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ACT Algebra — practice questions

Explore 30 free Algebra questions in ACT Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

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Algebra questions and exercises with answers

Showing questions 1–30 of 30.

A line rises 6 units while running 3 units across. Its slope is:Read the answer and worked solution →A line passes through (1, 2) and (4, 8). Its slope is:Read the answer and worked solution →Two lines have the same slope but different y-intercepts. Those lines are:Read the answer and worked solution →One line has slope 4. A line perpendicular to it has slope:Read the answer and worked solution →A student knows one point on a line and its slope, and wants the equation. She should use the:Read the answer and worked solution →An equation is written as y = mx + b. The value of b tells you the:Read the answer and worked solution →The endpoints of a segment are known and a student wants the point exactly halfway between them. She uses the:Read the answer and worked solution →A student needs the straight-line length between two plotted points. She uses the:Read the answer and worked solution →The plane is divided by the two axes into four sections. Each section is called a:Read the answer and worked solution →A quadratic will not factor neatly and completing the square looks messy. The reliable method left is the:Read the answer and worked solution →Before solving, a student computes the discriminant. What it tells her is the:Read the answer and worked solution →An equation reads x squared equals 49. The quickest route to both answers is:Read the answer and worked solution →Another method rewrites a quadratic as a perfect square trinomial before solving. That method is:Read the answer and worked solution →Whatever number you start with, its absolute value is always:Read the answer and worked solution →A statement joins two inequalities together in one line, such as 2 < x < 7. That statement is a:Read the answer and worked solution →Rather than drawing a number line, a student writes the solution set with brackets and parentheses. That is:Read the answer and worked solution →Complex numbers cannot sit on an ordinary number line, so they are plotted on a plane whose horizontal axis carries the:Read the answer and worked solution →To clear a complex number from a denominator, a student multiplies by the term found by flipping the sign of the imaginary part. That term is the complex:Read the answer and worked solution →An equation contains at least one rational expression, with a variable in a denominator. That equation is:Read the answer and worked solution →Solving such an equation, a student clears every denominator at once by multiplying through by the:Read the answer and worked solution →After squaring both sides of a radical equation, a student finds a root that fails the original check. That root is:Read the answer and worked solution →Simplifying an equation, a student reaches a statement that can never be true. The equation therefore has:Read the answer and worked solution →Catch the line formulasRead the answer and worked solution →Pop the quadratic methodsRead the answer and worked solution →Run the algebra gatesRead the answer and worked solution →Slice the algebra wordsRead the answer and worked solution →Lines or quadraticsRead the answer and worked solution →Sort the algebra wordsRead the answer and worked solution →Type the numberRead the answer and worked solution →Algebra bingoRead the answer and worked solution →

Worked practice questions

A line rises 6 units while running 3 units across. Its slope is:

  1. 2
  2. 3
  3. 6
  4. 9
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Correct answer: A. 2

1. Slope compares vertical change with horizontal change. 2. Divide 6 by 3. 3. The slope is 2. _Source: OpenStax College Algebra 2e, Chapter 2, Equations and Inequalities._

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A line passes through (1, 2) and (4, 8). Its slope is:

  1. 1
  2. 2
  3. 3
  4. 6
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Correct answer: B. 2

1. Change in y is 8 minus 2, which is 6. 2. Change in x is 4 minus 1, which is 3. 3. The slope is 2. _Source: OpenStax College Algebra 2e, Chapter 2, Equations and Inequalities._

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Two lines have the same slope but different y-intercepts. Those lines are:

  1. Parallel lines
  2. Meeting lines
  3. Identical lines
  4. Crossing lines
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Correct answer: A. Parallel lines

1. Equal slopes mean equal steepness. 2. Different intercepts keep them apart. 3. They are parallel lines. _Source: OpenStax College Algebra 2e, Chapter 2, Equations and Inequalities._

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MathematicsEquations and InequalitiesQuantitative AptitudeArithmeticPercentsPercents and Proportion