MTH/215T: Quantitative Reasoning I 10 questions

1. Convert 4 years to hours (neglecting leap years).

2. A solution consisting of 176 mg of dopamine in 16 mL of solution is administered at a rate of 2 mL/hr. Complete parts (a) and (b) below.

A. What is the flow rate in mb of dopamine per hour?

__mg/hr

B. If a patient is prescribed to receive 88mg of dopamine, how long should the infusion last?

__hours

3. Which of the following best summarizes the strategic hint “There may be more than one answer” and provides an example of the meaning?

If a problem has more than one answer, it is not valid. Every problem in mathematics will have one unique answer. For example, x equals 2x=2

is the only solution to

x plus 1 equals 3x+1=3.

Some problems in mathematics have more than one answer. Without further information, there is no way to determine whether both solutions are valid for a particular problem. For example, both x equals 2x=2

and

x equals negative 2x=2

are solutions to

x squared equals 4x2=4.

Every problem in mathematics has more than one answer. For example, both x equals 2x=2

and

x equals negative 2x=2

are solutions to

x squaredx2equals=4.

There may be several ways to get an answer. For example, you can find a solution for one third x equals 413x=4

by multiplying each side by 3 or by dividing each side by

one third13.

Which of the following best summarizes the strategic hint “There may be more than one strategy” and provides an example of the meaning?

There may be several strategies to solving a problem. However, not all of the strategies are equally efficient. For example, there is more than one strategy to solve x squared plus 3 x plus 2 equals 0x2+3x+2=0,

however, using the quadratic formula involves more time and work.

There may be several strategies to solving a problem and all of the strategies are equally efficient. For example, there is more than one strategy to solve x squared plus 3 x plus 2 equals 0x2+3x+2=0,

all taking the same amount of time and work.

There may be several strategies to solving a problem, however only one of them will find the correct answer. For example, there is more than one strategy to solve x squared plus 3 x plus 2 equals 0x2+3x+2=0,

however, only one of them will provide the correct answer.

If there is more than one strategy that can be used to find an answer, the problem is not valid. For example, since there is more than one way to solve five fourths x plus 7 equals one eighth54x+7=18,

this problem is not valid.

Which of the following best summarizes the strategic hint “Use appropriate tools” and provides an example of the meaning?

For any given task, there will be a choice of tools to use in any problem. Choose only the most basic tools so the problem does not get too difficult. For example, one fourth x equals 614x=6

can be solved with multiplication or division. Use only multiplication because it is easier.

Choosing only the tools most suited to the job will make tasks much easier. For example, if a problem can be solved one way with calculus and another way with multiplication, using multiplication will make the solving process easier.

For any problem, the appropriate tools needed will always be stated in the problem statement. For example, if a problem can be solved one way with calculus and another with multiplication, the problem statement will provide that information.

When given a choice of tools for a problem, use as many tools as possible. This will make the problem-solving process much simpler. For example, one fourth x equals 614x=6

can be solved with multiplication or division. Thus, both methods should be used.

Which of the following best summarizes the strategic hint “Consider simpler, similar problems” and provides an example of the meaning?

The exact strategy used to solve simpler, similar problems is always used to solve the more difficult problems. For example, if a problem involves dividing polynomials and a simplier problem involves dividing integers, model that exact strategy to find a correct answer.

The exact strategy used to solve simpler, similar problems is almost never used to solve the more difficult problems. For example, if a problem involves subtracting decimals to 3 places and simplier problem involves subtracting decimals to 1 place, the exact strategy is not used to find a correct answer.

Sometimes, it is easier to consider simpler, similar problems. If there are no simpler problems, the question has no solution. For example, if a problem involves adding monomials, there is no simpler, similar method. So, there is no solution to that particular question.

Sometimes, the insight gained from solving the easier problem may help to understand the original problem. For example, instead of picturing molecules mixing together, try to picture marbles mixing together.

Which of the following best summarizes the strategic hint “Consider equivalent problems with simpler solutions” and provides an example of the meaning?

A useful approach to a difficult problem is to look for an equivalent problem, which does not have the same numerical answer but may be easier to solve. For example, suppose you cannot remember the formula for surface area of a cube. Instead, compare the dimensions to another cube with a known surface area.

A useful approach to a difficult problem is to look for an equivalent problem, which has the same numerical answer but may be easier to solve. For example, suppose you cannot remember the formula for surface area of a cube. Instead, find the surface area of each square and add them together.

