Grade: Grade 11 Subject: Mathematics Unit: Algebra II Completion Lesson: 6 of 6 SAT: AdvancedMath ACT: Math

Unit Quiz

Demonstrate your mastery of complex numbers, polynomial functions, and problem-solving strategies from this unit.

Quiz Instructions

This quiz covers all topics from the Algebra II Completion unit. Read each question carefully and show all your work.

Quiz Details

  • Total Questions: 12
  • Recommended Time: 45-60 minutes
  • Topics Covered: Complex numbers, polynomial functions, word problems, error analysis
  • Materials Allowed: Pencil, paper, scientific calculator (no graphing calculators)

Tips for Success

  • Read each problem completely before starting
  • Show all steps for full credit
  • Check your answers for common errors
  • Manage your time - do not spend too long on any single problem
  • If stuck, move on and return to difficult problems later

Quiz Questions

Part A: Complex Numbers (Questions 1-4)

Question 1: Simplify and express in standard form: (4 - 3i)(2 + 5i)

Question 2: Divide and express in standard form: (6 + 8i) / (2 - i)

Question 3: Simplify: i^47

Question 4: Find all values of x such that x^2 + 4x + 13 = 0. Express your answers in the form a + bi.

Part B: Polynomial Functions (Questions 5-8)

Question 5: Use synthetic division to divide x^4 - 3x^3 + 2x^2 - x + 5 by (x - 2). State the quotient and remainder.

Question 6: Factor completely: x^3 + 3x^2 - 4x - 12

Question 7: Find all zeros (real and complex) of f(x) = x^4 - 6x^3 + 11x^2 - 6x

Question 8: Write a polynomial function of least degree with integer coefficients that has zeros at x = 2, x = -1, and x = 3i.

Part C: Word Problems (Questions 9-10)

Question 9: A manufacturer finds that the profit P(x) in dollars from producing and selling x units of a product is given by P(x) = -0.5x^2 + 80x - 1200. Find:

  1. The number of units that must be sold to maximize profit
  2. The maximum profit
  3. The number of units that must be sold to break even (when profit equals zero)

Question 10: Two water pipes together can fill a swimming pool in 6 hours. If the larger pipe alone can fill the pool 5 hours faster than the smaller pipe alone, find how long it takes each pipe to fill the pool individually.

Part D: Error Analysis (Questions 11-12)

Question 11: A student solved the equation sqrt(2x + 3) = x and got x = 3 and x = -1. Explain which solution(s), if any, are valid and why.

Question 12: Identify and correct the error in this work:

"Solve x^2 - 6x + 8 = 0"

Step 1: (x - 4)(x - 2) = 0

Step 2: x - 4 = 0 or x - 2 = 0

Step 3: x = 4 or x = 2

"Therefore, the sum of the roots is 4 + 2 = 6 and the product is 4 * 2 = 8."

"But by Vieta's formulas, the sum should be -(-6)/1 = 6 and product should be 8/1 = 8, so there must be an error in my factoring."

Self-Assessment

After completing the quiz, reflect on your performance:

  1. Which topic areas did you feel most confident about?
  2. Which problems were most challenging for you?
  3. Did you make any of the common mistakes covered in the previous lesson?
  4. What topics should you review before moving to the next unit?

Scoring Guide

  • 11-12 correct: Excellent - You have mastered this unit
  • 9-10 correct: Good - Review any missed topics briefly
  • 7-8 correct: Satisfactory - Review the lessons for missed topics
  • Below 7: Needs improvement - Review all lessons before proceeding

Next Steps

  • Check your answers and identify areas for improvement
  • Review any lessons where you missed questions
  • Practice additional problems in weak areas
  • When ready, move on to the next unit in the Mathematics curriculum
  • Consider retaking this quiz after reviewing to confirm mastery