Multiple-Choice Items
1. Which real number is not rational?
2. Which of the following statements about −9 is correct?
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A
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It is an integer and a natural number.
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B
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It is a real number and a whole number.
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C
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It is a real number, integer, and irrational number.
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D
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It is a real number, rational number, and integer.
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3. Which of the following lists the real numbers in order from least to greatest?
4. Given , which is a point on the line with an x-value of −6?
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A
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(−6, −89)
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B
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(−6, 87)
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C
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(−6, −105)
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D
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(−6, 71)
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5. For an x-value of −16, which function has the largest y-value?
6. Which linear function is steepest?
7. Which representation is not linear?
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A
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y = −x + 9
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B
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The rate of dominos falling
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C
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D
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5 trees planted per hour
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8. Which representation is linear?
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A
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y = x2 – 9
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B
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(2, 4), (6, 36), (−3, 9)
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C
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−8, −16, −32, −64, …
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D
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x
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y
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−10
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183
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−6
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−107
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3
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64
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7
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140
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9. Which is most likely to have a linear relationship?
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A
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Number of candy bars bought per hour on the playground
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B
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Number of cups of coffee consumed per day by an individual
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C
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Amount of money subtracted from a checking account each week
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D
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Number of donations given per hour at a fundraiser
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Multiple-Choice Answer Key
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1. C
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2. D
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3. B
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4. C
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5. B
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6. D
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7. B
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8. D
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9. B
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Short-Answer Items:
10. Write the function rule for the data shown in the following table:
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x
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−6
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−3
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0
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4
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9
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y
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96
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51
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6
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−54
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−129
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Show the process and graph the function.
11. Given , highlight the slope in the equation, table, and graph.
12. Write any linear function representation of your choosing. Provide a justification for the linearity and provide at least one alternative representation.
Short-Answer Key and Scoring Rubrics:
10. Write the function rule for the data shown in the following table:
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x
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−6
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−3
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0
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4
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9
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y
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96
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51
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6
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−54
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−129
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Show the process and graph the function.
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Points
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Description
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3
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The student does all of the following:
- writes .
- shows the correct process for finding the rule.
- correctly graphs the function.
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2
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The student correctly provides two of the three answers or extends the pattern correctly with both positive and negative x terms.
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1
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The student correctly provides one of the three answers, or extends the pattern correctly with a positive or negative x term.
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0
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The student does not provide an answer or incorrectly answers all three parts.
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11. Given , highlight the slope in the equation, table, and graph.
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Points
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Description
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3
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- The student correctly highlights the −3 in the equation.
- The student correctly highlights the change of −3 per consecutive
y-values or the slope (change in y-values/change in x-values).
- The student draws rise and run on the graph and calculates the slope from two points.
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2
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The student correctly writes two of the three answers.
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1
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The student correctly writes one of the three answers.
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0
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The student does not provide an answer or incorrectly answers all three parts.
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- Write any linear function representation of your choosing. Provide a justification for the linearity and provide at least one alternative representation.
Sample correct response: (justification: highest power of the independent variable = 1); acceptable alternative:
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Points
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Description
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3
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The student provides all of the following requirements:
- an acceptable linear function.
- a justification.
- an acceptable alternative.
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2
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The student provides two accurate requirements.
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1
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The student provides one accurate requirement.
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0
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The student does not provide an answer or incorrectly provides all three requirements.
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Performance Assessment:
Write a narrative paper on linear functions. Clearly address and provide the following:
- important ideas learned, with supporting detail.
- topic(s) you wish to explore further.
- at least five mathematical examples/illustrations of situations to support a key idea in your paper.
Performance Assessment Scoring Rubric:
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Points
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Description
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5
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The paper includes:
- clear explanation of important ideas learned, with supporting details.
- topic(s) you wish to explore further.
- at least five examples/illustrations to support a key idea or ideas in your paper.
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4
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The paper includes four of the five examples/illustrations, all of which are mathematically correct.
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3
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The paper includes three of the five examples/illustrations, all of which are mathematically correct.
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2
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The paper includes two of the five examples/illustrations, both of which are mathematically correct.
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1
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The paper includes one of the five examples/illustrations, which is mathematically correct.
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0
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The student does not present any parts of the paper as assigned, or provides incorrect information for all five examples/illustrations.
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