Consider equivalent problems with simpler solutions in any case except for when looking for numerical answers. For example, instead of finding an equivalent problem to find surface area of a cube, look for any simpler way to solve the problem.

A useful approach to a difficult problem is to look for a similar problem, although it may have a different answer. For example, suppose you cannot remember the formula for surface area of a cube. Instead, use dimensions of another cube with a known surface area and solve.

Which of the following best summarizes the strategic hint “Approximations can be useful” and provides an example of the meaning?

An approximation should always be within one tenth of the exact solution. If this is not true, something has gone wrong. For example, if an exact solution is 7.232 and the approximation is 7, something is wrong in the solution process.

Approximations can always be used instead of an “exact solution”, unless otherwise noted. For example, if an exact solution is 3.1, an approximation of 3 can always be used.

Most real-world problems approximate numbers to begin with, so an approximation is often good enough for a final answer. Approximations also provide a useful check. For example, if a real-world problem involves long lengths with several decimals, approximating the final answer is often good enough for a final answer.

Approximations are only used to check solutions and are never good enough for a final answer. For example, if a real-world problem involves long lengths with several decimals, approximating the final answer is never appropriate.

Which of the following best summarizes the strategic hint “Try alternative patterns of thought” and provides an example of the meaning?

Avoid patterns of thought that tend to suggest the same ideas and methods. Instead, create new ways to solve each problem, avoiding the fastest way to solve a problem. For example, when solving a problem that requires more thought, always create your own ways to solve the problem.

Avoid patterns of thought that tend to suggest the same ideas and methods. Instead, approach problems with an openness that allows new ideas and solving methods. For example, when solving a problem that requires more thought, a moment of insight may be useful and make the problem easier to solve.

Have a list of basic solving methods to solve problems. Keeping a narrow list of options is more efficient. For example, when solving a problem that requires more thought, use basic solving methods, making the question easier to solve.

Avoid using any common patterns to solve problems. Common patterns create common mistakes and may yield an incorrect answer. For example, when solving a problem that requires more thought, avoid the most common way to solve the problem to avoid an incorrect answer.

Which of the following best summarizes the strategic hint “Do not spin your wheels” and provides an example of the meaning?

Do not use different strategies to solve problems. The known strategy is always the most efficient. For example, if you are struggling with a problem involving long division with polynomials, only use strategies you know to solve the problem.

Often the best strategy in problem solving is to put a problem aside for a few hours or days. For example, if you are struggling with a problem involving long division with polynomials, set it aside and come back to it in a few hours.

Often the best strategy in problem solving is to put a problem aside and immediately ask for help. For example, if you are struggling with a problem involving long division with polynomials, set it aside and go find help.

Do not try problems that you have not seen before. For example, if you have never seen long division with polynomials, do not attempt it.


4. Express the given percentage as a reduced fraction and a decimal.

what is the reduced fraction form of 260%?

what is the decimal form of 260%?

5. Express the first number as a percentage of the second number.

26 pounds of recyclable trash in a barrel of 51 pounds of trash.

The 26 pounds of recyyclable trach is __% of the barrel of 51 pounds of trash.

6. The sales tax rate in a city is 8.3%. Find the tax charged on a purchase of $220, and a total cost.

how much tax is charged on a purchase of $220?

What is the total price?

7. rewrite the following statement using a number in scientific notation.

The diameter of a certain bacterium is about 0.00000003 meters.

The diameter of a certain bacterium is about __ meters.

8. What is the order of magnitude estimate for the number of steps you take in an average day?

Choose the correct answer below.

The order of magnitude estimate is 3000 to 4000 steps; assuming an average person walks 2 miles per day.

The order of magnitude estimate is 375 to 575 steps; assuming an average person walks 16 miles per day.

The order of magnitude estimate is 100 to 200 steps; assuming an average person walks 8 miles per day.

The order of magnitude estimate is 375 to 500 steps; assuming an average person walks one fourth14

of a mile per day.

9. An issue of a magazine contained the following statement.

Dropping less than two inches per mile after emerging from the mountains, a river drains into the ocean. One day’s discharge at its mouth, 5.4 trillion gallons, could supply all of country A’s households for three months.

Based on this statement, determine how much water an average household uses each month. Assume that there are 200 million households in country A.

Country A uses approximately __ gallons per household per month.

10. Use the four basic rules of algebra to solve the following equation.

8x – 24 = 54 6x

x=

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