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1. Solve the equation 35 = 9x 19. SHOW YOUR WORK and explain how you got your answer.
A. x = 5
B. x = 6
C. x = 7
D. x = 8
2. Allen is loading a wheelbarrow full of bricks. Each brick weighs three pounds and the wheelbarrow weighs forty pounds. Allens total load (bricks plus wheelbarrow) weighs 73 pounds. How many bricks are in the wheelbarrow? WRITE AN EQUATION TO SHOW HOW YOU WOULD SOLVE THIS.
A. 0 bricks
B. 11 bricks
C. 43 bricks
D. 73 bricks
3. A math teacher is stranded on a deserted island with 562 cans of soup. She finishes 4 cans of soup per week. Write an equation to model the number of cans of soup the teacher has left after x weeks.
A. y = 562 4x
B. y = 562 (x  4)2
C. y = 562(1/4)x
D. y = 562 4x
Use this scenario for questions 4 through 6
Rachel scoops ice cream at the Twist n Shout ice cream parlor in town. She charges $1 for a single scoop cone and $2 for a double scoop cone. On Sunday, she charged a total of $342.
4. Which equation represents this situation? (Let s stand for the number of single scoop cones and d stand for the number of double scoop cones.)
A. 1s + 2d = 342
B. 2s + 1d = 342
C. d = 1s + 2
D. 342 = 3s
5. Rachel scooped 241 cones altogether. Again, let s stand for the number of single scoop cones and d stand for the number of double scoop cones. Which equation represents the number of each kind of cones she scooped?
A. s + d = 342  241
B. s " d = 241
C. s + d = 241
D. 1s + 2d = 241
6. Given the two equations you identified in problems 4 and 5 above, solve them together to find how many single scoop cones and how many double scoop cones Rachel served on Sunday. Show your work. Check your answers to make sure you are using the correct equations.
Equation 1 (from problem 7):
Equation 2 (from problem 8):
Solve them together to find s and d:
7. Find the solution to this system of equations. SHOW YOUR WORK. CIRCLE THE ANSWER.
y = 5x 3
y = 2x + 21
8. Solve this system of three equations in three variables. Then add x, y and z to get a single number. Circle the answer that corresponds to that number. For example, if x = 2, y = 1 and z = 3, then x + y + z = 6.
Show all your work, and circle the values of x, y and z.
x + 2y + z = 2
2x  3z = 3
x = 3
A. x + y + z = 7
B. x + y + z = 3
C. x + y + z = 2
D. x + y + z = 6
9. Solve for x: 5x < 75
A. x < 15
B. x > 15
C. x > 15
D. x < 80
10. A test had 50 questions on it. The teacher doubled each students number of correct answers to get a percentage. Then she added 5 points to each score to adjust for how difficult it was. Students final scores were all above 65%.
Let A stand for the number of correct answers. Which inequality shows the range of possible correct answers in the class?
A. 0 < 2A +5 < 50
B. 65 > 2A + 5 > 105
C. 65 < 2A + 5 < 105
D. 100 > A + 5 > 65
11. Solve 3x2 x = 5 SHOW ALL YOUR WORK.
A. x = 3.28 or 2.71
B. x = (1.26
C. x = 1.14 or 1.47
D. x = 2.31 or 1.49
12. Solve: 2x2 9x 5 = 0 SHOW ALL YOUR WORK.
A. x = 3 or 2
B. x = 1/3 or 5/4
C. x = 5 or 3
D. x = 1/2 or 5
13. Solve (x5)3 = 8
A. 517
B. 29
C. 13
D. 7
20062007 Ingham County Algebra 1 Credit Assessment: Pt. 2 Functions
Use this scenario for questions 1516:
A cell phone company has a plan that charges $20 per month plus $0.05 per minute. Think about a situation where a person makes 100 minutes of calls in one month using this plan.
