CMClearMathAcademy

College Algebra Midterm Exam

A free College Algebra lesson from the “Rational Expressions and Equations” unit, with a worked example and practice problems including step-by-step solutions.

This midterm exam covers the first half of College Algebra: linear equations and inequalities; functions (notation, domain and range, composition, inverses); quadratics (products, factoring, graphs, solving, applications); complex numbers; exponents and radicals; and rational expressions and equations.

What you'll learn

Why it matters: The midterm is a cumulative checkpoint: it shows whether the linear, function, quadratic, and rational tools have become a connected toolkit rather than separate tricks — the transfer that later College Algebra topics and placement tests assume.

Worked example

Problem. Solve x^2 - 7x + 12 = 0 by factoring.

  1. Find two numbers that multiply to 12 and add to -7.
  2. -3 and -4 work, so (x - 3)(x - 4) = 0.
  3. Therefore x = 3 or x = 4.

Answer: x = 3 or x = 4

Lesson preview: this page shows 5 practice items. The interactive activity contains 45 practice items and 45 quiz items (typed response and multiple choice). Counts include repeated prompts and variants.

Practice problems

1. Solve for x: 3x + 4 = 13.

Show solution
  1. Subtract 4 from both sides: 3x = 13 - 4 = 9.
  2. Divide both sides by 3: x = 9 / 3.
  3. So x = 3.

Answer: 3

2. Solve for the boundary value: 3x < 9. Enter the number x must stay below.

Show solution
  1. Divide both sides by 3 (positive — no sign flip).
  2. x < 9/3.
  3. So the boundary is x < 3.

Answer: 3

3. Solve |x + 2| = 8. Give the negative solution (the smaller value).

Show solution
  1. Split into two cases: x + 2 = 8 or x + 2 = -8.
  2. The first gives x = 6; the second gives x = -10.
  3. The smaller (negative) solution is x = -10.

Answer: -10

4. Solve (x - 3)(x - 6) > 0. Give the solution in interval notation.

Show solution
  1. The zeros are x = 3 and x = 6, splitting the line into three intervals.
  2. Test x = 4 (between the roots): (1)(-2) < 0, so the middle is negative; the outer intervals are positive.
  3. For > 0 take the outer intervals (strict, so roots excluded): (-infinity, 3) U (6, infinity).

Answer: (-infinity, 3) U (6, infinity)

5. Find the slope of the line through (3, 2) and (6, 8).

Show solution
  1. Slope = (y2 - y1) / (x2 - x1).
  2. = (8 - 2) / (6 - 3) = 6 / 3.
  3. = 2.

Answer: 2

Practice this interactively with instant feedback and an AI tutor.

Practice College Algebra Midterm Exam Take the free placement check

More College Algebra lessons