Math Placement Test
AE109 - FOUNDATIONS OF ALGEBRA
Description and Objectives
The AE109 course - Foundations of Algebra - is a continuation of AE108. Topics covered include signed numbers, basic algebra operations, exponents, word problems, charts, basic graphing, and English-Metric methods of measurement. Placement in this class is based on the results of assessment or Placement Test scores, successful completion of AE108, or permission of the instructor.
Completion of AE109 provides students with the minimum requirements for enrollment into college level mathematics courses. Students must meet minimum requirements before enrolling in college level mathematics courses. If minimum requirements are not met, the student receives a grade of "Incomplete" (I) and repeats the course.
Developmental in nature, credit in this course does not apply towards graduation.
In relationship with the college mission and objectives to provide Native American Tribes of Michigan and their surrounding community with educated and trained human resources, and to prepare and encourage students to pursue further education at the end of this course, the student will be able to perform each of the following objectives.
The AE109 course assumes a working knowledge of the basic mathematical operations. Topics which are covered in the AE108 course and which you are expected to understand include whole numbers, fractions, decimals, percents, ratios and proportions, word problems, and some applications for business and industry. The material below is organized as presented in each chapter in the textbook.
Chapter 1
A. To identify the order relation between two numbers B. To write whole numbers in words and in standard form C. To write whole numbers in expanded form D. To round a whole number to a given place value E. To add whole numbers F. To subtract whole numbers--with and without borrowing G. To multiply whole numbers H. To divide whole numbers--with and without remainders I. To simplify expressions that contain exponents J. To use the Order of Operations Agreement to simplify expressions K. To factor numbers L. To find the prime factorization of a number A sample of each of these objectives follows:
A. To identify the order relation between two numbers
whole numbers = 0, 1, 2, 3, ...
7 > 4 , 5 < 7
B. To write whole numbers in words and in standard form
25,048,732 = Twenty five million forty eight thousand seven hundred thirty two
C. To write whole numbers in expanded form
62,749 = 60,000 + 2,000 + 700+ 30 + 2
D. To round a whole number to a given place value
13,864 => 13,800
E. To add whole numbers
54 + 72 + 981 + 882 = 1,989
F. To subtract whole numbers--with and without borrowing
8465 - 7839 = 626
G. To multiply whole numbers
7596 x 8475 = 64,376,100
H. To divide whole numbers--with and without remainders
64853 / 743 = 87 r212
I. To simplify expressions that contain exponents
23 x 52 = 200
J. To use the Order of Operations Agreement to simplify expressions
5 x ( 9 - 5) 2 / 4 - 2 = 18
K. To factor numbers
Factors of 60 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 22, 23,30, 60
L. To find the prime factorization of a number
Prime factors of 60 are 2, 2, 3, 5
Chapter 2
A. To find the least common multiple (LCM) B. To find the greatest common factor (GCF) C. To write a fraction that represents part of a whole D. To write an improper fraction as a mixed number or a whole number, and a mixed number as an improper fraction E. To find equivalent fractions by raising to higher terms F. To write a fraction in simplest form G. To add fractions, whole numbers, and mixed numbers H. To subtract fractions, whole numbers, and mixed numbers I. To multiply fractions, whole numbers, and mixed numbers J. To divide fractions, whole numbers, and mixed numbers K. To identify the order relation between two fractions L. To simplify expressions containing exponents M. To use the Order of Operations Agreement to simplify expressions A sample of each of these objectives follows:
A. To find the least common multiple (LCM)
LCM of 3, 5, 12, 15 is 60
B. To find the greatest common factor (GCF)
GCF of 24, 36, 60 and 96 is 12
C. To write a fraction that represents part of a whole
Convert from pictures to fractions
D. To write an improper fraction as a mixed number or a whole number, and a mixed number as an improper fraction
3 1 4 3 E. To find equivalent fractions by raising to higher terms
6 15 8 20 F. To write a fraction in simplest form
75 15 100 20 G. To add fractions, whole numbers, and mixed numbers
3 5 H. To subtract fractions, whole numbers, and mixed numbers
6 3 5 I. To multiply fractions, whole numbers, and mixed numbers
6 7 9 J. To divide fractions, whole numbers, and mixed numbers
2 1 2 K. To identify the order relation between two fractions
5 11 8 18 L. To simplify expressions containing exponents
Simplify 3 2 2 3 M. To use the Order of Operations Agreement to simplify expressions
Simplify 3 5 2 4 8 Chapter 3
A. To write decimals in standard form and in words B. To round a decimal to a given place value C. To add decimals D. To subtract decimals E. To multiply decimals F. To divide decimals G. To convert fractions to decimals H. To convert decimals to fractions I. To identify the order relation between two decimals or between a decimal and a fraction A sample of each of these objectives follows:
A. To write decimals in standard form and in words
273.158 = Two hundred seventy three and one hundred fifty eight thousandths
B. To round a decimal to a given place value
291.6951 to the nearest hundredth = 291.70
C. To add decimals
23.419 + 451.2 + 8.1234 = 482.7424
D. To subtract decimals
451.2 - 23.419 - 8.1234 = 419.6576
E. To multiply decimals
451.2 x 23.419 = 10566.6528
F. To divide decimals
0.1325 ÷ 0.01325 = 10
G. To convert fractions to decimals
H. To convert decimals to fractions
I. To identify the order relation between two decimals or between a decimal and a fraction
Is 0.63 Chapter 4
A. To write the ratio of two quantities in simplest form B. To write rates and unit rates C. To determine whether a proportion is true D. To solve proportions A sample of each of these objectives follows:
A. To write the ratio of two quantities in simplest form
B. To write rates and unit rates
390 miles in 6.5 hours = 60 miles per hourC. To determine whether a proportion is true
D. To solve proportions
Chapter 5
A. To write a percent as a fraction or a decimal B. To write a fraction as a decimal or a percent C. To find the amount when the percent and the base are given D. To find the percent when the base and the amount are given E. To find the base when the percent and the amount are given F. To solve percent problems using proportions A sample of each of these objectives follows:
A. To write a percent as a fraction or a decimal
B. To write a fraction as a decimal or a percent
C. To find the amount when the percent and the base are given
15 % of 60 = 9
D. To find the percent when the base and the amount are given
34 out of 40 = 85%
E. To find the base when the percent and the amount are given
20 is 80% of what? (Ans = 25)
F. To solve percent problems using proportions
Word problems on the above objectives
PLACEMENT TEST
Our purpose in having you write a placement test is to attempt to put you in the highest level math course that you can comfortably handle.
The material above is covered in the AE108 course. The Placement test for AE109 measures your understanding of this material. If you feel you understand the above objectives and examples quite well, then you should write the placement test for AE109. Click on the AE109 Test link below.
If, on the other hand, you feel you that the material listed above is fairly new or that it has been a long time since you had Math, then it would probably be better to start at the basic level - AE108. Click on the AE108 Requirements link below.
To look at the course objectives for any of the other courses, click on the respective courses buttons.
Bay Mills Community College