Reasoning with Equations and Inequalities

High School Algebra Practice


This quiz illustrates the range of difficulty expected by the following Common Core State (CCS) standards:

QuestionCommon Core Standard #
9A.REI.8 +
10A.REI.9 +
indicates a modeling standard.
+ indicates a college and career ready standard.

All questions of this quiz illustrate the difficulty of the high school A.REI standards required for all students, including the college and career ready students.

Question 1: Solve the following equation:

Question 2: Solve the following equation:

Question 3: Solve for x the following equation:

Question 4: Solve the following equation:

-3x - 5 > 7 - x

Question 5: Solve the quadratic equation:

(x - 1)2 = (2x + 7)2

Question 6: Consider the functions f(x) and g(x) defined below:

f(x) = |x| and g(x) = x2

The number of solutions of the equation f(x) = g(x) is: .

Question 7: Solve the following system of linear equations:

3x - 4y = 14
x - 2y = -8

Question 8: Find the points of intersection between the line y = -2x - 3 and the parabola y = (x + 1)2 - 9.

Question 9: Represent the system of linear equations below as a single matrix equation in a vector variable.

2x - 3y = 5
x + y = 0





Question 10: Find the determinant of matrix A:

Question 11: The population of a town is initially 10,000 people and is increasing at 2% per year. The town's number of houses, condominiums and apartments is initially adequate for 12,000 people and is increasing at a constant rate for an additional 80 people per year. This town first experiences a real estate crisis in the .

Question 12: The graphs of two lines, y = f(x) and y = g(x) are given below, and four regions, M, N, O, and P are also shown with different colors on the same graph.

Which region is the solution set of the system of inequalities y < f(x) and y > g(x)?

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