Math Courses
Here is what you can expect to see on the tests:
Elementary Algebra
A total of 12 questions are administered in this test.
• The first type involves operations with integers and rational numbers, and
includes computation with integers and negative rationals, the use of absolute
values , and ordering.
• A second type involves operations with algebraic expressions using evaluation
of simple formulas and expressions, and adding and subtracting monomials and
polynomials. Questions involve multiplying and dividing monomials and
polynomials, the evaluation of positive rational roots and exponents,
simplifying algebraic fractions , and factoring.
• The third type of question involves the solution of equations , inequalities,
word problems. solving linear equations and inequalities, the solution of
quadratic equations by factoring, solving verbal problems presented in an
algebraic context, including geometric reasoning and graphing, and the
translation of written phrases into algebraic expressions.
Integers and Rationals
Algebraic Expressions
Equations, Inequalities, and Word Problems;
Sample question: 2x + 3x + y =
a) 6xy
b) 5x + y
c) 5(x + y)
d) 6x + y
(correct answer is b)
•Here are some of the knowledge and skills associated with the elementary
algebra test:
•a sense of order relationships and the relative size of signed numbers
•the ability to multiply a whole number by a binomial
•perform operations with signed numbers
•combine like terms
•multiply binomials
•evaluate algebraic expressions
•add radicals, add algebraic fractions, and evaluate algebraic expressions
• factor quadratic expressions in the form ax2 + bx + c, where a = 1
•factor the difference of squares
•square binomials
•solve linear equations with integer coefficients
•simplify algebraic expressions
• factor quadratic expressions where a = 1
•solve quadratic equations
•solve linear equations with fractional and literal coefficients and linear
inequalities with integer coefficients
•solve systems of equations
•identify graphical properties of equations and inequalities
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College Level Math Test
There are 20 questions on the College-Level Mathematics.
The College-Level Mathematics test assesses from intermediate algebra through
precalculus.
Algebraic operations includes simplifying rational algebraic expressions,
factoring, expanding polynomials, and manipulating roots and exponents.
• Solutions of equations and inequalities includes the solution of linear and
quadratic equations and inequalities, equation systems and other algebraic
equations.
• Coordinate geometry includes plane geometry, the coordinate plane , straight
lines, conics, sets of points in the plane, and graphs of algebraic functions.
• Applications and other algebra topics ask about complex numbers, series and
sequences, determinants, permutations and combinations , fractions, and word
problems.
• The last category, functions and trigonometry, presents questions about
polynomials, algebraic, exponential, logarithmic and trigonometric functions .
Algebraic Operations
Solutions of Equations and Inequalities
Coordinate Geometry
Functions
Trigonometry
Applications and other Topics
The Algebraic Operations content area includes simplification of rational
algebraic expressions, factoring and expanding polynomials, and manipulating
roots and exponents. The Solutions of Equations and Inequalities content area
includes the solution of linear and quadratic equations and inequalities,
systems of equations, and other algebraic equations. The Coordinate Geometry
area presents questions involving plane geometry, the coordinate plane, straight
lines, conics, sets of points in the plane, and graphs of algebraic functions.
The Functions content area includes questions involving polynomial, algebraic,
exponential, and logarithmic functions. The Trigonometry area includes
trigonometric functions. The Applications and other Algebra Topics area contains
complex numbers, series and sequences, determinants, permutations and
combinations, factorials, and word problems. A total of 20 questions are
administered on this test.
Sample question: If the 1st and 3rd terms of a geometric sequence are 3
and 27, respectively, then the 2nd term could be
a) 6
b) 9
c) 12
d) 15
e) 18
(the correct answer is b)
Here are some of the knowledge and skills associated with
the College-Level Math test.
•identify common factors
•factor binomials and trinomials
•manipulate factors to simplify complex fractions.