15. Figure out the cost of talking for 100 minutes in one month, using this plan. Show all your work:
16. Which type of function best models this situation? Let y stand for the total cost for a month of calls. Let x stand for the number of minutes used. If you need help with this, look back at how you figured out the total cost and think about how that would be represented with an equation. (Let a stand for the cost per minute. Let b stand for the monthly charge. You can put in the actual values for a and b if that will help you figure this out.)
A. A linear function, where y = ax + b
B. A quadratic function, where y = ax2 + b
C. An exponential function, where y = abx
17. Amandas grandmother said that she will put money into a savings account for Amanda if Amanda will also save some money. She said she would put twice as much money as Amanda saves, plus $12, each time Amanda adds money to her savings account. What function represents this, if x is the money that Amanda adds to her savings?
A. f(x) = x2 + 12
B. f(x) = 2(x + 12)
C. f(x) = 2x +12
D. f(x) = 2x + 12
Explain why you chose your answer:
18. Which table of values shows the correct function for #17?
A.Money that Amanda saves: xTotal money in her account: f(x)B.Money that Amanda saves: xTotal money in her account: f(x)C.Money that Amanda saves: xTotal money in her account: f(x)101121044103220412206420523091230843072401612401044092
19. Which family of functions is represented by this graph?
A. Linear
B. Quadratic
C. Exponential
D. Absolute Value
Explain how you know this.
20. Which family of functions is represented by the equation y = 2x ?
A. Linear
B. Quadratic
C. Exponential
D. Absolute Value
21. For EMBED Equation.DSMT4 which of the following is true? (You can write a table of values and draw a graph of this function if it will help you answer the question.)
(i). f(x) approaches positive infinity as x approaches negative infinity
(ii). f(x) approaches negative infinity as x approaches positive infinity
(iii). f(x) approaches zero as x approaches positive infinity
(iv). f(x) approaches zero as x approaches negative infinity
A. i and ii and iii are true.
B. iii and iv are true
C. all are true
D. none are true
Use this scenario for problems 2225:
At the beginning of the day, 3 people know a secret. Each person tells another person the secret every hour. Therefore, the number of people who know the secret doubles every hour.
22. Is this an exponential growth or decay function? Why?
23. Which function represents the number of people P who know the secret after t hours?
A. P = 3+2t
B. P = t3
C. P = 3t2
D. P = 3(2t)
24. Evaluate the function to find the number of people who know the secret after 7 hours.
A. 17 B. 343 C. 147 D. 384
25. Graph the function. Label your axes!
Use this scenario for questions 26 and 27:
The value of a certain car brand (a) can be modeled by the function Va = 18000 (.89)t where Va is the value of the car in dollars and t is the number of years after it was bought. The value of a different car brand (b) can be modeled by the function Vb = 18000 (.75)t where Vb is the value of the car in dollars and t is the number of years after it was bought.
26. Which of the following is true?
A. Both cars are increasing in value.
B. Car a is losing its value faster than car b.
C. Car b is losing its value faster than car a.
D. None of these is true.
Explain why you believe your answer.
27. Calculate the value of Car a after 3 years. Round to the nearest whole dollar. You can use a calculator for this if you like.
A. $4.1113 E12
B. $12,689
C. $48,060
D. $12,060
28. Which of the following accurately shows a quadratic function with zeros of 3 and 11 and a maximum value at y = 12 ?
A. f(x) = EMBED Equation.3 (x  3)(x + 11)
B. f(x) = EMBED Equation.3 (x  3)2 + 11
C. f(x) = EMBED Equation.3 (x + 3)(x  11)
D. f(x) = EMBED Equation.3 (x  11)2 + 3
29. Consider the function f(x) = x2  3x + 2.
Pt. 1. What are the zeros of the function (the x values where y = 0)?
Pt. 2. What is the maximum or minimum value of this function?
Pt. 3. Is the ordered pair you found in B a maximum value or minimum?
Pt. 4. Sketch a graph of this function, given the information you found in A, B and C.
