how to identify slopes and y-intercepts from graphs.
  • Includes practice problems for finding equations of vertical and horizontal lines.
  • Details the characteristics of perpendicular and parallel lines in relation to their slopes.
  • Provides insights into mathematical models and their applications in real-world scenarios.
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MAT 1033
FINAL REVIEW PACKET EXPLANATIONS
Matching examples for each review question plus a list of vocabulary (vocabulary only mentioned first time it is
introduced) and objectives covered. For each question, think about how it may change if different numbers or pictures
were used.
1. See example 2 in 1.5 and example 9 in 2.1.
Vocabulary: domain, range, function.
Objectives: be able to list domain and range given a table
or set of ordered pairs; apply the definition of a function
to determine if a table or list of ordered pairs represents
a function
2. See example 7 in 2.4
Objectives: Know how to find the equation of a vertical
line; recognize when you have a vertical line
3. See example 1 in 2.3
Vocabulary: slope-intercept form of line; slope; y-
intercept
Objectives: Know the connection between the sign of the
slope and the direction of a line; the slope of horizontal
and vertical lines; how to identify the y-intercept off a
picture, how to read inequality symbols
4. See example 1 and 4 in 2.1
Vocabulary: table, function notation
Objectives: know how to read a table; how to use
function notation to identify matching inputs and
outputs on a table
5. See example 7 in 2.3; see example 3 in 2.4
Vocabulary: rate of change
Objectives: be able to interpret a point by reading the
labels off the picture; find the equation of a line given
any two points; interpret slope as a rate of change; use
function notation when writing an equation
6. See example 4 in 2.4; see example 11 in 3.1
Vocabulary: x-intercept values and y-intercept values
Objectives: be able to write x- and y- intercept values as
points; find slope between two points; write an equation
in slope-intercept form if slope and y-intercept are
known
7. See example 9 in 2.4
Vocabulary: perpendicular lines
Objectives: know that perpendicular lines have slopes
that are opposite reciprocals; how to find the equation of
a line perpendicular to another line; how to graph lines
8. See example 4 in 2.1
Objectives: know how to use an equation to fill in a table;
how to simplify fractions; the difference between
decimal answers and simplified fraction answers
9. See example 8 in 2.4
Vocabulary: parallel lines
Objectives: know that parallel lines have the same
slopes; know how to find the equation of a line parallel
to another line
10. See example 7 in 2.4, and example 5 in 2.3
Vocabulary: horizontal lines
Objectives: Know how to find the equation of a
horizontal line; how to recognize when you have a
horizontal line
11. See examples 2 and 3 in 2.4
Objectives: be able to find the equation of a line given
two points on a picture but not the y-intercept, to count
slope off a picture, to read scale off a picture, to label a
point on a graph using the given gridlines
12. See example 7 in 2.3
Objectives: be able to calculate slope, or rate of change,
from information off a graph; to interpret slope in
context
13. See example 10 in 2.1
Vocabulary: vertical line test
Objectives: know how to apply the definition of a
function to determine if a graph represents a function, to
give domain and range using inequality notation using
the information from a graph
14. See example 2 in 2.2
Objectives: be able to decide if a table represents a linear
function or not; be able to find the equation of a line
from information off a table
15. See examples 2 and 3 in 2.3
Objectives: be able to plot points, find the slope between
two points, connect points to make a graph
16. See example 7 in 2.4
Vocabulary: standard form of a line
Objectives: Know how to find the equation of a
horizontal line; how to recognize when you have a
horizontal line
17. See example 2 and 5 in 2.3
Objectives: be able to find slope of any line using a graph;
recognize special lines and know their slopes
18. See example 7 in 2.1
Objectives: be able to describe the domain of any
equation; know that you cannot divide by zero and that
you cannot take the even root of a negative number –
and how those conditions determine the correct domain
of an equation
19. See example 1 in 1.5, example 9 in 2.1
Objectives: be able to list domain and range given a table
or set of ordered pairs; apply the definition of a function
to determine if a table or list of ordered pairs represents
a function
20. See example 4 in 2.4, example 5 in 3.1
Vocabulary: mathematical models
Objectives: be able to translate information into points;
know whether to use the actual year number or a count
of years passed; be able to find the linear function and
use the function to answer questions
21. See example 1 in 4.3
Vocabulary: inequalities
