- A Journey with Self-Assessment
- as a Compass
- © 1995, 1998, 2001, 2016, A. Azzolino

Before considering some of the higher order thinking skills assignments, we will consider verbs used on tests.

The first two tests are teacher-written tests. They are low on higher-order thinking skills question, likely due to the time those questions require.

The last tests are *The NY Algebra I Regents Test* and the *PARCC Algebra I Test* which are mixtures of multiple choice, open-ended, and
blends of open-ended and multiple choice.

The last tests provide perfect examples of ways in which the verbs are not the focus of the questioning. Entire sentences, often beginning what or which, ask the question.

Examine them at will.

Multiple guess remedial college algebra I final exam: 0, 1, 0, 5, 1, 8 | |||||

EVALUATION: | |||||

SYNTHESIS: evaluate | |||||

ANALYSIS: | |||||

APPLICATION: add, factor, graph, simplify, subtract | |||||

COMPREHENSION: evaluate | |||||

KNOWLEDGE: add, answer, divide, factor, graph, multiply, simplify, subrtact |

Spring 2016 Open-ended county-college precalc final exam: 2, 6, 0, 3, 1, 4 |

EVALUATION: prove, solve |

SYNTHESIS: find, graph, list, prove, sketch, write |

ANALYSIS: |

APPLICATION: graph, sketch, state |

COMPREHENSION: sketch |

KNOWLEDGE: complete, graph, sketch, state |

The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION
- ALGEBRA I (COMMON CORE) June 3, 2014, 3 hours http://www.nysedregents.org/algebraone/ laptop algebra I exam | |||||

- 1. Which property justifies Emily's first step?
- 2. What would be the most appropriate domain for the function?
- 3. If A = ... and B = ... the A - B equals?
- 4. Which graph shows the solution of the given set of inequalities?
- 5. What value of x satisfies the equation ...?
- 6. Which type of function best models the given data?
- 7. If the cost of manufactoring r radios is given by the function c(r)= ...
- then the value 5.25 best represents
- 8. Which equation has the same solution as ...?
- 9. For which interval is the ball's height always
*decreasing*? - 10. What are the roots of the equation ...?
- 11. What is the correlation coefficient of the linear fit of the data show
- below, to the
*nearest hundredth*? - 12. What coulb be Keith's function?
- 13. Which expression results in a rational number?
- 14. Which system of equations has the same solution as the system below?
- 15. The equation that represents this function is
- 16. Which equation could be used to determine the number or dines, x, in his pocket?
- 17. If f(x)= ..., which statement is always true?
- 18. During which interval was their average speed the greatest?
- 19. Which statement about Christopher's performance is correct?
- 20. Which point could be used to find f(2)?
- 21. Which function(s) shown below can be used to determine the height, f(n),
- of the sunflower in n weeks?
- 22. If
*d*represents the number of additional megabytes used adn*c*represents - the charges at the end of the month, which linear equation can be used to
- determine a user's monthly bill?
- 23. The radius,
*r*, of the come may be expressed as - 24. Assuming the pattern continues, which formula determines
*a*, the number_{n} - of shaded squares in the
*n*th term?
Multiple choice.
- 25. Draw the graph of y = ... on the set of axes below.
- 26. In the function
*p(t)*, explain what .05 and 300 represent. - 27. Given [f(x,a)]> [constant], determine the largest integer value of a when x=-1.
- 28. Find the coordinates of the vertex of the parabola defined by
*g(x) = f(x-2)*. - Explain how you arrived at your answer.
- 29. On the set of axes below, draw the graph of the equation
*y= [line]*. - Is the point (3,2) a solution to the equation?
- Explain your answer based on the graph drawn.
- 30. Could
*f*be represented by {[ordered pairs]}? - Justify your answer.
- 31. Factor the expression [fourth degree quadratic-like polynomial].
- 32. Using an appropriate scale on the number line below, construct a
- box plot for the 15 values.
- 33. Write an equation that fefines
*m(x)*as a trinomial where *m(x) = [second degree polynomial]*.- Solve for
*x*where*m(x)*= 0. - 34. Write an equation that can be used to find
*x*, the width of the walkway. - Describe how your equation models the situation.
- Determine and state the width of the walkway, in meters.
- 35. Assuming the pattern continues, write an equation to define
*A(n)*, - the amount of money on the rental card after
*n*rentals. - How many weeks in a row can she affort to rent a movie, using her rental card only?
- Explain how you arrived at your answer.
- 36. Write an equation to represent the possible number of cats and dogs that could have
- been at the shelter on Wednesday.
- Are Pat's numbers possible?
- Use your equation to justify your answer.
- How many cats were at the shelter on Wednesday?
- 37. Graph the production cost functions on the set of axes below and label them site
*A*and*B*. - State the positive value(s) of x for whcih the production costa at the two sites are equal.
- Explain how you determined your answer.
- If the company plans on manufacturing 200 products per week, which site should they use?
- Justify your answer.
Open-ended, partial credit.
Open-ended section only, with number of times used indicated: 2, 5, 1, 5, 1, 3. EVALUATION: determine (2), solve (1) SYNTHESIS: construct (1), find (1), graph (1), justify (3), write (4) ANALYSIS: describe (1) APPLICATION: draw (2), graph (1), state (2), factor (1), construct (1) COMPREHENSION: explain (5) KNOWLEDGE: graph (1), state (2), factor (1) |

