This exam covers topics such as real number systems; sets and logic; metric system, conversions and geometry; algebra, graphs and functions (as applied to real life applications); linear systems and inequalities; exponents and logarithms including financial literacy and counting, probability theory and statistics The exam contains 80 questions to be answered in 2 hours. The use of a non-programmable calculator is permitted in this exam.
EXAM CONTENT OUTLINE
The following is an outline of the content areas covered in the examination. The approximate percentage of the examination devoted to each content area is also noted.
I. Real Number Systems – 11%
a. Real numbers: Natural Numbers, Integers, Rational Numbers, Irrational Numbers, The real number line. ( Percentages; Fractions and reducing fractions; conversion between decimal numbers and fractions; operations with fractions (including distributive property))
b. Operations with real numbers and their properties (including the distributive properties) c. Prime and composite numbers; divisibility rules; prime factors of composite numbers d. Systems of Numeration: Place value or positional value numeration, Base 10 expanded forms; base 2 numbers; conversion between base 10 and base 2; (Including Roman Numerals) e. Rules of exponents including rational exponents f. Scientific notation
II. Sets and Logic – 16%
a. The Nature of Sets
b. Subsets and Set Operations, (set-builder notation; roster form, using sets to solve problems)
c. Using Venn Diagrams to Study Set Operations
d. Infinite Sets
e. Simple and compound statements; qualifiers “and” and “or” and their symbols; conjunction and disjunction; conditional and biconditional statements including Qualifiers
f. Truth value of a compound statement including Truth Tables g. Types of Statements ( Negations of Conditional Statements and De Morgan’s Laws)
h. Logical Arguments including Euler Circles
III. Metric system, conversions and geometry – 12%
a. Introduction to metrics and U.S. customary unit systems
b. Conversions between metric and U.S. customary unit systems, including Dimensional Analysis
c. Properties of lines and angles
d. Perimeter and area of 2D geometric objects e. Area, Surface area and volume of 3D solid objects
IV. Algebra, graphs and functions (as applied to real life applications)– 11%
a. Order of operations
b. Simplifying expressions; equations with one variable; proportion problems
c. Evaluation of formulas
d. Graphs of linear equations in the rectangular coordinate system e. Functions including polynomials (not to include rational, exponential and logarithmic Functions)
V. Linear Systems and Inequalities – 8%
a. Solving Linear Equations including applications and systems
b. The Rectangular Coordinate System and Linear Equations in Two Variables
c. Graphing and solving Linear inequalities
d. Graphing and solving systems of inequalities
VI. Exponents and Logarithms including Financial Literacy – 22%
a. Properties of Logarithms
b. Logarithmic and Exponential Functions
c. Simple Interest
d. Compound Interest
e. Installment Buying
f. Student Loans and Home Buying
g. Investing in Stocks and Bonds
VII. Counting, Probability Theory and Statistics – 20%
a. Fundamentals of Probability including the Counting Principle
b. Permutations and Combinations
c. Events Involving Not and Or
d. Odds and Conditional Probability
e. Mean, Median and Mode
f. Range, Variance and Standard Deviation
g. Graphical representation (including Bar graph, pie chart, histogram, line graph, scatterplots etc.)