•work with algebraic expressions involving real number exponents
•factor polynomial expressions
•simplify and perform arithmetic operations with rational expressions, including
complex fractions
•solve and graph linear equations and inequalities
•solve absolute value equations
•solve quadratic equations by factoring
•graph simple parabolas
•understand function notation, such as determining the value of a function for a
specific number in the domain
•a limited understanding of the concept of function on a more sophisticated
level, such as determining the value of the composition of two functions
•a rudimentary understanding of coordinate geometry and trigonometry
•understand polynomial functions
•evaluate and simplify expressions involving functional notation, including
composition of functions
•solve simple equations involving trigonometric functions, logarithmic functions,
and exponential functions
•perform algebraic operations and solve equations with complex numbers
•understand the relationship between exponents and logarithms and the rules that
govern the manipulation of logarithms and exponents
•understand trigonometric functions and their inverses
•solve trigonometric equations
•manipulate trigonometric identities
•solve right-triangle problems
•recognize graphic properties of functions such as absolute value, quadratic, and
logarithmic
Note: Here are the USU course descriptions. If you
don’t recognize part of the description, plug it into the suggested above web
sites or your internet search box. There is an abundance of information for you
to review.
MATH 0900 Elements of Algebra 3©
Review of elementary
algebra in preparation for MATH 1010. Remedial class not carrying USU or
transfer credit. Remedial fee required. Graded Pass /Fail only.
MATH 1010 Intermediate Algebra 4©
Linear equations and
inequalities, polynomials and exponents, rational expressions, roots and
radicals, quadratic equations, lines and systems of linear equations.
Prerequisite: C- or better in MATH 0900 or Math ACT score of at least 23 (Math
SAT score of at least 540) within the Math prerequisite acceptability time
limit; or satisfactory score on Math Placement Test . Course fee required.
MATH 1030 QL Quantitative Reasoning 3
Exploration of
contemporary mathematical thinking, motivated by its application to problems in
modern society. Emphasizes development of skill in analytical reasoning.
Prerequisite: C- or better in MATH 1010 or Math ACT score of at least 23 (Math
SAT score of at least 540) within the Math prerequisite acceptability time
limit; or satisfactory score on Math Placement Test.
MATH 1050 QL College Algebra 4©
Real and complex number
systems, graphs, inverse functions, polynomial and rational functions,
exponential and logarithmic functions, systems of equations, elementary matrix
algebra, induction, binomial theorem, permutations and combinations. Graphing
calculator required . Prerequisite: C- or better in MATH 1010, or Math ACT score
of at least 23 (Math SAT score of at least 540), or AP calculus score of at
least 3 on the AB exam within the Math prerequisite acceptability time limit; or
satisfactory score on Math Placement Test.
MATH 1060 Trigonometry 2©
Trigonometric functions,
equations, identities, and applications. Graphing calculator required .
Prerequisite: C- or better in MATH 1010 (or MATH 1050), or Math ACT score of at
least 23 (Math SAT score of at least 540), or AP calculus score of at least 3 on
the AB exam within the Math prerequisite acceptability time limit; or
satisfactory score on Math Placement Test. May be taken concurrently with MATH
1050.
MATH 1100 QL Calculus Techniques 3
Techniques of
elementary calculus, differentiation, integration, elementary optimization, and
introduction to partial derivatives. Applications in business, social science,
and natural resources. Graphing calculator required. Prerequisite: C- or better
in MATH 1050 or Math ACT score of at least 25 (Math SAT score of at least 580)
within the Math prerequisite acceptability time limit; or satisfactory score on
Math Placement Test.
MATH 1210 QL Calculus I 4 Analytic geometry, differential and integral calculus,
transcendental functions, and applications. Graphing calculator required.
Prerequisite: C- or better in
MATH 1050 and 1060, or Math ACT score of at least 27 (Math
SAT score of at least 620), or AP calculus score of at least 3 on the AB exam
within the Math prerequisite acceptability time limit; or satisfactory score on
Math Placement Test.
STAT 1040 QL Introduction to Statistics 3©
Descriptive and
inferential statistical methods. Emphasis on conceptual understanding and
statistical thinking. Examples presented from many different areas.