Pearson PARCC Algebra I Paper-Bases Practice Test https://parcc.pearson.com/resources/Practice_Tests/Algebra_I/Math/PC194882-001_AlgIOPTB_PT.pdf lap-top parcc.pdf Part 1 https://parcc.pearson.com/resources/practice-tests/math/algebra-1/eoy/PC194891-001_ALG1TB_PT.pdf lap-top parcc.pdf Part 2 |

- 1. Which expression is equivalent to ... ?
- 2. Which points are on the graph of the equation ...?
- Select all that apply.
- 3. Which graph best represents the solution to this system of inequalities?
- 4. Which factorization can be used to reveal the zeros of the function ?= - - +
- 5. For what value of x does
*f(x) = 0*? - Enter your answer in the box.
- 6. Use the graph to estimate the average rate of change of the height of the ball for the first 0.25 second after being hit.
- 7. Which graph represents the equation [linear equation, not y = ...].
Part 1. Multiple Choice, Non-Calculator Section
- 8. Which formula shows how the length of a rectangle can be determined from the perimeter and the width?
- 9. Which value and unit represent the average rate of change in the number of bacteria for the first 5 minutes of the experiment?
- Select all that apply.
- Use the information provided to answer Part A through Part C for question 10.
- Consider the three points [3 points]. .
- 10. Part A: Consider the three points [3 points].
- Which points are on the same line that passes through [3 points]?
- Select all that apply.
- 10. Part B: Use the information from Part A to explain why the ratio of the y-coordinate to the x-coordinate is
- the same for any point on the line except the y-intercept.
- Explain why this is not true for the y-intercept.
- Enter your explanations in the space provided.
- 10. Part C: Do the points on the line have a constant ratio of the y-coordinate to the x-coordinate for any point
- on the line except the y-intercept?
- Explain your answer.
- Enter your answer and your explanation in the space provided.
- Use the information provided to answer Part A through Part C for question 11.
- 11. Part A: Create an equation to represent the total amount of money Matt and Phil
- earned at the fundraiser based on the number of cookies Matt made.
- Explain how you determined your equation.
- Enter your equation and your explanation in the space provided.
- 11. Part B: How many cookies did Phil make and how many cookies did Matt make?
- Show your work.
- Enter your answers and your work in the space provided.
- 11. Part C: Based on their prediction, should Phil and Matt raise the price of the cookies?
- Justify your answer.
- Enter your answer and your justification in the space provided.
- 12. Determine the number of points that would be on the graph of the equation for each given case:
- Justify your answers.
- Enter your answers and justifications in the space provided.
- 13. What is one solution of the equation [quadratic equation]?
- Enter your answer in the box.
- 14. If a is a non-zero, real number and [quadratic equation with some literal terms]
- Prove that
*x= quadratic expression with some literal terms]* - Show your work.
- If
*a=[constant]*and*b=[constant]*, determine what condition(s) on*c*will restrict the - solutions for
*x*to real numbers. - Explain your reasoning.
- Enter your proof, your answer, and your explanation in the space provided
- 15. Consider the following claim: If the point
*[(expression in d, y)]*is on the graph of the function *f(x)=[factored quadratic expression]*,- then the point
*[(expression in d, y)]*is also on the graph. - Use algebra to show that the claim is true.
- What is the relationship between the line
*[vertical line]*and the graph of*f(x)*? - Justify your reasoning.
- Enter your work, your answer, and your justification in the space provided.
- Use the information provided to answer Part A and Part B for question 16.
- 16. Part A: Create a model that can be used to determine the cost savings, in dollars, for the family
- to purchase and use a low-flow showerhead in terms of the number of days.
- Then determine the number of days at which the family will start saving money.
- Justify your answer in terms of the context.
- Enter your model, answer, and justification in the space provided.
- 16. Part B: Create a new model to determine the cost savings, in dollars,
- with the increase in the cost of water.
- Use your model to determine the number of days at which the family will start saving money after the increase in the cost of water.
- Justify your answer.
- Enter your model, answer, and justification in the space provided.
- 17. Will the shorter tour be possible if the riverboat travels at the same speed as it does
- in the 3.25-hour tour?
- Show your steps and justify your answer.