30. A stone is dropped off a cliff 100 meters high. Gravity pulls down on it with a constant force. Its speed increases constantly because of the constant force of gravity. Because its speed is constantly increasing, the distance it travels every second gets larger and larger. The table below shows this. Distances are how far it has fallen from the top of the cliff, approximately.
time tdistance f(t)after 0 seconds0 metersafter 1 sec5 mafter 2 sec20 mafter 3 sec45 mafter 4 sec80 m
What family of functions models this motion most accurately?
A. linear functions, because the speed increase is constant
B. exponential functions, because there is a constant multiplier
C. quadratic functions, because the distance goes up with the square of the time
D. absolute value functions, because all the values are positive
Answer Keys and HSCE Alignment for Parts 1 and 2 of the 20072008 Ingham County Algebra I Secondary Credit Assessment
These assessments are in two parts, one that focuses on equations and one that focuses on functions. Both parts are short because they only assess the power standards for Algebra I. You can give these any time during the year, preferably close to when you study these topics. Or you can use the items to make unit tests and administer them throughout the year when you have completed a unit.
Alignment to HSCEs: A list of HSCEs and corresponding items numbers is included in this answer key. Please share this list with students as you go over the assessments (and all throughout instruction), so they know what their learning targets are. The power standards are also listed below for each part.
Using the assessments for determining credit: The purpose of the secondary credit assessments, as mandated by state law, is to contribute to your determination of whether a student has successfully learned the HSCEs for the course. Your district is allowed to determine how much weight to put on the score from these assessments. You should also consider scores on other assessments, projects, etc. done throughout the year. If you want to assign a grade to these assessments, your district is allowed to determine your own cut score. It should be the same across all Algebra I classes, for all students.
Types of items on the assessments: These assessments contain a mix of multiple choice, multiple choice with Explain your answer, and constructed response items, such as drawing a graph, solving an equation, making an explanation, and so forth. You may choose to change some of the multiple choice items into constructed response, if you think that having a few possible answers to choose from might give your students too much information. In some cases, the wrong answers to a multiple choice item (the distractors) are based on common patterns of mistakes or misconceptions, which might give you insight into your students thinking.
Using bubble sheets for automatic scoring: If you use bubble sheets for the multiple choice items, make sure to have students go through the bubble sheet before taking the test, and put an X through the item numbers of constructed response items, so they remind themselves to skip that line as they bubble in answers to multiple choice items.
Pt. 1 Equations Answer Key
Power Standard 1: Solve equations and inequalities
Write, simplify, and find solutions of linear equations, inequalities and systems of equations (up to three unknowns) that represent mathematical or applied situations. (A1.2.1, A1.2.3, A1.2.8, A.FO.08.09)
1. BA1.2.3 Solve linear and quadratic equations and inequalities, including systems of up to three linear equations with three unknowns. Justify steps in the solutions, and apply the quadratic formula appropriately.2. B
3x + 40 = 73 (or equivalent)A1.2.1 Write and solve equations and inequalities with one or two variables to represent mathematical or applied situations.3. DA1.2.1 Write and solve equations and inequalities with one or two variables to represent mathematical or applied situations.4. AA1.2.1 Write and solve equations and inequalities with one or two variables to represent mathematical or applied situations.5. CA1.2.1 Write and solve equations and inequalities with one or two variables to represent mathematical or applied situations.6. A1.2.3 Solve linear and quadratic equations and inequalities, including systems of up to three linear equations with three unknowns. Justify steps in the solutions, and apply the quadratic formula appropriately.7. A1.2.3 Solve linear and quadratic equations and inequalities, including systems of up to three linear equations with three unknowns. Justify steps in the solutions, and apply the quadratic formula appropriately.8. B (3, 1, 1) Other foils represent A. (3,2,2), C. (3,2,1), D. (3,1,4)A1.2.3 Solve linear and quadratic equations and inequalities, including systems of up to three linear equations with three unknowns. Justify steps in the solutions, and apply the quadratic formula appropriately.9. BA1.2.3 Solve linear and quadratic equations and inequalities, including systems of up to three linear equations with three unknowns. Justify steps in the solutions, and apply the quadratic formula appropriately.10. CA1.2.1 Write and solve equations and inequalities with one or two variables to represent mathematical or applied situations.11. CA1.2.3 Solve linear and quadratic equations and inequalities, including systems of up to three linear equations with three unknowns. Justify steps in the solutions, and apply the quadratic formula appropriately.12. DA1.2.3 Solve linear and quadratic equations and inequalities, including systems of up to three linear equations with three unknowns. Justify steps in the solutions, and apply the quadratic formula appropriately.13. DA1.2.6 Solve power equations (e.g., (x + 1)3 = 8) and equations including radical expressions (e.g., EMBED Equation = 7), justify steps in the solution, and explain how extraneous solutions may arise.
