Pre-Calculus - Chapter 3 & 9 Practice Test

Front

What is a complex number?

Back

A complex number is a number that can be expressed in the form a + bi, where a and b are real numbers, and i is the imaginary unit, defined as the square root of -1.

Front

How do you simplify the expression (5+15i)/(1+2i)?

Back

The simplified form is 7 + i.

Front

What is a horizontal asymptote?

Back

A horizontal asymptote is a horizontal line that the graph of a function approaches as x approaches positive or negative infinity.

Front

What is the horizontal asymptote of the function (2x^2-5x +1)/(x^2-x)?

Back

The horizontal asymptote is y = 2.

Front

What is a zero of a polynomial?

Back

A zero of a polynomial is a value of x that makes the polynomial equal to zero.

Front

If one zero of the polynomial 3x^3-4x^2-28x-16 is 4, what is another zero?

Back

Another zero is -2.

Front

How do you simplify √-500?

Back

The simplified form is 10i√5.

Front

What is the Remainder Theorem?

Back

The Remainder Theorem states that the remainder of the division of a polynomial f(x) by (x - c) is equal to f(c).

Front

What is the remainder when (6x^2 + 19x + 13) is divided by (2x + 5)?

Back

The remainder is 3.

Front

What is the formula for finding the roots of a quadratic equation?

Back

The roots of a quadratic equation ax^2 + bx + c = 0 can be found using the quadratic formula: x = (-b ± √(b² - 4ac)) / (2a).