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Algebra Sample Problems

1. Add/subtract fractions



2. Absolute Value


b. Solve the equation for x.

(Answer: x= -4, x=7)

3. Exponents


4. Factor a quadratic equation
Example: Factor the following expression.

Answer :

5. Simplify a radical function
Example: Simplify the following expression.

Answer :

6. Simplify a complex fraction.
Example: Simplify.

Answer :

7. Simplify radical expressions.
Example: Simplify.

Answer :

8. Given an equation, solve for x.

9. Solve an inequality
Example: Solve the inequality and write the solution set in interval notation.

Graph the solution set.

10. Find coordinates of a point
Example: Find the coordinates of the point C.

11. Read data from graph.
Example: Suppose the following graph represents sales of DVD players (in
dollars) for Locke Industries in 2007.

a. What was the sales amount on June 1? (Answer: $3500. 00)
b. What was the maximum sales amount? (Answer: $4500. 00)
c. In what month did the maximum sales occur? (Answer: August)
d. In what months was sales equal to $3000. 00?
(Answer: April, November, December)

12. Find x and y intercepts.
Example: Find the x-and y-intercepts of the graph of the equation

Answer: x-intercept is (12,0), y-intercept is (0,-4)

13. Lines
a. Find the slope of the line.

b. Find the equation of the line that passes through the points (4,-1) and (-6,14).


14. Domain and range of a function.
Example: Find the domain and range of


domain is [-7,∞], range is [0,∞]

15. Graph a function by making a table of values and plotting points.

16. Find values of a function by looking at a graph.
Example: Given below is the graph of y=g(x) .

a. What is the value of g(2)?

Answer: -5

b. What are the values of x such that g(x)=0?

Answer:-3. 5, 3. 1

17. Function Values
Example: If f(x)=2x+8 what is the value of f(z+2)?


18. Composition of functions
Example: If f(x)=x^2 and g(x)=x+4, what is ?