Objectives: be able to graph an inequality on the xy-
plane
22. See example 2 in 5.4
Vocabulary: factor, trinomial
Objectives: be able to factor in several steps, pull out
greatest common factors, factor three terms by
whatever method you prefer
23. See examples 4 and 5 in 5.2
Vocabulary: FOIL, binomials
Objectives: be able to multiply binomials, simplify
algebraic expressions
24. See example 4 in 3.2
Objectives: be able to translate sentences into equations,
solve one-variable equations
25. See example 4 in 5.3
Vocabulary: quadratic equation
Objectives: be able to solve quadratic equations by
factoring; check answers by plugging back into original
equation
26. See example 7 in 4.1, example 8 in 4.2
Vocabulary: system of equations
Objectives: be able to solve a system of linear equations
using whatever method you prefer, be able to recognize
how many solutions a system of linear equations might
have
27. See example 2 in 3.3
Vocabulary: set builder notation
Objectives: be able to solve a linear inequality, know the
rules for working with inequalities
28. See example 6 in 5.1
Vocabulary: subtraction, distribution
Objectives: be able to change subtraction to addition by
distributing the negative sign, know how to work with
parentheses, be able to gather like terms
29. See example 12 in 4.2, example 11 in 3.2
Vocabulary: simple interest
Objectives: be able to translate account and interest
information (totals and parts) into an equation, recognize
this is a system of equations, solve a system of equations
30. See example 7 in 2.4
Objectives: Know how to find the equation of a vertical
line; recognize when you have a vertical line
31. See examples 1 and 2 in 3.2
Objectives: be able to isolate a variable in an equation
32. See examples 2 and 10 in 4.1, example 3 in 2.3
Objectives: be able to solve a system by graphing; be
able to graph lines
33. See examples 3 and 7 in 3.4
Vocabulary: three-part inequalities, interval notation
Objectives: solving three-part inequalities, using interval
notation
34. See examples 4 and 5 in 3.3, example 7 in 3.1
Objectives: use a graph to solve an equation or inequality
35. See examples 8 and 9 in 7.1
Vocabulary: radical notation, fractional exponents
Objectives: be able to translate between radical notation
and fractional exponent notation
36. See example 11 in 3.1
Objectives: be able to rewrite an equation into slope-
intercept form; graph a line when given its equation
37. See the “real world” example at the beginning of 4.3
Objectives: be able to translate a situation into a graph,
know the difference between less than and less than or
equal to
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FAQs

What key topics are covered in the MAT 1033 Final Review Packet?
The MAT 1033 Final Review Packet covers essential topics such as functions, linear equations, and inequalities. It explains the concepts of domain and range, slope-intercept form, and the characteristics of vertical and horizontal lines. Additionally, it includes sections on mathematical models and their applications, helping students understand how to apply these concepts in real-world scenarios. Each topic is supported by examples and practice problems to reinforce learning.
How does the packet help students prepare for exams?
This review packet aids exam preparation by providing clear explanations of key mathematical concepts along with practical examples. It includes objectives for each section, ensuring students understand what they need to focus on. The packet also features practice problems that mimic exam questions, allowing students to apply their knowledge and assess their understanding. By working through these exercises, students can build confidence and improve their problem-solving skills.
What is the significance of understanding slope in MAT 1033?
Understanding slope is crucial in MAT 1033 as it forms the foundation for analyzing linear relationships in mathematics. The packet explains how to calculate slope and interpret its meaning in various contexts, such as rate of change. Recognizing the difference between positive, negative, and zero slopes helps students understand the behavior of linear functions. This knowledge is essential for graphing lines and solving real-world problems involving linear relationships.
What types of equations are students expected to work with in this packet?
Students are expected to work with various types of equations, including linear equations in slope-intercept form and standard form. The packet also covers quadratic equations, providing methods for solving them through factoring and using the quadratic formula. Additionally, students will encounter systems of equations and inequalities, which are integral to understanding more complex mathematical concepts. Each type of equation is accompanied by examples and practice problems to enhance comprehension.

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