Prerequisite: C- or better in MATH 1010 or Math ACT score of at least 23 (Math
SAT score of at least 540) within the Math prerequisite acceptability time
limit; or satisfactory score on Math Placement Test.
STAT 2000 QI Statistical Methods 3©
Introduction to
statistical concepts, graphical techniques, probability, distributions,
estimation, one and two sample testing, chi-square tests, and simple linear
regression. Prerequisite: C- or better in MATH 1050 or Math ACT score of at
least 23 (Math SAT score of at least 540) within the Math prerequisite
acceptability time limit; or satisfactory score on Math Placement Test.
STAT 2300 QL Business Statistics 4©
Descriptive and
inferential statistics, probability, sampling, estimation, tests of hypotheses,
linear regression and correlation, chi-square tests, analysis of variance, and
multiple regression. Prerequisite: C- or better in MATH 1050 or Math ACT score
of at least 25 (Math SAT score of at least 580) within the Math prerequisite
acceptability time limit; or satisfactory score on Math Placement Test.
Syllabus for Finite Mathematics
I. COURSE DESCRIPTION:
This course emphasizes mathematical skills and techniques applicable to
business, life sciences and
social sciences. Course topics include linear functions, quadratic functions,
mathematics of finance,
systems of equations, matrices, linear programming , set theory, combinatorics,
and basic probability .
The use of a graphing calculator is required for this course to further the
exploration of these topics
and their applications.
This course meets the SUNY General Education Requirements for Mathematics.
II. COURSE PREREQUISITE:
MAT100-Introductory Algebra or equivalent
III. TEXT AND MATERIALS:
• Finite Mathematics for Business, Economics, Life Sciences, and Social
Sciences, 11th edition, by
Raymond A. Barnett, Michael R. Ziegler, and Karl E. Byleen.
Prentice Hall . ISBN # 0-135-14385-3
• A graphing calculator (TI-83 Plus or TI-84 Plus recommended)
• Pencils
• A 3-ring binder and highlighter (recommended)
Supplemental Resources (not required):
CourseCompass with MyMathLab is an online course that can be used to access
online activities and
resources, such as video lectures, practice problems, and sample tests. You need
a MyMathLab
Student Access Code to access the course.
IV. COURSE OBJECTIVES AND SUNY GENERAL EDUCATION KNOWLEDGE
AREA LEARNING OUTCOMES:
Course Objectives:
As the result of instructional activities, students will be able to:
1. Determine the x- and y- intercepts of a graph algebraically and graphically
2. Calculate the slope of a line
3. Write an equation of a line given the y-intercept and the slope
4. Write an equation of a line given one point and the slope
5. Write an equation of a line given two points
6. Write an equation of a vertical line
7. Write an equation of a horizontal line
8. Use a graphing calculator to draw a scatterplot
9. Use a graphing calculator to find a linear regression model, where
appropriate
10. Use a linear regression equation to make predictions
11. Solve a linear inequality
12. Determine if a given relation is a function
13. Identify the family to which a function belongs
14. Identify the domain and range of a function
15. Evaluate a function
16. Graph a function
17. Apply transformations to basic functions
18. Create cost, revenue and profit functions
19. Find a break-even point
20. Find the equilibrium quantity and price given supply and demand functions
21. Determine whether a parabola opens upward or downward
22. Determine the vertex of a parabola graphically and algebraically using –b/2a
23. Determine the axis of symmetry of a parabola
24. Determine the maximum or minimum value of a quadratic function
25. Use a graphing calculator to find a quadratic regression model, where
appropriate
26. Use a quadratic regression equation to make predictions
27. Use the simple interest formula
28. Use the compound interest formula
29. Determine whether a system of equations is consistent and independent,
dependent, or inconsistent
30. Solve a system of linear equations graphically
31. Solve a system of linear equations algebraically using substitution
32. Solve a system of linear equations algebraically using elimination
33. Solve a system of linear equations using a matrix
34. Graph a linear inequality in two variables
35. Graph a system of linear inequalities and identify the feasible region
36. Formulate a linear programming model
37. Solve a linear programming model graphically
38. Define set, subset, empty set, universal set
39. List the elements of a set
40. Identify the number of elements in a set
41. Use the set operations of union, intersection, and complementation
42. Draw Venn Diagrams to illustrate relationships between sets
43. Determine the sample space of an experiment
44. Determine if two events are disjoint (mutually exclusive)
45. Calculate a factorial
46. Distinguish between a permutation and a combination
47. Calculate a permutation
48. Calculate a combination
49. Calculate basic probabilities
50. Use the addition rule for probability
51. Use the complement rule for probability
52. Calculate a conditional probability
53. Determine if two events are independent
54. Use the product rule for probability
SUNY General Education Knowledge Area Learning Outcomes:
Students will demonstrate the ability to:
1. interpret and draw inferences from mathematical models such as formulas,
graphs, tables and
schematics;
2. represent mathematical information symbolically, visually, numerically and
verbally ;
3. use arithmetical, algebraic, geometric and statistical methods to solve
problems ;
4. estimate and check mathematical results for reasonableness, determine
alternatives and select
optimal results; and
5. recognize the limits of mathematical and statistical methods.
