Core Academic Skills for Educators: Mathematics (5732) · PDF file Rationale for correct...

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Transcript of Core Academic Skills for Educators: Mathematics (5732) · PDF file Rationale for correct...

  • Core Academic Skills for Educators: Mathematics (5732) Practice Test: Version C

    * Developed by the VCSU Fall 2018 Math 491 Capstone Course

  • Taking the Practice Test

    Actual Time Allowed on Test Day: 85 minutes

    Number of Questions: 56

    Format: Multiple Choice, Multiple Answer, and Numeric Entry

    Calculator: When taking the actual test an online four- function calculator (i.e. add, subtract, multiply, divide) is available. For this practice test you are encouraged to use your own four-function calculator

  • Question 1

    The correct answer is: D Rationale for correct answer: If the units for x represent the number of feet and y represents inches. The numbers would be equivalent to 12 inches in a foot, so it would read from bottom to top 12,24, 36, 48, 60. This would move up 12 inches on the y-axis for every 1 foot on the x-axis.

    Related ND Math Standards: 7.RP.2, 8.EE.5, 6.EE.9

    For any point (x,y) on the graph, if y represents number of inches, then x could represent the equivalent number of feet. What would the numbers from bottom to top on the y-axis be?​

    A. 6, 12, 18, 24, 30​ B. 2, 4, 6, 8, 10​ C. 10, 20, 30, 40, 50​ D. 12, 24, 36, 48, 60​ E. 24, 48, 72, 96, 120

  • Question 2

    The correct answer is: D Rationale for correct answer: Two good points to check are when x = 0 and when y = 0. In this case, that would be (0, −1) and (, 0). So, Graph D is the correct answer.

    Related ND Math Standards: 8.EE.5 8.F.1 8.F.3 8.F.4 HS.ACED.1* HS.FIF.4*

    Graph f(x) = 2x – 1. Which of the following graphs is correct?

  • Question 3

    The correct answer is: C Rationale for correct answer: 2 minutes ans 30 seconds equals 150 seconds. 150 divided by 25 equals 6. 6 times .25 equals 1.5 liters

    Related ND Math Standards: 7.EE.3

    Imagine you are drinking out of a big bottle of soda. You are drinking the soda at a rate of .25 liters per 25 seconds. How much will you drink after 2 minutes and 30 seconds?

    A) 2 liters B) 1.75 liters C) 1.5 liters D) 3 liters E) .75 liters

  • Question 4

    The correct answer is: C Rationale for correct answer: 1 and 4 cannot be proven that they add up to 180 or 90 degrees, so they cannot be supplementary or complimentary. There are no parallel lines, therefore 1 and 4 cannot be corresponding angles. This results in angles 1 and 4 being vertical angles because they are opposite angles of two intersecting lines.

    Related ND Math Standards: HS.G-CO.9, 8.G.5, 7.G.5 , MP.8

    A) Supplementary

    B) Complimentary

    C) Vertical Angles

    D) Corresponding Angles

    4 1

    2

    3

    Using the image below, angles 1 and 4 are:

  • Question 5

    The correct answer is: B Rationale for correct answer: Write the equation of the line in the form of y=mx+b. Since the line goes through the origin, the y-intercept (b) is 0. Next, find the slope. Since the line goes through the origin, the slope (m) will equal y/x. Use the point (0.4,1.4). Slope (m) = y/x = 1.4/0.4 = 3.5. Now use these values to create the equation of the line. Y = 3.5x. Plug 3 in for x to get the answer of y=10.5

    Related ND Math Standards: 7.RP.2 , 8.EE.5 , HS.FIF.6*, MP1, MP4, MP7

  • Question 6

    The correct answer is: A Rationale for correct answer: Only order that is correct

    Related ND Math Standards: 7.SP.1

    A city council member wanted to know how her constituents felt about a planned rezoning. She randomly selected 757575 names from the city phone directory and conducted a phone survey. Identify the population and sample in this setting.

    A) The population is everyone listed in the city phone directory; the sample is the 757575 people selected. B) The population is residents of the city; the sample is the registered voters in the city. C) The population is registered voters in the city; the sample is everyone listed in the city phone directory. D) Both A and B C) No correct answer

  • Question 7

    The correct answer is: C Rationale for correct answer: The total is 45,000 total property – 25000 yard – 6000 house- 12000 garage = 2000 square feet for the family's deck.

    Related ND Math Standards: S.ID.1, 2, 3

  • Question 8

    The correct answer is: D Rationale for correct answer: the equation created by the statement above is "7=(3x+5)/2. Multiply by 2 on each side that gives you 14=3x+5. And solving that equation for x gives you letter D x=3

    Related ND Math Standards: HS.F-BF.2* MP(1,2,4,7)

    In the following written expression solve for the value of the unknown number:

    seven equals one half of 5 more than three times a number.

