Placement Exam

Topics from Pre-Algebra

• Perform operations (+, –, x, ÷) with whole numbers, decimals , fractions and integers.

Exs: 234.45 + 23.6 – 16.78 =;

• Convert from standard notation to scientific notation and back.

Exs: Express in scientific notation: 23 million; 15 hundredth; 12,500; 0.00047.
Perform the indicated operations and express the answer in scientific notation:

Express in standard form: 2 .45 ×10³; 4.7 ×10^-4 .

• Find multiples and factors of integers .

Exs: Express as a product of prime factors: 108
Find the LCM of 12 & 16; of 12, 16 & 18.
Find the GCF of 12 & 16; of 12, 16 & 18.

• Work problems involving ratios, proportions and percents.

Ex: A gourmet coffee shop offers a blend containing 2 pounds of Colombian coffee for
every 3 pounds of Brazilian coffee. How many pounds of Colombian coffee are
needed to prepare 120 pounds of this blend?

• Evaluate arithmetic expressions involving absolute values.

Ex: − 3 + 4−| −8|= ?

Topics from Elementary Algebra

• Evaluate algebraic expressions for specified values of the variables .

Ex: Evaluate: for a = −2, b = −1, c = 0 .

• Evaluate one of the variables in a formula , given the values of all the other variables.

Exs: The area A, of a trapezoid with bases a & b and height h is given by the formula:
Find b, if
is the formula for the balance A, when P dollars are invested for t
years at an interest rate r, which is compounded n times a year. How much
should be invested at a fixed interest rate of 8% compounded quarterly, if after 3
years the balance is to be $25,000.00?

• Perform operations with integral exponents.

Exs: Assuming all variables positive, simplify the following expression . Give your
answer in terms of positive exponents only.

• Perform basic operations (simplification, +, –, × ) on polynomials.

Exs: Perform the indicated operations and simplify:

• Factor polynomials.

Exs. Factor completely over the real numbers:

Topics from Intermediate Algebra

• Set up equations that model a problem situation.

Ex 1: The longer leg of a right triangle is 4 more than the length of the shorter leg. The
hypotenuse is 18 cm. If x is the measure in cm of the shorter leg, apply the
Pythagorean theorem to write an equation, which models the problem situation.
This equation written in the form a x ² + bx + c = 0 is: ??

Ex 2: A telephone company charges a flat fee of C cents for the first 3 minutes of a
phone call. The cost of each additional minute over the first 3 minutes is A. If
Jesse’s call was M minutes long (M ≥ 3). What was the cost D of his phone call?
(Express D in terms of all the given variables.)

• Solve linear inequalities & compound linear inequalities, and express their solutions: 1)
in interval notation using the symbols as deemed necessary; 2) using set notation.
Finally, be able to draw the solution set on the number line .

Exs: In the following exercises, solve the inequalities for x and express their solution
using interval notation, set notation, and also draw the solution set on the
number line.

• Set up inequalities or compound inequalities that model a problem situation.

Ex: To get a B, Rita’s average on all 3 tests plus the final must be between 80 and 89
inclusively. Each test is out of 100 possible points, except for the final, which is
out 200 possible points. Let x represent Rita’s grade on the final. If she got 92,
75, and 70 on her three tests, set up a compound inequality in x, which models
the problem situation, and whose solution will provide Rita with a range of grades
necessary to obtain a B in the course.

• Perform basic operations with polynomial expressions .

Exs: Perform the indicated operations and simplify:
2 (2x − 3y )(2x + 3y) − 2(2x − 3y)² − 6xy ;

• Perform basic operations (simplification, +, - , x, ÷ ) with rational expressions.

Exs: Perform the indicated operations and/or simplify:

• Solve linear equations and equations that reduce to linear.

Exs: Solve for x: 7x + 4 = 5x – 12
Solve for x:
Solve for x: 2(x – 3) = 4x – 2(x + 3)
Solve for x: 2(x – 3) = 4x – 2(x + 5)
Solve for x: 4 (2x −1)² = 36 .

• Solve quadratic equations or equations that reduce to quadratic ones, using factoring,
&/or using the quadratic formula.

Exs: Solve for x: 3 x² − 5 x + 2 = 0; x ² − x = 20 ; ; 4 (2x −1)² = 36 .
Solve for x using the quadratic formula: 3 x² − 4x = 2 . Give the exact solutions in
their simplest form.

• Find the roots or zeros of polynomials (by factoring).

Ex: Find the zeros of the given polynomial using factoring along with the zero
product property: P (x) = 8x ³ −12x ² −18x + 27 .

• Solve literal equations (i.e., solve for one variable in terms of others).

Ex: Solve for :

• Perform operations on rational exponents.

Exs: Simplify and express the answer in terms of positive exponents only.
Evaluate: (No calculators please)

• Perform operations with radical expressions (simplification, +, - , x, ÷ ) and rationalize
denominators or numerators.

Exs: Simplify
Multiply out and simplify:
Rationalize the denominator and simplify:
Perform all indicated operations and simplify:

Topics from Coordinate Geometry

• Be able to obtain information from the graph of a function in the coordinate plane.

Exs:
Given the graph of y =f(x) and some value a, be able to determine from the graph
the value of f(a).
Given the graph of y = f(x), find all the x values for which f(x) = c, where c is some
given number.
Given the graph of y = f(x), determine the x intervals over which the graph of the
function is increasing, decreasing or is constant.
Given the graph of y = f(x), determine the domain and the range of y = f(x).

• Determine and interpret slope of lines , equations of lines and their graphs.

Exs:
Find an equation of the vertical line through (5,3) and its slope.
In the xy-coordinate plane, which straight lines have an undefined slope? Which
straight lines have a slope equal to 0?
Find an equation of the straight line through (3,4) parallel (or perpendicular) to
the line whose equation is 2y – 3x = 6.

Which of the graphs below is the graph of the equation 2x + 3y = 6?

Recommended resource
to help you review the above objectives

Intermediate Algebra, by Martin-Gay, 4^th edition, Prentice Hall, is the Math 0110 textbook
starting this fall semester 2004. Its “chapter highlights” at the end of every chapter offer a quick
review of Intermediate Algebra. Review Chapters 1, 2, 3, 5, 6, 7, & 8 (You may omit Chapter 4.).

Any high school Algebra II textbook, or any Elementary & Intermediate Algebra textbook would
also help you review the above objectives.