Unit Quiz
Assess your understanding of polynomial operations and radical expressions with this comprehensive unit quiz. Try to complete all 12 questions without looking at the answers first.
Quiz Instructions
Before You Begin
- Time recommendation: 20-25 minutes
- Materials needed: Pencil and scratch paper
- Strategy: Try each problem before checking the answer
- Scoring: Aim for at least 10/12 correct (83%)
Topics Covered
- Polynomial addition and subtraction
- Polynomial multiplication (including FOIL)
- Simplifying radical expressions
- Rationalizing denominators
- Word problems with polynomials and radicals
Quiz Questions
Complete all 12 questions. Record your answers before checking.
Question 1
Expand and simplify: (x + 6)(x - 2)
Show Answer
Answer: x2 + 4x - 12
Solution: FOIL: x*x + x*(-2) + 6*x + 6*(-2) = x2 - 2x + 6x - 12 = x2 + 4x - 12
Question 2
Simplify: sqrt(180)
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Answer: 6sqrt(5)
Solution: 180 = 36 * 5, so sqrt(180) = sqrt(36) * sqrt(5) = 6sqrt(5)
Question 3
Expand: (3x - 4)2
Show Answer
Answer: 9x2 - 24x + 16
Solution: (a-b)2 = a2 - 2ab + b2 = 9x2 - 2(3x)(4) + 16 = 9x2 - 24x + 16
Question 4
Rationalize the denominator: 6 / sqrt(3)
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Answer: 2sqrt(3)
Solution: (6/sqrt(3)) * (sqrt(3)/sqrt(3)) = 6sqrt(3)/3 = 2sqrt(3)
Question 5
Add: (5x2 - 3x + 7) + (2x2 + 8x - 4)
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Answer: 7x2 + 5x + 3
Solution: Combine like terms: (5+2)x2 + (-3+8)x + (7-4) = 7x2 + 5x + 3
Question 6
Simplify: sqrt(48) + sqrt(27)
Show Answer
Answer: 7sqrt(3)
Solution: sqrt(48) = 4sqrt(3), sqrt(27) = 3sqrt(3). Sum: 4sqrt(3) + 3sqrt(3) = 7sqrt(3)
Question 7
Expand: (2x + 5)(3x - 1)
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Answer: 6x2 + 13x - 5
Solution: FOIL: 6x2 - 2x + 15x - 5 = 6x2 + 13x - 5
Question 8
Subtract: (4x3 - 2x2 + x) - (x3 + 5x2 - 3x)
Show Answer
Answer: 3x3 - 7x2 + 4x
Solution: Distribute negative: 4x3 - 2x2 + x - x3 - 5x2 + 3x = 3x3 - 7x2 + 4x
Question 9
Rationalize: 8 / (sqrt(5) - 1)
Show Answer
Answer: 2(sqrt(5) + 1) or 2sqrt(5) + 2
Solution: Multiply by conjugate: 8(sqrt(5)+1) / ((sqrt(5)-1)(sqrt(5)+1)) = 8(sqrt(5)+1)/(5-1) = 8(sqrt(5)+1)/4 = 2(sqrt(5)+1)
Question 10
A rectangle has length (x + 7) and width (x - 3). Write an expression for its area.
Show Answer
Answer: x2 + 4x - 21
Solution: Area = (x+7)(x-3) = x2 - 3x + 7x - 21 = x2 + 4x - 21
Question 11
Find the distance between points (0, 0) and (5, 12). Express as a simplified number.
Show Answer
Answer: 13
Solution: d = sqrt((5-0)2 + (12-0)2) = sqrt(25 + 144) = sqrt(169) = 13
Question 12
Expand: (x + 2)(x - 2)(x + 3)
Show Answer
Answer: x3 + 3x2 - 4x - 12
Solution: First: (x+2)(x-2) = x2 - 4. Then: (x2 - 4)(x + 3) = x3 + 3x2 - 4x - 12
Score Your Quiz
Scoring Guide
- 12/12 correct: Excellent! You've mastered this unit.
- 10-11/12 correct: Great work! Review any missed concepts.
- 8-9/12 correct: Good effort. Consider reviewing the lessons you struggled with.
- Below 8/12: Revisit the unit lessons before moving on.
Self-Reflection: Which topics do you need to review?
Review Recommendations
- If you missed Q1, Q3, Q7, or Q12: Review Polynomial Operations
- If you missed Q2, Q4, Q6, or Q9: Review Radical Expressions
- If you missed Q5 or Q8: Practice adding/subtracting polynomials in Guided Practice
- If you missed Q10 or Q11: Review Word Problems
Next Steps
- If you scored 10+ correct, you're ready for the next math unit
- Review any topics where you made errors
- Consider retaking the quiz after reviewing
- Move on to explore other Grade 10 Math units: Geometry Theorems, Coordinate Geometry, or Trigonometry Basics
Continue Your Learning
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