HiSET: Math : Mathematical Process Categories
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Example Questions
Example Question #1 : Mathematical Process Categories
Consider the following statement:
"If an integer is odd and is between 10 and 20, then it must be prime."
Which of the following is a counterexample to the statement?
The integer 16 is not prime.
The integer 15 is not prime.
The integer 9 is not prime.
Odd numbers are not evenly divisible by 2.
The integer 13 is prime.
The integer 15 is not prime.
A counterexample is a single example that disproves a statement. In order to disprove "If an integer is odd and is between 10 and 20, then it must be prime," you must show that there is an integer that is odd and is between 10 and 20, but is not prime.
While 9 is odd and is not prime, it is not between 10 and 20. 16 is also not prime, but it is not odd.
15 is the answer because it is odd and is between 10 and 20, but is not prime, because it is divisible by 5 and 3, in addition to being divisible by itself and 1.
Example Question #1 : Make Inferences Or Predictions Based On Data Or Information
A swimming pool was drained of water. At 8:56 AM, the water in the pool was 5.7 ft high. At 9:10 AM, the water level in the pool was 2.9 ft high.
Using this information, determine the average rate of change in water height during this period of time.
The value we are trying to find is an average rate of decrease. In other words, we are looking for how much, on average, the water level decreased in a minute. To find the average, take the total difference in water level and divide it by the total difference in time.
The total change in water height is given by the ending height minus the starting height:
The total change in time is the amount of minutes that pass between 8:56 AM and 9:10 PM:
Therefore, the average rate of decrease is 
Example Question #2 : Mathematical Process Categories
Three friends go in on a pizza, which costs $10.49 before 6% tax. Mike agrees to pay $4, and Mickey and Morris agree to split the remainder of the cost evenly. How much will Morris pay?
6% of 10.49 is equal to
which, to the nearest cent, rounds to 
Add this tax to the price of the pizza; the amount paid is
Mike pays $4, so Morris will pay half the remainder, or
Example Question #1 : Synthesize Data And Solve Problems
Which of the following would be a reasonable answer to the question
"What is the length of a candy bar?"
Ten centimeters
Ten hectares
Ten milliliters
Ten kilograms
Ten kilowatts
Ten centimeters
The question is asking for unit of length. Of the units given in the five choices, only centimeters is a unit of length, and ten centimeters—the metric equivalent of about four inches—is a reasonable length for a candy bar.
Of the other units:
The kilogram is a unit of mass which corresponds to a little over two ounces.
The hectare is a unit of area, usually land, and is equivalent to about two and a half acres.
The milliliter is a very small unit of volume.
The kilowatt is a unit of power.
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