Sunday, November 6, 2011

Sample Test Questions - Polynomials and Their Operations

Sample 10-question Elementary Algebra test covering topics found in Chapter 5 - Polynomials and Their Operations.

1. Simplify.
{\left( {\frac{{2{x^3}}}{{3{y^2}}}} \right)^3}

Apply the rules of exponents.

2. Simplify.
{(5x{y^{ - 3}}{z^4})^{ - 3}}

Apply the rules of exponents.

3. Calculate f(-2) given
f(x) =  - 3{x^2} + 2x - 9

Replace every instance of x with -2.

4. Add.
(3{x^2} + 2x - 9) + ( - 5{x^2} - 7x + 7)

Combine like terms.


5. Subtract.
( - 5{x^2} - 3x + 4) - (2{x^2} - 3x - 5)

Distribute the -1 and then combine like terms.


6. Multiply.
 - 2{x^2}(3{x^3} + 2{x^2} - 5x + 1)

Distribute the monomial in front of the parentheses.


7. Multiply.
{(2x - 3)^3}

Distribute and then combine like terms.


8. Divide.
\frac{{20{x^6} + 18{x^5} - 4{x^3}}}{{2{x^3}}}

Divide each term by the monomial in the denominator.


9. Divide.
\frac{{3{x^4} + 4{x^3} - 13{x^2} + 9x + 3}}{{3x - 2}}

Perform the polynomial long division.

10. A projectile is fired from the top of an 80 ft building with an initial velocity of 64 feet per second. The height of the projectile in feet after t seconds is given by the following function and is graphed below.
h(t) =  - 16{t^2} + 64t + 80

a. Use the graph to determine how long it takes to reach the maximum height.
b. Use the graph to determine how long will it take to hit the ground?
c. Use the function to determine the height of the projectile after 4 seconds?