College-Level Algebra and Advanced Math

The college-level algebra part of the Compass is also known as the advanced math exam.

On the college algebra section of the test, you will see the following types of problems.

Advanced Exponential Calculations

You may need to add or multiply exponents. You may also see exponents that contain fractional numbers or radicals with exponents.

Problem 1: 35 ÷ 32 = ?

Solution 1: Remember that problems like this have a base number and exponents.

The base number in the example above is 3.

The exponents are 5 and 2.

When the base numbers are the same, and the problem is asking you to divide, you subtract the exponents.

35 ÷ 32 = 35 − 2 = 33

Problem 2: 89 × 85 = ?

Solution 2: When the base numbers are the same and you need to multiply, you add the exponents to get your solution.

89 × 85 = 89 + 5 = 814

Imaginary Numbers

Imaginary numbers are not integers or real numbers, such as the whole numbers or fractions we use in basic algebraic expressions.

They are also not rational numbers or complex numbers, like those that are often used to express geometric concepts.

An imaginary number is normally expressed as a real number which multiplied by the imaginary variable or unit i.

Problem: xi and yi are imaginary numbers. a and b are real numbers.

When does xia = yib?

Solution: xia = yib only when a = b and x = y.

Two imaginary numbers are equal only when their real number counterparts are also equal.

Functions

Functions might appear complicated, but they are simply relationships between numbers. Look at this example.

Problem: f1(x) = x2. What is the value of f1(4)?

Solution: So for this function, we always need to square the value of x.

f1(4) = 42

42 = 4 × 4 = 16

Arithmetic and Geometric Series and Sequences

For these types of questions, you have to look at the numbers in order to attempt to discover the relationship between them.

Problem: What number is next in this sequence 1, −4, 16, −64

Solution: Isolate the first two numbers in the sequence and try to find the relationship. Then prove your theory on the other numbers.

Here, we see that we can arrive at −4 from 1 by subtracting 5 or by multiplying times −4.

If we then look at the relationship between the second and third numbers, we see that 16 = −4 × −4

So, each subsequent number is calculated by multiply by −4.

The next number is −64 × −4 = 256

Operations with Matrices

These types of advanced math problems can include the addition and subtraction of matrices and the calculation of determinants.

Problem: What is the determinat of the following matix?

Compass Algebra

Solution: To find the determinant of a matrix, you need to cross-multiply and then subtract.

(3 × 7) − (2 × 1) = 21 − 2 = 19

Now have a look at the geometry and trigonometry exercises.

Alternatively, you can go on to the sample of our math download.

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