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Common Core Standard HSN-Q.A.1 Questions

Use units as a way to understand problems and to guide the solution of multi-step problems; choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays.

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Grade 10 Problem Solving Strategies CCSS: HSN-Q.A.1
Use dimensional analysis to find how many minutes are in a year. Round to the nearest minute if necessary.
  1. 525,600 minutes
  2. 21,900 minutes
  3. 8,760 minutes
  4. 913 minutes
Grade 10 Problem Solving Strategies CCSS: HSN-Q.A.1
Near the end of class, Jillian's physics teacher writes a formula up on the board. Jillian quickly writes it down before leaving. Later that night while doing homework, she is unsure if she correctly copied the formula. What she wrote is:
[math]d = d_0 + v_0t + 1/2 at^2[/math]
where [math]d, d_0[/math] are distances measured in meters; [math]v_0[/math] is velocity, measured in meters per second; [math]t[/math] is time, measured in seconds; and [math]a[/math] is acceleration, measured in meters per second squared.

She decides she will use dimensional analysis to determine if it is correct or not. She reasons that each term has to have the same units, and since the term on the left side of the equation and the first term on the right side of the equation are in meters, the other two terms need to be as well. The second term on the right side of the equation is

[math]"m"/"s" *"s"/1 = "m"[/math]

and the last term is

[math]"m"/"s"^2 * "s"^2/1 = "m"[/math].

Since all terms are in meters, she decides that the equation she wrote down is right. Is she correct, and if not, what mistake did she make?
  1. Yes, she is correct.
  2. No. She assumed that all terms need to have the same units, when all terms need to be without units.
  3. No. Although the variable [math]t[/math] is squared, the units are not. Therefore, the units of the last term are m/s, which are different than the rest of the terms.
  4. No. Jillian did the dimensional analysis incorrectly. The units of the second term on the right side come out to [math]"m"//"s"^2[/math] and the units of the last term are [math]"m"//"s"^4[/math].
Grade 10 Problem Solving Strategies CCSS: HSN-Q.A.1
Using dimensional analysis, the following calculation can be performed to convert between 3 pounds and its equivalent in grams (using the rate of 1 oz equals 28.3 g).

[math](3 \ "lb")/1 xx (16 \ "oz") / (1 \ "lb") xx (28.3 \ "g")/(1 \ "oz") = 1,358.4 \ "g"[/math]

Mathematically, why can 3 be multiplied by the factors [math] (16 \ "oz") / (1 \ "lb")[/math] and [math](28.3 \ "g")/(1 \ "oz") ?[/math]
  1. Because this is dimensional analysis, regular rules of math do not apply.
  2. Since the necessary units cancel out, there is no problem.
  3. Because each of these factors is equal to one (the numerator and denominator are equal, but in different units).
  4. By the Multiplicative Property of Equality.
Grade 9 Linear Equations CCSS: HSN-Q.A.1
When graphing the distance vs. time for a car traveling for a full day, the most appropriate units would be
  1. miles and minutes.
  2. kilometers and hours.
  3. meters and hours.
  4. feet and minutes.
Grade 9 Line Graphs CCSS: HSN-Q.A.1
A graph with units of meters and minutes would be most appropriate for tracking
  1. a falling stone.
  2. a car on the highway.
  3. a person walking.
  4. a jet flying.
Grade 11 Line Graphs CCSS: HSN-Q.A.1
A graph showing the re-entry and landing of a space craft to Earth would best be in which units?
  1. Kilometers and Minutes
  2. Miles and Hours
  3. Meters and Seconds
  4. Miles and Days
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