Math for Liberal Arts

Course Description

“What is mathematics? … It’s certainly not just a fixed body of knowledge, … its hidden tendrils pervade every aspect of modern life.” — Ian Stewart

The Math for Liberal Arts DSST 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 use of a non-programmable calculator is permitted in this exam.

Exam 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%

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)
Operations with real numbers and their properties (including the distributive properties)
Prime and composite numbers; divisibility rules; prime factors of composite numbers
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)
Rules of exponents including rational exponents
Scientific notation

II. Sets and Logic – 16%

The Nature of Sets
Subsets and Set Operations, (set-builder notation; roster form, using sets to solve problems)
Using Venn Diagrams to Study Set Operations
Infinite Sets
Simple and compound statements; qualifiers “and” and “or” and their symbols; conjunction and disjunction; conditional and biconditional statements including Qualifiers
Truth value of a compound statement including Truth Tables
Types of Statements ( Negations of Conditional Statements and De Morgan’s Laws)
Logical Arguments including Euler Circles

III. Metric system, conversions and geometry – 12%

Introduction to metrics and U.S. customary unit systems
Conversions between metric and U.S. customary unit systems, including Dimensional Analysis
Properties of lines and angles
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%

Order of operations
Simplifying expressions; equations with one variable; proportion problems
Evaluation of formulas
Graphs of linear equations in the rectangular coordinate system
Functions including polynomials (not to include rational, exponential and logarithmic Functions)

V. Linear Systems and Inequalities – 8%

Solving Linear Equations including applications and systems
The Rectangular Coordinate System and Linear Equations in Two Variables
Graphing and solving Linear inequalities
Graphing and solving systems of inequalities

VI. Exponents and Logarithms including Financial Literacy – 22%

Properties of Logarithms
Logarithmic and Exponential Functions
Simple InterestCompound Interest
Compound Interest
Installment Buying
Student Loans and Home Buying
Investing in Stocks and Bonds

VII. Counting, Probability Theory and Statistics – 20%

Fundamentals of Probability including the Counting Principle
Permutations and Combinations
Events Involving Not and Or
Odds and Conditional Probability
Mean, Median and Mode
Range, Variance and Standard Deviation
Graphical representation (including Bar graph, pie chart, histogram, line graph, scatterplots etc.)

Sample Questions

All test questions are in a multiple-choice format, with one correct answer and three incorrect options. The following are samples of the types of questions that may appear on the exam.

1. Heidi and Oliver are planning to buy a bedroom furniture set that costs $4,100 plus 6% taxes. They would like to apply for a 0% APR store credit card on purchases for 10 months. How much money do they need to pay in equal installments monthly for the next 10 months such that they will be able to pay off the bedroom furniture set before the 0% APR offer expires?

$43.46 per month.
$385.40 per month.
$410.00 per month.
$434.60 per month.

2. An electronics store sold 1,500 computers and smartphones in a month. Out of the total number of consumers who purchased these items, 2% bought a computer and a smartphone, while the others bought only a computer or a smartphone. If 1,206 consumers bought smartphones, how many people bought computers?

324 consumers.
2.16% of all consumers.
19.6% of all consumers.
294 consumers.

3. If the figure below is constructed out of two semicircles and a square, what is the area of the whole figure? (Round to the nearest tenth of a meter squared)

37.3 m2
50.1 m2
64.3 m2
149.1 m2

4. Write a variable expression for the area of a square whose side length is (x + 8) units.

x² – 16x + 64 square units
x² + 16x + 64 square units
x² + 16x – 64 square units
x² + 64x + 16 square units

5. The population growth of an animal species is described F(t) = 320 log(4t + 4), where t is the number of months since the species was introduced. Find the population of this species 8 months after the species is introduced to an area. Round to the nearest whole number.

-1
320
498
1147

6. Find the mode for the following data: 12, 12, 12, 14, 16, 18, 20, 22, 25, 25, 29, 33, 37, 37, 39.

7. The function f(x) = 2.4 + 8 ln x, given in centimeters, models the height of a certain animal species where x is the number of days the animal has been alive. Determine the height of the animal after it has been alive for 16 days.