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US High School Mathematics — practice by topic

Browse 50 questions across 9 Mathematics topics. Choose what you want to revise, then open a question to check its answer and worked solution.

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Mathematics topics

Using the Normal Distribution (9)Linear Inequalities (8)Solving Linear Equations (8)Absolute Value Equations and Inequalities (6)Mixture and Uniform Motion (6)Compound Inequalities (5)Problem Solving with Equations (4)Solving a Formula for a Variable (2)The Standard Normal Distribution (2)

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What makes a particular number a solution of an equation?Read the answer and worked solution →Which form defines a linear equation in one variable?Read the answer and worked solution →What is the first step in the general strategy for solving a linear equation?Read the answer and worked solution →Solve 5(x - 3) + 7 = 2x + 10.Read the answer and worked solution →

Worked practice questions

What makes a particular number a solution of an equation?

  1. It makes the equation easier to read
  2. It makes the equation a true statement
  3. It appears on the left of the equation
  4. It is the largest number in the equation
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Correct answer: B. It makes the equation a true statement

1. Substitute the number in place of the variable everywhere it appears. 2. Simplify both sides of the equation separately. 3. If the two sides come out equal, the number is a solution, and otherwise it is not. _Source: OpenStax Intermediate Algebra (CC BY 4.0), Ch 2 "Solving Linear Equations", section 2.1 Use a General Strategy to Solve Linear Equations_

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Which form defines a linear equation in one variable?

  1. ax + b = 0 with a equal to 0
  2. ax squared + b = 0 with a not zero
  3. a over x + b = 0 with a not zero
  4. ax + b = 0 with a not zero
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Correct answer: D. ax + b = 0 with a not zero

1. A linear equation holds one variable raised only to the first power. 2. It can always be rearranged into ax + b = 0 with real numbers a and b. 3. The coefficient a must not be zero, or the variable disappears entirely. 4. A squared term would make it quadratic instead, so that form is ruled out. _Source: OpenStax Intermediate Algebra (CC BY 4.0), Ch 2 "Solving Linear Equations", section 2.1 Use a General Strategy to Solve Linear Equations_

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What is the first step in the general strategy for solving a linear equation?

  1. Simplify each side as much as possible
  2. Divide both sides by the coefficient
  3. Move every constant to the left side
  4. Check the answer in the original
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Correct answer: A. Simplify each side as much as possible

1. Start by tidying each side on its own before moving anything across. 2. That means clearing parentheses and combining like terms. 3. Only once both sides are simple do you begin collecting variable terms. _Source: OpenStax Intermediate Algebra (CC BY 4.0), Ch 2 "Solving Linear Equations", section 2.1 Use a General Strategy to Solve Linear Equations_

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