MA.912.A.7.2Archived Standard

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Solve quadratic equations over the real numbers by factoring and by using the quadratic formula.

Remarks

Example 1: Solve the following equation for x:
x² - 3x + 2=0

Example 2: Solve the following equation for x:
x² - 7x + 9=0

General Information
Subject Area: X-Mathematics (former standards - 2008)
Grade: 912
Body of Knowledge: Algebra
Idea: Level 2: Basic Application of Skills & Concepts
Standard: Quadratic Equations - Draw graphs of quadratic functions. Solve quadratic equations and solve these equations by factoring, completing the square, and by using the quadratic formula. Use graphing calculators to find approximate solutions of quadratic equations.
Date Adopted or Revised: 09/07
Content Complexity Rating: Level 2: Basic Application of Skills & Concepts - More Information
Date of Last Rating: 06/07
Status: State Board Approved - Archived
Assessed: Yes
Test Item Specifications
  • Item Type(s): This benchmark may be assessed using: MC , FR item(s)
    • Also Assesses:

    MA.912.A.1.8 Use the zero product property of real numbers in a variety of contexts to identify solutions to equations.

    MA.912.A.7.8 Use quadratic equations to solve realworld problems.
  • Clarification :
    Students will solve quadratic equations over the set of real numbers.
  • Content Limits :

    Items must have real solutions only.

    Quadratic equations must have integer coefficients only.

    Items may assess special forms like the difference of squares and perfect square trinomials.

    Items will not require the use of the “completing the square” method of solving quadratic equations.

  • Stimulus Attributes :
    Items may be set in either real-world or mathematical contexts.
  • Response Attributes :

    MC options may be given in the form that results from application of the quadratic formula, e.g.,

    MC options may be given using set notation.

    Fill-in response items may ask the student to provide the greater (or lesser) of two solutions explicitly or implicitly.

    Fill-in response items may have a negative answer.

Sample Test Items (2)
  • Test Item #: Sample Item 1
  • Question: Jeannie solved the quadratic equation shown below by factoring.
    x² + 2x - 8 = 0
    Which of the following shows a step in solving the equation shown?
  • Difficulty: N/A
  • Type: MC: Multiple Choice
  • Test Item #: Sample Item 2
  • Question: A ball is kicked from ground level into the air. Its height y, in feet, after x seconds can be represented by the equation y = 40x - 16x². What is the total elapsed time, in seconds, from the time the ball is kicked until it reaches ground level again?
  • Difficulty: N/A
  • Type: FR: Fill-in Response

Related Access Points

Alternate version of this benchmark for students with significant cognitive disabilities.

Related Resources

Vetted resources educators can use to teach the concepts and skills in this benchmark.

Educational Game

Timed Algebra Quiz:

In this timed activity, students solve linear equations (one- and two-step) or quadratic equations of varying difficulty depending on the initial conditions they select. This activity allows students to practice solving equations while the activity records their score, so they can track their progress. This activity includes supplemental materials, including background information about the topics covered, a description of how to use the application, and exploration questions for use with the java applet.

Type: Educational Game

Student Resources

Vetted resources students can use to learn the concepts and skills in this benchmark.

Educational Game

Timed Algebra Quiz:

In this timed activity, students solve linear equations (one- and two-step) or quadratic equations of varying difficulty depending on the initial conditions they select. This activity allows students to practice solving equations while the activity records their score, so they can track their progress. This activity includes supplemental materials, including background information about the topics covered, a description of how to use the application, and exploration questions for use with the java applet.

Type: Educational Game

Parent Resources

Vetted resources caregivers can use to help students learn the concepts and skills in this benchmark.