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Algebra I - EC: A1.1.1.5.1

Algebra I - EC: A1.1.1.5.1

Continuum of Activities

Continuum of Activities

The list below represents a continuum of activities: resources categorized by Standard/Eligible Content that teachers may use to move students toward proficiency. Using LEA curriculum and available materials and resources, teachers can customize the activity statements/questions for classroom use.

This continuum of activities offers:

  • Instructional activities designed to be integrated into planned lessons
  • Questions/activities that grow in complexity
  • Opportunities for differentiation for each student’s level of performance

Activities

  1. Rewrite the following polynomial in standard form. f(x) = x - 4 + 3x3 - 2x4 + 5x2
  1. What is the degree, leading coefficient and constant term of the following polynomial?
    f(x) = x – 4 + 3x3 – 2x4 + 5x2
  1. Rewrite the following polynomial in standard form. f(x) = 3x – 1 + 4x – 7
  1. Rewrite the following polynomial in standard form. f(x) = 3x – (1 + 4x – 7)
  1. Simplify the following polynomial expression.  (4x2 + 7x – 5) + (3x – 1 – 9x2)
  1. Simplify the following polynomial expression.  (4a – 3a3 + 2a) – (6a2 – a3 – 11a + 2)
  1. Simplify the following polynomial expression.  (3x – 4) (2x + 5)
  1. Simplify the following polynomial expression. (5m2 – 7m – 1)(2m + 3)
  1. Simplify the following polynomial expression.  2x(x – 1) – x(9 + x)
  1. Simplify the following polynomial expression. ((3x + 2) – (x – 1))(4 – 2x)
  1. Simplify the following polynomial expression.  (x2 – y + 3x)(2y – 4x)
  1. A polynomial is shown below.

(kx – 7)(3x + 2)

For what value of k does the above polynomial expression equal 15x2 – 11x – 14?

  1. Given the equation (4x – 8) – p = -x + 4 where p can be written in terms of x, what is p?
  1. What is the product of ax + b and cx + d?
  1. A rectangle with a length of 3x – 4 is shown below.

 

The perimeter of the rectangle is -16 + 10x, what is the width of the rectangle?

  1. A rectangular prism has height of 2x – 1 feet, a width of 4 – x feet, and a length of 3x feet. What is the volume of the prism in terms of x?
  1. Samantha’s front porch measures 5x + 1 feet by 4x – 3 feet. A small carpet outside the front door has an area of 2x + 1 feet squared. What is the area of Samantha’s front porch that is not carpeted?
  1. An equation is shown below.

(3x2 – 4x + 9)(mx + 5) – (9x3 + 4x2 + x – 11) = 6x3 – 9x2 + 24x + 56

For what value of m is this equation true?

  1. Jhamir is trying to solve an equation of the form 2a + b = c, where a, b, and c are all polynomials of the 2nd degree. What could polynomial a and b equal so that c would be the third degree polynomial, 

2x3 – x2 + 5x – 1.

Answer Key/Rubric

  1. f(x) = -2x4 + 3x3 + 5x2 + x – 4
  2. Degree: 4 (Quartic), Leading coefficient: -2, Constant: -4
  3. f(x) = 7x – 8
  4. f(x) = -x + 6
  5. -5x2 + 10x – 6
  6. -2a3 – 6a2 + 17a – 2
  7. 6x2 + 7x – 20
  8. 10m3 + m2 – 23m – 3  
  9. x2 – 11x
  10. = -4x2 + 2x + 12
  11. -4x3 – 12x2 + 2x2y + 10xy – 2y2
  12. k = 5
  13. p = 5x – 12
  14. acx2 + adx + bcx + bd
  15. width = 2x – 4
  16. Volume = -6x3 + 27x2 – 12x
  17. 20x2 – 13x – 4
  18. m = 5
  19. Various answers: could be a = 2x3 + x2 + 3x + 1 and b = -2x3 – 3x2 – x – 3
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