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Tenth Grade (Grade 10) Mathematical Process Questions

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Grade 10 Logical Thinking
Which of the following is the biconditional statement for the conditional statement below?

If today is Saturday or Sunday, then it is the weekend.
  1. It is the weekend if and only if it is Saturday or Sunday.
  2. If is not the weekend, then it not Saturday or Sunday.
  3. If it is not Saturday or Sunday, then it is not the weekend.
  4. It is not Saturday or Sunday if and only if it is the weekend.
Grade 10 Problem Solving Strategies CCSS: HSN-Q.A.1
Grade 10 Problem Solving Strategies CCSS: HSN-Q.A.2
A moving company chargers $65 per hour, plus a fee that depends on the distance between where the objects are being moved ($35 for every mile). What variable(s) would be good to define if one were to create an expression that would determine the total cost of moving?
  1. One variable: C, the cost of moving.
  2. One variable: t, for the amount of time.
  3. Two variables: C, for the total cost, and t, for the amount of time.
  4. Two variables: t, for the amount of time, and d, for the distance traveled.
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 10 Logical Thinking
Grade 10 Problem Solving Strategies CCSS: HSN-Q.A.2
There is a leak in the ceiling of Kara's room. She puts a bucket underneath the drip. After an hour, there's about a half liter of water. She checks back in another 3 hours, and there is about 2 liters of water. If she wants to determine how much water there will be in 12 hours, what quantity or quantities would she need to determine?
  1. The rate of the water's increase, in liters per hour.
  2. The amount of water in the bucket, in liters.
  3. The amount of water in the bucket in liters and the amount of time that has passed in hours.
  4. The size of the bucket in liters and the rate of the drip in liters per hour.
Grade 10 Logical Thinking
Given the statement: "If you eat all your vegetables, then you will grow," which of the following choices is its converse?
  1. If you grow, then you will eat all of your vegetables.
  2. If you do not eat all of your vegetables, then you will not grow.
  3. If you do not grow, then you will not eat all of your vegetables.
Grade 10 Logical Thinking
Grade 10 Problem Solving Strategies CCSS: HSN-Q.A.2
Colin has been asked to create a mathematical model of the penguin population on a remote island. He wants to be able to predict the growth of the penguin colony. He decides that important variables and quantities to consider in the model include: availability of food, presence of predators, the current number of penguins, and the historic growth rate of penguin population. Is Colin's list correct? Why or why not?
  1. Yes, this is the correct model, and there are no more important factors to consider.
  2. No, this model leaves out many important variables, such as climate, water currents, diseases, and many more.
  3. No, only the current number of penguins and the historic rate of population growth are important. All the other factors are simply over-complicating the problem.
  4. Neither correct nor incorrect. Any real world problem can be modeled in multiple ways and with varying degrees of complexity.
Grade 10 Problem Solving Strategies CCSS: HSN-Q.A.2
Grade 10 Logical Thinking
Given the statement: "If you eat all your vegetables, then you will grow," which of the following choices is its inverse?
  1. If you grow, then you will eat all of your vegetables.
  2. If you do not grow, then you will not eat all of your vegetables.
  3. If you do not eat all of your vegetables, then you will not grow.
Grade 10 Logical Thinking
Grade 10 Problem Solving Strategies CCSS: HSN-Q.A.2
Angela sells baked goods at a summer market each year. The two main baked goods are apple turnovers and chocolate caramel cupcakes. Unfortunately, she does not keep very good records, and cannot remember exactly what price she sold each for last year. She remembers that one day she sold 50 cupcakes and 30 turnovers, and made about $135. Another day, she sold 40 cupcakes and 40 turnovers, and made $140. If she were to create a model to solve for how much she sold each baked good for, what would be a good variable(s) to create?
  1. Just one variable, the average cost of a baked good.
  2. Two variables, one for the cost to make the baked goods, and another for the total revenue of the baked goods.
  3. Two variables, one for the total number of turnovers sold, and another for the total number of cupcakes sold.
  4. Two variables, one for the cost of a turnover, and one for the cost of a cupcake.
Grade 10 Problem Solving Strategies CCSS: HSN-Q.A.2
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