V. GENERAL TOPICS OUTLINE
1. Linear Equations and Inequalities ( textbook chapter 1)
including intercepts, slope, writing equations, graphing, inequalities, linear
regression
2. Functions and Graphs (textbook chapter 2)
including identifying functions, evaluating functions, graphing, domains,
applications
3. Quadratic Functions (textbook chapter 2)
including graphing, vertex, axis of symmetry, quadratic regression, applications
4. Mathematics of Finance (textbook chapter 3)
including simple interest, compound interest
5. Systems of Linear Equations and Matrices (textbook chapter 4)
including solving 2x2 systems of linear equations algebraically and graphically,
solving 3x3 systems,
applications
6. Linear Programming (textbook chapter 5)
including graphing systems of linear inequalities, linear programming
7. Set Theory and Combinatorics (textbook chapter 7)
including definitions, Venn diagrams, set operations, permutations,
combinations, applications
8. Probability (textbook chapter 8)
including addition rule, complement rule, conditional probability, independence,
applications
Unit Planning Sheets for Grade 5 Math
POTENTIAL
CHALLENGES - UNIT 4: |
word problems and multistep problems ; division
algorithms; friendly
numbers; measuring (on pg. 226 TLG); Math Messages 4.2-4.4;
interpreting remainders |
| ACCOMMODATIONS: |
repeatedly divide by 10 instead of magnitude
estimates on division;
Division Dash directions |
SKILLS STUDENTS
WILL LIKELY DO WELL
ON: |
secure skills; mental math; multiplication in
math boxes ; division game |
POTENTIAL 2-DAY
LESSONS: |
typically none; pace as you feel is necessary |
OTHER
CONSIDERATIONS: |
watch for place value practice for assessment |
POTENTIAL
CHALLENGES - UNIT 5: |
visualizing fractions; converting from fractions
to decimals to percents |
| ACCOMMODATIONS: |
a lot of hands on activities; have students
demonstrate concepts |
SKILLS STUDENTS
WILL LIKELY DO WELL
ON: |
increased ability to use abstract thinking to
problem solve |
POTENTIAL 2-DAY
LESSONS: |
typically none (or possible 5.4 -
Developing/Secure); fraction skills are
embedded in almost every lesson in units 6 and 7 |
OTHER
CONSIDERATIONS: |
keep Study Link 5.10 for lesson 6.1 |
POTENTIAL
CHALLENGES - UNIT 6: |
stem/leaf plots; slide rule; measurement (all
kinds); finding median of
data; lesson 6.5 (sample size); find a ready set of data for plotting
and
reviewing; collect jumping data (6.4) ; interpreting and analyzing data;
fraction to decimal to percent |
| ACCOMMODATIONS: |
Do some lessons as a class instead of in pairs;
enlarge a ruler and make
a transparency - color code 1/4, 1/8, 1/16; calculators for some
fraction work; clock model; probability meter; data ahead of time; use
Post It notes to remind self of things needed in next lesson; 6.4 -
collect data in P.E. class; collect data from weather map, sports page.
