Advanced Problems

For advanced problems in math, please have a look at the examples and study tips below and then follow the link at the bottom of this page.

The excerpts below are from our math course download and study guide, which provide further practice in college-level math.

Advanced problems on the test includes topics that you may have studied in an advanced math course in high school.

The advanced problems on the math section of the Accuplacer contains twenty questions.

College-Level Math – Question Types and Tips

1) Trigonmetric, logarithmic, and exponential functions

An example of this type of college math problem is as follows:

What is the equivalent of the following logarithmic function in exponential form?

college-level-math-exercises-4

2) Geometry: graphs, coordinates, slope, lines, cones, and sets of points on a plane

If the problem is asking you about points on a plane, for instance, you will need to use the distance formula.

So, a sample question on this part of the examination would be similar to this one:

In the standard (x,y) plane, what is the distance between

(3, 4) and (6, 2)?

3) Systems of equations

Problems in this skill set will include the variables x and y and you will need to solve the problem by finding the factors of the numbers in the problem.

For instance, you might see something like this on the actual test:

What ordered pair is a solution to the following system of equations?

x + y = 12

xy = 35

4) Series and sequences

For these problems, you have to discover the pattern that exists among of the numbers in the list provided.

Example: What number is next in the sequence? 2, 4, 16 . . .

5) Complex numbers

Questions in this skill set will include operations with imaginary numbers.

6) Factoring

In order to factor an equation, you must figure out what variables are common to each term of the equation.

So, here is an example of a factoring problem:

What are the factors of:

college-level-math-exercises-3

7) Simplifying mathematical expressions

Here is an example of a simplification problem, containing fractions within fractions, like you will see on the test.

Simplify the following:

college-level-math-exercises-1

8) Manipulating square roots and exponents

These types of college-level math problems can be extremely challenging for most students.

So, when you see a fraction in an exponent, you need to remember how to express it in square root form. For example:

college-level-math-exercises-2

You may also wish to have a look at our college-level math exercises in Advanced Algebra and Geometry and Trigonometry.