- Enter your answer, your work, and your justification in the space provided.
- Use the information provided to answer Part A and Part B for question 18.
- 18. Part A: Create a model that can be used to determine the total amount of prize money based
- on the value of the first place prize.
- Enter your model in the space provided.
- 18. Part B: What is the amount of money for each of the five prizes?
- Show your work.
- Enter your answers and your work in the space provided.
Multiple Choice, Calculator Section
- 1. If it costs $398 to manufacture 4 pairs of sunglasses, which of the following is true?
- Select the correct equation.
- 2. Which is a graph of the solution set of the inequality [linear inequality]?
- 3. Which of the plotted points on the graph represent the zeros of the function
*f(x) = [partially factored cubic]*?- Select all that apply.
- 4. Which statements are true?
- Select all that apply.
- Use the information provided to answer Part A and Part B for question 5.
- Consider the equation
*[equation with quadratics on both sides]*. - 5. Part A: Let
*u=[quadratic binomial]*. - Which equation is equivalent to
*[equation with quadratics on both sides]*in terms of*u*? - 5. Part B: What are the solutions of the equation
*[equation with quadratics on both sides]*? - Select all that apply.
- 6. In the xy-coordinate plane, the graph of the equation
*y= [quadratic]* - has zeros at
*x=a*and*x=b*, where*a < b*. The graph has a minimum at*(c, [constant])*. - What are the values of a, b, and c ?
- Use the information provided to answer Part A and Part B for question 7.
- Let a represent a non-zero rational number and let b represent an irrational number.
- 7. Part A: Which expression could represent a rational number?
- Part B: Consider a quadratic equation with integer coefficients and two distinct zeros.
- If one zero is irrational, which statement is true about the other zero?
- 8. The figure shows the graphs of the functions
*y=f(x)*and*y=g(x)*. - The four indicated points all have integer coordinates.
- If
*g(x)= k · f(x)*, what is the value of*k*? - Enter your answer in the box.
Multiple Choice. Part 2. Non-Calculator
- 9. What does the value 2,649 represent?
- 10. Which number(s) can be placed in the empty cell so that the table of values
- satisfies the definition of a function?
- Select all that apply.
- 11. Based on the information given, which of the given statements are true?
- Select all that apply.
- 12. What are the zeros of the function defined by
*[quadratic]*? - Select all that apply.
- 13. Find the equation that is equivalent to the quadratic equation shown.
- 14. What is the meaning of the
*[constant]*in the expression? - 15. The function
*M(n)*represents the amount of money the theater takes in on Thursday nights, - where n is the number of customers.
- What is the domain of
*M(n)*in this context? - 16. Which formula can she use to determine the radius of the vase?
- 17. Which expression is equivalent to the expression shown?
- 18. Which of the following graphs shows all of the ordered pairs in the solution set of this
- linear equation?
- 19. What is the y-coordinate of the point of intersection?
- 20. Which equation can be used to find the number of plants in the pond at time
*t*? - 21. According to the graph, what is the approximate average rate of change in the radius
- of the circle as the area increases from 3 square feet to 7 square feet?
- 22. If
*f(x)= [quadratic]*, which statement regarding the vertex form of*f(x)*is true? - 23. In the equations listed,
*a*,*b*,*c*, and*d*are real numbers. - Which of the equations could have solutions that are non-real?
- Select all that apply.
- Use the information provided to answer Part A and Part B for question 24.
- During the 1st day of a canned-goods drive, Jasmine’s homeroom teacher collected 2 cans.
- During the 3rd day, the teacher collected 8 cans.
- Let D represent each collection day, and let N represent the number of canned goods collected on that day.
- 24. Part A: Based on the situation, Jasmine claims that the number of canned goods collected can be
- modeled by an exponential function.
- What is the number of canned goods collected on the 6th day based on an exponential model?
- Enter your answer in the box.
- 24. Part B: Ramon disagrees with Jasmine and claims that the number of canned goods collected can be modeled by a linear function.
- Which statement is true about the number of cans predicted to be collected on the 6th day based on the two models?
- Use the information provided to answer Part A and Part B for question 25.
- In a basketball game, Marlene made 16 field goals.
- Each of the field goals were worth either 2 points or 3 points, and Marlene scored a total of 39 points from field goals.
