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MTEL General Curriculum Mathematics Practice

Question 1

If  x  is an integer, which of the following must also be an integer?

A
\( \large \dfrac{x}{2}\)
Hint:
If x is odd, then \( \dfrac{x}{2} \) is not an integer, e.g. 3/2 = 1.5.
B
\( \large \dfrac{2}{x}\)
Hint:
Only an integer if x = -2, -1, 1, or 2.
C
\( \large-x\)
Hint:
-1 times any integer is still an integer.
D
\(\large\sqrt{x}\)
Hint:
Usually not an integer, e.g. \( \sqrt{2} \approx 1.414 \).
Question 1 Explanation: 
Topic: Integers (Objective 0016)
Question 2

Use the samples of a student's work below to answer the question that follows:

This student divides fractions by first finding a common denominator, then dividing the numerators.

\( \large \dfrac{2}{3} \div \dfrac{3}{4} \longrightarrow \dfrac{8}{12} \div \dfrac{9}{12} \longrightarrow 8 \div 9 = \dfrac {8}{9}\) \( \large \dfrac{2}{5} \div \dfrac{7}{20} \longrightarrow \dfrac{8}{20} \div \dfrac{7}{20} \longrightarrow 8 \div 7 = \dfrac {8}{7}\) \( \large \dfrac{7}{6} \div \dfrac{3}{4} \longrightarrow \dfrac{14}{12} \div \dfrac{9}{12} \longrightarrow 14 \div 9 = \dfrac {14}{9}\)

Which of the following best describes the mathematical validity of the algorithm the student is using?

A

It is not valid. Common denominators are for adding and subtracting fractions, not for dividing them.

Hint:
Don't be so rigid! Usually there's more than one way to do something in math.
B

It got the right answer in these three cases, but it isn‘t valid for all rational numbers.

Hint:
Did you try some other examples? What makes you say it's not valid?
C

It is valid if the rational numbers in the division problem are in lowest terms and the divisor is not zero.

Hint:
Lowest terms doesn't affect this problem at all.
D

It is valid for all rational numbers, as long as the divisor is not zero.

Hint:
When we have common denominators, the problem is in the form a/b divided by c/b, and the answer is a/c, as the student's algorithm predicts.
Question 2 Explanation: 
Topic: Analyze Non-Standard Computational Algorithms (Objective 0019).
Question 3

Exactly one of the numbers below is a prime number.  Which one is it?

A
\( \large511 \)
Hint:
Divisible by 7.
B
\( \large517\)
Hint:
Divisible by 11.
C
\( \large519\)
Hint:
Divisible by 3.
D
\( \large521\)
Question 3 Explanation: 
Topics: Identify prime and composite numbers and demonstrate knowledge of divisibility rules (Objective 0018).
Question 4

If two fair coins are flipped, what is the probability that one will come up heads and the other tails?

A
\( \large \dfrac{1}{4}\)
Hint:
Think of the coins as a penny and a dime, and list all possibilities.
B
\( \large \dfrac{1}{3} \)
Hint:
This is a very common misconception. There are three possible outcomes -- both heads, both tails, and one of each -- but they are not equally likely. Think of the coins as a penny and a dime, and list all possibilities.
C
\( \large \dfrac{1}{2}\)
Hint:
The possibilities are HH, HT, TH, TT, and all are equally likely. Two of the four have one of each coin, so the probability is 2/4=1/2.
D
\( \large \dfrac{3}{4}\)
Hint:
Think of the coins as a penny and a dime, and list all possibilities.
Question 4 Explanation: 
Topic: Calculate the probabilities of simple and compound events and of independent and dependent events (Objective 0026).
Question 5

Below are front, side, and top views of a three-dimensional solid.

Which of the following could be the solid shown above?

A

A sphere

Hint:
All views would be circles.
B

A cylinder

C

A cone

Hint:
Two views would be triangles, not rectangles.
D

A pyramid

Hint:
How would one view be a circle?
Question 5 Explanation: 
Topic: Match three-dimensional figures and their two-dimensional representations (e.g., nets, projections, perspective drawings) (Objective 0024).
There are 5 questions to complete.

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