Section 1: Numerical Skills/Pre- algebra Placement Test
| Content Areas |
Percentage of
Items in Pool |
| Basic ope rations with integers |
11 |
| Basic operations with fractions |
20 |
| Basic operations with decimals |
14 |
| Exponents |
9 |
| Ratios and proportions |
10 |
| Percentages |
15 |
| Conversions between fractions and decimals |
1 |
| Multiples and factors of integers |
3 |
| Absolute values of numbers |
3 |
| Averages (arithmetic means) |
10 |
| Order concepts (greater than; less than) |
1 |
| Estimation skills |
<1 |
| Number theory |
1 |
| Counting problems and simple probability |
2 |
Computing and Arithmetic Average
1. What is the average (arithmetic mean) of 8,7,7,5,3,2 and 2?
Basic Operations with Decimals
2. Ben is making wooden toys for the next arts and crafts sale. Each toy
costs Ben $1.80 to make. If he sells
the toys for $3.00 each, how many will he have to sell to make a profit of
exactly $36.00 ?
Basic Operations with Fractions
3. How many yards of material from a 24-yard length of cloth remain after 3
pieces, each
yards long,
and 5 pieces, each 
yards long are removed ?
Percentages
4. Phillip charged $400 worth of goods on his credit card. On his first bill, he
was not charged any interest,
and he made a payment of $20. He then charged another $18 worth of goods. On his
second bill a month
later, he was charged 2% interest on his entire unpaid balance. How much
interest was Phillip charged on
his second bill ?
Order Concepts (greater than; less than)
5. From <, ≤, =, >, ≥, ≠, choose all the symbols that make the statement: 25 - 5
__ 14 + 3 true.
Exponents
6. Evaluate and simplify: 52 + 30
Section 2: Algebra Placement Test
The Algebra Placement Test comprises topics from three major mathematics
curricular areas, as follows:
| Curricular Area |
Content Areas |
Percentage of
Items in Pool |
| Elementary Algebra |
Substituting values in algebraic equations |
9 |
| |
Setting up equations for given situations |
9 |
| |
Basic operations with polynomials |
9 |
| |
Factoring polynomials |
9 |
| |
Solving polynomial equations by factoring |
3 |
| |
Formula manipulation and field axioms |
2 |
| |
Linear equations in on variable |
12 |
| |
Exponents |
5 |
| |
Linear inequalities in on variable |
2 |
| In termediate Algebra |
Rational expressions |
9 |
| |
Exponents |
5 |
| |
Systems of linear equations in 2 variables |
2 |
| |
Quadratic formulas |
<1 |
| |
Absolute value equations and inequalities |
<1 |
| Coordinate Geometry |
Linear equations in 2 variables |
13 |
| |
Distance formulas in the plane |
4 |
| |
Graphing conics (circles, parabola, etc.) |
3 |
| |
Graphing relations in the plane |
2 |
| |
Graphing systems of equations & functions |
<1 |
| |
Midpoint formulas |
<1 |
Elementary Algebra: Linear Equations in One Variable
1. A student has earned scores of 87, 81, and 88 on the first of 3 of 4 tests.
If the student wants an average
(arithmetic mean) of exactly 87, what score must she/he earn on the fourth test
?
Elementary Algebra: Basic Operations with Polynomials
2. Which of the fol lowing expressions re presents the product of 3 less than
twice x and 2 more than the
quantity 3 times x ?
Elementary Algebra: Substituting Values in Algebraic
Expressions
3. If x = −1 and y = 2, what is the value of the expression 2x3 − 3xy ?
Intermediate Algebra: Rational Expressions
4. For all r ≠ ±2, 
Coordinate Geometry: Linear Equations in 2 Variables
5. What is the equation of the line that contains the points with (x, y)
coordinates (-3,7) and (5,-1) ?
Systems of linear equations in 2 variables
6. The x-coordinate of the solution of the system
is
Basic operations with polynomials
7. Solve: 
Solving polynomial equations by factoring
8. The solutions of x2 - 2x - 24 = 24 are:
Section 3: College Algebra Placement Test
| Content Areas |
Percentage of
Items in Pool |
| Functions |
40 |
| Exponents |
25 |
| Complex numbers |
15 |
| Arithmetic and geometric sequences and series |
7 |
| Factorials |
6 |
| Matrices (basic operations, equations, and
determinants) |
3 |
| Systems of linear equations in three or more
variables |
1 |
| Logic and proof techniques |
1 |
| Roots of polynomials |
2 |
Complex Numbers
1. For 
, if 3i (2+5i) = x + 6i, then x = ?
Functions
2. If f(4) = 0 and f(6) = 6, which of the following could represent f(x) ?
Roots of polynomials
3. What is the value of m in the equation 3x2 - 5x = m if one root is equal to
zero?
Exponents
4. Find a number with no negative exponents equivalent to
Roots of polynomials
5. Which of the following is true of the roots of the equation x2 - 6x + 8 = 0?
A. They are opposite in sign and equal .
B. They are opposite in sign and the larger root is positive.
C. They are opposite in sign and the larger root is negative.
D. They are both positive.
E. They are both negative
Arithmetic and Geometric Sequences and Series
6. Find the fifth term, and the eighth term of the geometric sequence:
8,4,2,1,...
7. Find the sums of the infinite geometric series:
Section 4: Trigonometry Placement Test
| Content Areas |
Percentages of
Items in Pool |
| Trigonometric functions and identities |
35 |
| Right-triangle trigonometry |
27 |
| Trigonometric equations & inequalities |
10 |
| Graphs of trigonometric functions |
20 |
| Special angles (multiples of 30 and 45 degrees) |
8 |
| Polar coordinates |
<1 |
Trigonometric Functions and Identities
1. Which of the following is equivalent to
?
Right Triangle Trigonometry
2. From a point on the ground the angle of elevation to a ledge on a building is
27°, and the distance to the base of the
building is 45 meters. How many meters high is the ledge?
Trigonometric Functions and Identities
3. Find the values of the trigonometric functions of θ if θ is the angle of the
pictured right triangle.
ie. in following order sin, cos, tan, csc, sec, cot
Answers to Sample Items
Section 1: Numerical Skills/Pre-algebra Placement Test
Section 2: Algebra Placement Test
Section 3: College Algebra Placement Test
Section 4: Trigonometry Placement Test
