Basic Algebra Practice Test
1.
Exponents and integers: Problem type 2
Evaluate.
2.
Exponents and signed fractions
Evaluate. Write your answers as fractions.
3.
Exponents and order of operations
Evaluate.
4.
Evaluation of a linear expression in two variables
Evaluate the expression when = 3 and = 6.

5.
+2
Distributive property: Advanced
Use the distributive property to remove the parentheses.
6.
Combining like terms in a quadratic expression
Simplify the following expression.
7.
Writing a mathematical expression
Write an algebraic expression to answer the question below.
If one notebook costs dollars, what is the cost, in dollars, of 8 notebooks?
8.
Solving a two-step equation with integers
Solve for .
7 + 4 = 23
Simplify your answer as much as possible.
9.
Solving a two-step equation with signed fractions
Solve for .
Simplify your answer as much as possible.
10. Solving a linear equation with several occurrences of the variable: Problem type 2
Solve for .
Simplify your answer as much as possible.
11. Solving a linear equation with several occurrences of the variable: Problem type 3
Solve for .
Simplify your answer as much as possible.
12. Solving a linear inequality: Problem type 3
Solve the inequality for .
Simplify your answer as much as possible.
13. Graphing a linear inequality on the number line
Graph the inequality below on the number line.
5 4 3 2 1 0 1 2 3 4
5
14. Algebraic symbol manipulation: Problem type 2
Solve the following equation for .
15. Solving a fraction word problem using a simple linear equation
The yearbook club had a meeting. The meeting had 24 people, which is two-thirds of
the club. How many people are in the club?
16. Solving a word problem using a linear equation: Problem type 2
Customers of a phone company can choose between two service plans for long distance
calls. The first plan has no monthly fee but charges $0.14 for each minute of calls. The
second plan has a $15 monthly fee and charges an additional $0.09 for each minute of
calls. For how many minutes of calls will the costs of the two plans be equal?
17. Set builder and interval notation
Graph the set
on the number line.
Then, write the set using interval notation.
5 4 3 2 1 0 1 2 3 4
5
18. Function tables
The function is defined by the following rule.
Complete the function table.
( )
5
1
0
2
3
19. Domain and range from ordered pairs
Suppose that the relation is defined as follows.
Give the domain and range of .
Write your answers using set notation.
20. Graphing a line given the x- and y-intercepts
Graph the line whose -intercept is 3 and whose -intercept is 2.
y
x
21. Graphing a line given its equation in slope-intercept form
Graph the line.
y
x
22. Graphing a line through a given point with a given slope
Graph the line with slope 2 passing through the point (1, 3).
y
x
23. Graphing a vertical or horizontal line
Graph the line = 1.
y
x
24. Finding x- and y-intercepts of a line given the equation in standard form
Find the -intercept and -intercept of the line given by the equation.
4 +9 =8
-intercept =
-intercept =
25. Finding slope given two points on the line
Find the slope of the line passing through the points (3, 4) and (8, 3).
26. Writing an equation of a line given the y-intercept and a point
Write an equation of the line below.
y
x
27. Writing the equations of vertical and horizontal lines through a given point
Write equations for the vertical and horizontal lines passing through the point (9, 3).
Vertical line:
Horizontal line:
28. Evaluating expressions with exponents of zero
Evaluate the expressions.
29. Writing a negative number without a negative exponent
Rewrite the following without an exponent.
30. Multiplying monomials
Multiply.
Simplify your answer as much as possible.
31. Product rule of exponents in a multivariate monomial
Simplify.
Use only positive exponents in your answer.
32. Quotients of expressions involving exponents
Simplify.
33. Power rule with negative exponents: Problem type 2
Simplify.
Write your answer using only positive exponents.
34. Using the power, product, and quotient rules to simplify expressions with negative
exponents
Simplify.
Write your answer using only positive exponents.
35. Ordering numbers with negative exponents
Order the expressions by choosing <, >, or =.
36. Simplifying a polynomial expression
Simplify.
37. Multiplying a monomial and a polynomial: Problem type 2
Multiply.
Simplify your answer as much as possible.
38. Multiplying binomials: Problem type 3
Multiply.
Simplify your answer.
39. Degree and leading coefficient of a polynomial in one variable
What are the leading coefficient and degree of the polynomial?
Leading coefficient =
Degree =
40. Factoring a quadratic with leading coefficient 1
Factor.
41. Factoring a quadratic with leading coefficient greater than 1
Factor.
42. Greatest common factor of two monomials
Find the greatest common factor of the two expressions
and
Simplify your answer as much as possible.
43. Factoring out a monomial from a polynomial: Problem type 2
Factor the following expression.
44. Factoring a product of a quadratic trinomial and a monomial
Factor completely.
45. Multiplying rational expressions: Problem type 1
Multiply.
Simplify your answer as much as possible.
46. Adding rational expressions with common denominators
Subtract.
Simplify your answer as much as possible.
47. Dividing rational expressions: Problem type 2
Divide.
Simplify your answer as much as possible.
48. Simplifying a ratio of polynomials: Problem type 1
Simplify.
49. Solving a rational equation that simplifies to a linear equation: Problem type 1
Solve for .
Simplify your answer as much as possible.
50. Finding the roots of a quadratic equation with leading coefficient 1
Solve for .