Power Standard 2: Translate among representations of functions
Represent, recognize and analyze the key features of functions in symbols, graphs, tables, diagrams or words and translate among representations. (A2.1.3, A2.1.6, A2.1.7)
Power Standard 3: Model realworld situations using functions
Choose the appropriate family of functions to model a realworld situation, write the symbolic form of the function, and use the specific function to draw conclusions about the situation. (A2.4.13, A2.3.13)
no question 1415. A
16. A2.4.1 Identify the family of functions best suited for modeling a given realworld situation.17. C
A2.1.3 Represent functions in symbols, graphs, tables, diagrams, or words and translate among representations.
A3.1.1 Identify the family of functions best suited for modeling a given realworld situation18. C
A2.1.3 Represent functions in symbols, graphs, tables, diagrams, or words and translate among representations.19. DA2.3.1 Identify a function as a member of a family of functions based on its symbolic or graphical representation. Recognize that different families of functions have different asymptotic behavior at infinity and describe these behaviors.20. CA2.3.1 Identify a function as a member of a family of functions based on its symbolic or graphical representation. Recognize that different families of functions have different asymptotic behavior at infinity and describe these behaviors.21. CA2.3.1 Identify a function as a member of a family of functions based on its symbolic or graphical representation. Recognize that different families of functions have different asymptotic behavior at infinity and describe these behaviors.22. Growth. The number of people who know the secret gets larger with every hour.A3.2.5 Relate exponential functions to real phenomena, including halflife and doubling time.23. DA3.2.1 Write the symbolic form and sketch the graph of an exponential function given appropriate information (e.g., given an initial value of 4 and a rate of growth of 1.5, write f(x) = 4 (1.5)x).
A2.4.1 Identify the family of functions best suited for modeling a given realworld situation.
A2.4.2 Adapt the general symbolic form of a function to one that fits the specifications of a given situation by using the information to replace arbitrary constants with numbers.24. 384
A2.4.3 Using the adapted general symbolic form, draw reasonable conclusions about the situation being modeled.
25.
(see graph in next cell)A2.1.3 Represent functions in symbols, graphs, tables, diagrams, or words and translate among representations.
26. C because the rate of exponential growth is given by the base of the exponent, the value of car b is multiplied by .75 each year, where the value of car a is multiplied by .89 each year.A3.2.4 Understand and use the fact that the base of an exponential function determines whether the function increases or decreases and how base affects the rate of growth or decay.27. BA2.1.2 Read, interpret, and use function notation and evaluate a function at a value in its domain.
A2.4.3 Using the adapted general symbolic form, draw reasonable conclusions about the situation being modeled. 28. CA3.3.2 Identify the elements of a parabola (vertex, axis of symmetry, and direction of opening) given its symbolic form or its graph and relate these elements to the coefficient(s) of the symbolic form of the function.29. Pt. 1 (1,0), (2,0)
Pt. 2 (1 ,  )
Pt. 3 minimum
Pt. 4 graph also includes the point (0,2)
A3.3.5 Express quadratic functions in vertex form to identify their maxima or minima and in factored form to identify their zeros.30. CA2.4.1 Identify the family of functions best suited for modeling a given realworld situation.
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