    A: (11/2)

    B: (19/3)

    C: (17/3)

    D: 3

  • Question 9

    The correct answer is: A Rationale for correct answer: 35% = .35. When we are finding the percent of a number, we multiply the percent by that number: $4,400 * (.35) = $1,540.

    Related ND Math Standards: 6.RP.3, 7.RP.3, MP1, MP6

  • Question 10

    The correct answer is: Length: 75 Width: 75

    Rationale for correct answer: To maximize area, the enclosure should be a square. Therefore the dimensions are 75x75.

    Related ND Math Standards: 3.MD8 ; MP 4, MP 2

    A farmer has 300 yards of fence to use to create a rectangular enclosure. What should the dimensions of the fenced enclosure be to maximize area?​

    Length:​

    Width:

  • Question 11

    The correct answer is: 11 ¼ or 45/4 Rationale for correct answer: Luther bought 4 ½ times 2 ½ pounds of turnips. Multiply those together after changing them into improper fractions. 4 ½ changes to 9/2. Additionally, 2 ½ changes to 5/2. Multiply 9/2 x 5/2. The numerators multiply to get 45 while the denominators multiply to get 4. The fraction would be 45/4 or simplified to 11 ¼.

    Related ND Math Standards: 3.NF.3,5.NF.6

    Luther bought a bag of parsnips that weighed 2 1/2 pounds. He also bought a bag of turnips that weighed 4 1/2 times as much as the parsnips. How many pounds of turnips did Luther buy?​

    Write your answer as a fraction or as a whole or mixed number.

    pounds

  • Question 12

    The correct answer is: as x increases, y remains the same. Rationale for correct answer: Looking at the graph, you see a horizontal line meaning that y is constant. As x changes, y remains the same concluding why the answer is D.

    Related ND Math Standards: 8.SP.1 8.SP.2 HS.SID.6 HS.SID.7* HS.SID.8*

    The scatterplot below suggests a trend between

    variables x and y. Which of the following best

    describes this trend?

    A. As x increases, y decreases.

    B. As x increases, y remains negative.

    C. As x increases, y increases.

    D. As x increases, y remains the same.

    E. There is no trend.

  • Question 13

    The correct answer is: D Rationale for correct answer: 17 times 8 equals 136

    Related ND Math Standards:

    1 face equals 8 children

    Look at the pictograph, how many students get to school in a car, bus, or on foot?

    A) 32 B) 112 C) 24 D) 136 E) 144

  • Question 14

    The correct answer is: A Rationale for correct answer: To find the least common factor of three terms, we can use the largest number and list its multiples until you find one that is divisible by both of the other two. So, 16 , 32, 48, 64, etc. We can see that 48 is a multiple of both 8 and 12 (8 * 6) and 12 * 4). Sok we need 48 of each item. Packs of cups are sold in 8, so 48/8 = 6 total packages needed.

    Related ND Math Standards: 4.MD.1, 6.NS.4, MP.3, MP.4

    Kyle is planning a Superbowl party at his house. He went to the store to buy paper plates, napkins, and cups. Paper plates are sold in packages of 12. Cups are sold in packages of 8, and napkins are sold in packages of 16. If Kyle wants the same amount of each item, how many packages of cups does he need to buy?

    A) 6 packages

    B) 2 packages

    C) 8 packages

    D) 10 packages

  • Question 15

    The correct answer is: D Rationale for correct answer: Volume of a sphere = (4/3) * pi * r^3. Plug in the given values and solve. 2144.66 = (4/3) * pi * r^3 1608.495 = pi * r^3 511.9998 = r^3 8 = r --> d=16

    Related ND Math Standards: 6.G.2 , 8.EE.7 , HS.GGMD.3* , MP1, MP6, MP7

  • Question 16

    The correct answer is: B Rationale for correct answer: Knowing that 72 = 49 is helpful because we can eliminate at least (C) and (D). If we actually compute the other two, we get 7.12 = 50.41 and 7.22 = 51.84. Since 7.1 is closer, that is the best approximation.

    Related ND Math Standards: 8.NS.1

    Which is the best approximation of the square root of 51? A) 7.1 B) 7.2 C) 7.5 D) 7.9 E) 25.1

  • Question 17

    The correct answer is: D Rationale for correct answer: As the X value increases the y values increase at a rapid rate which looks close to exponential.

    Related ND Math Standards: S.ID.7, 8, 9

  • Question 18

    The correct answer is: C Rationale for correct answer: If it is currently 5 PM where you are now, then in 5 hours when you are at your destination it will be 10 PM. With it being 5 PM at your destination when it is 10 PM. This shows that at home is 5 hours later than your destination , so if it it 8 PM at my destination, it is 5 Hours later aka 1 AM back at your destination.

    Related N