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Tenth Grade (Grade 10) Mathematical Process Questions

You can create printable tests and worksheets from these Grade 10 Mathematical Process questions! Select one or more questions using the checkboxes above each question. Then click the add selected questions to a test button before moving to another page.

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Grade 10 Logical Thinking
Which best describes what a conditional is?
  1. A rule
  2. If p then q
  3. A proof
  4. If q then p
Grade 10 Logical Thinking
What is the contrapositive of the following statement? If an angle is obtuse, then it is greater than 90.
  1. If an angle is obtuse then it is greater than 90.
  2. If an angle is not greater than 90 then it is not obtuse.
  3. If an angle is not obtuse then it is not greater than 90.
  4. If an angle is greater than 90 then it is obtuse.
Grade 10 Logical Thinking
Is the converse of this statement true? If not, select the specific counter example. "If an angle is 117 degrees, then it is obtuse."
  1. True
  2. Not true - 90 degrees
  3. Not true - 116 degrees
  4. Not true - 75 degrees
Grade 10 Logical Thinking
Determine the inverse of the statement: if p, then q.
  1. If ~q, then p
  2. If p, then ~q
  3. If ~p, then q
  4. If ~p, then ~q
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:
d=d0+v0t+12at2
where d,d0 are distances measured in meters; v0 is velocity, measured in meters per second; t is time, measured in seconds; and a 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

ms⋅s1=m

and the last term is

ms2⋅s21=m.

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 t 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 m/s2 and the units of the last term are m/s4.
Grade 10 Problem Solving Strategies CCSS: HSN-Q.A.1
Rob is writing a physics test. For one of the problems, he needs the gravitational force formula for the force of gravity between two objects. He's not sure he remembers it correctly. He believes it is
Fg=G m1 m2r,
where Fg is the force, measured in Newtons; G is the gravitational constant, measured in N⋅m2/kg2; m1,m2 are the masses of the two objects measured in kilograms; and r is the distance between the objects, measured in meters. Using dimensional analysis, is his formula correct? Why or why not?
  1. Yes, since N⋅mkg2×kg1×kg1×1m=N.
  2. No, since N⋅m2kg2×kg1×kg1×1m=N⋅m.
  3. No, since N⋅m2kg2×1kg×1kg×m1=N⋅m3kg4.
  4. No, since N⋅m2kg2×kg1×kg1×m1=N⋅m3.
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 Logical Thinking
Determine the contrapositive of the statement: if p, then q.
  1. if ~q, then ~p
  2. If p, then ~q
  3. If ~p, then q
  4. If q, then p
Grade 10 Logical Thinking
Determine the converse of the statement: if p, then q.
  1. If ~q, then p
  2. If p, then ~q
  3. If ~p, then q
  4. If q, then p
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