- 25. Part A: Let x represent the number of 2-point field goals and y represent the number
- of 3-point field goals.
- Which equations can be used as a system to model the situation? Select all that apply.
- 25. Part B: How many 3-point field goals did Marlene make in the game?
- Enter your answer in the box.
- Use the information provided to answer Part A and Part B for question 26.
- 26. Part A: What is a function for the monthly revenue, in dollars, from sales of the drum, R(x),
- where x represents the number of price increases of $1?
- 26: Part B Which statements are true about R, the monthly revenue from sales of the small drum?
- Select all that apply.
- Use the information provided to answer Part A and Part B for question 27.
- 27. Part A: Based on the graph of the function, which statements are true?
- Select all that apply.
- 27. Part B: Based on the graph of the function, which statements are true?
- Select all that apply.
- 28. Use the information provided to answer Part A and Part B for question 28.
- 28. Part A: Which histogram represents the times from Team R on the obstacle course?
- 28. Part B: Which statements are true about the data for team R and team S?
- Select all that apply.
- Use the information provided to answer Part A through Part D for question 29.
- Consider the function
*f(x)*, shown in the xy-coordinate plane, as the parent function. - 29. Part A: Which expression defines the transformation shown?
- 29. Part B: Which expression defines the transformation shown?
- 29. Part C: Which expression defines the transformation shown?
- 29. Part D: Which value must be less than 0?
- Use the information provided to answer Part A through Part D for question 30.
- 30. Part A: Assuming that the population of the city has grown linearly since
- 2005 and continues to grow at the same rate,
- what will be the population in 2015?
- Enter your answer in the box.
- 30. Part B: Which expression is an appropriate exponential model for the population of the city?
- Let t represent the time, in years, since 2005.
- 30. Part C: Assuming that the population of the city has grown exponentially since
- 2005 and continues to grow at the same rate, what will be the population in 2015?
- Give your answer to the nearest whole number.
- Enter your answer in the box.
- 30. Part D: Based on the model, by approximately what percent does the population
- of this town increase each year?
- Use the information provided to answer Part A and Part B for question 31.
- 31. Part A: If the function is graphed in a coordinate plane, which statement would be true?
- 31. Part B: What is the missing value?
- Enter your answer in the box.
- Use the information provided to answer Part A and Part B for question 32.
- Consider the function f(x)= [quadratic in standard form].
- 32. Part A: What is the vertex form of f(x)?
- 32. Part B: What is a factored form of f(x)?
- Use the information provided to answer Part A through Part D for question 33.
- 33. Part A: Which graph shows the set of points that represents the number
- of hours that Leah can work in order to earn at least $120 and
- not work more than 20 hours per month?
- 33. Part B: Which pairs (x,y) represent hours that Leah could work to meet the given conditions?
- Select all that apply.
- 33. Part C: If Leah babysits for 7 hours this month, what is the minimum number of hours
- she would have to work at the ice cream shop to earn at least $120?
- Give your answer to the nearest whole hour.
- Enter your answer in the box.
- 33. Part D: Out of 20 total hours, what is the maximum number of hours she can babysit
- to be able to earn at least $120 per month?
- Give your answer to the nearest whole hour.
- Enter your answer in the box.
- Use the information provided to answer Part A and Part B for question 34.
- The diagram shows two cylinders with bases that have the same center and
- heights of 12 millimeters.
- 34. Part A: Which is a function for the volume, V, that is inside the larger cylinder but
- outside the one with the smaller radius, r?
- 34. Part B: What is the domain of V?
- Use the information provided to answer Part A and Part B for question 35.
- 35. Part A: If f(x=3) = [quadratic polynomial with linear coefficient k], what is the value of k?
- Enter your answer in the box.
- 35. Part B: What are the zero(s) of f(x+3)?
- Select all that apply.
Multiple Choice. Part 2. Calculator
PARCC Algebra I, Parts 1 and 2: 3,3,0,4,0,1,other 4
EVALUATION: consider (6), determine (3), prove (1) SYNTHESIS: create (4), find (1), prove (1) ANALYSIS: APPLICATION: show ( 4) COMPREHENSION: KNOWLEDGE: select ( 17) OTHER: enter (23), give (3), let (5), use (21) |

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