etc. |
SKILLS STUDENTS
WILL LIKELY DO WELL
ON: |
landmark skills; changing fractions to mixed
numbers and reverse;
equivalent fractions; reading data; math box skills ; measurement |
POTENTIAL 2-DAY
LESSONS: |
6.1- Organizing Data (Secure); 6.6 - Analysis of
Sample Data (Secure);
6.8 - Using a Slide Rule to Add and Subtract Fractions (Dev./Secure);
6.9 - Clock Fractions and Common Denominators (Developing - 1 1/2
days) |
OTHER
CONSIDERATIONS: |
need map from lesson 5.10 for lesson 6.1; number
line (6.1) class tally
chart/graph (6.2); stem and leaf plot on transparency (6.3); need candy
& circle with center mark (6.5); post it notes; prepare slide rules &
set up way to assist students with slide rule; save
sample data sheet
for next unit; collect slide rule for next unit; must play First to 21
at
least 50 times; review landmarks |
POTENTIAL
CHALLENGES - UNIT 7: |
comparing positive and negative numbers ; powers
of 10; order of
operations ; slide rule as a tool; math message (7.2, 7.4) |
| ACCOMMODATIONS: |
transparencies for direct teaching; partners for
shared thinking (divide
and conquer!); display rules for order of operations ; incorporate more
whole group activities instead of partners; have students write PEMDAS
(Please Excuse My Dear Aunt Sally) next to each Order of Operations
problem. Cross off letters as you work through the problem ; give kids
# cards & scramble - they have to get in correct order |
SKILLS STUDENTS
WILL LIKELY DO WELL
ON: |
exponential notation; using a calculator for
exponents; many of the
mental math and math box activities |
POTENTIAL 2-DAY
LESSONS: |
possibly 7.4, 7.5 |
OTHER
CONSIDERATIONS: |
cut +/- counters; learn games (7.1, 7.4, 7.6);
can't do study link 7.1
without 10-digit calculator; post definitions; post number line (7.6);
locate book , The King's Chessboard; MMR for 7.4 on sentence strips;
overhead of slide rule; make +/- # cards; practice vocabulary
(especially prefixes); NOTE: order of operations is listed as
developing,
but it is on ISTEP test |
POTENTIAL
CHALLENGES - UNIT 8: |
comparing fractions with unlike denominators; GCD
leaves some room
for student error; renaming mixed numbers containing improper
fractions; "of" means to multiply; area using fractions; multistep
problems (8.8) |
| ACCOMMODATIONS: |
use LCD in some cases (ONLY IF KIDS ARE
READY...DON'T UNDERMINE
CONCEPTUAL UNDERSTANDING); use manipulatives to help with concept
building; somewhat slower pace with new concepts |
SKILLS STUDENTS
WILL LIKELY DO WELL
ON: |
some of the games; one whole is also a fractional
part (8/8, 5/5);
finding area |
POTENTIAL 2-DAY
LESSONS: |
8.5; 8.8; 8.9; 8.10 |
OTHER
CONSIDERATIONS: |
calculators may not have all features needed;
teachers should practice
8.5 before doing with students; Fraction Spin (8.5) is ESTIMATION, not
exact answers |
POTENTIAL
CHALLENGES - UNIT 9: |
journal 324-326 (Four Fours problem - do not
spend a lot of time doing
this); concept of volume is developing |
| ACCOMMODATIONS: |
use of calculator and/or multiplication chart |
SKILLS STUDENTS
WILL LIKELY DO WELL
ON: |
graphing on one-quadrant grid (D/S) |
POTENTIAL 2-DAY
LESSONS: |
9.4 and 9.5 - 1 1/2 days each (Secure) |
OTHER
CONSIDERATIONS: |
use literature links; 9.4 need display of unit
squares; 9.7 need floor plan
of school; 9.8 make example of activity sheet 7; 9.9 need triangular
prism and parallelogram; enrichment activity for 9.9 needs Post It notes |
