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MTEL General Curriculum Mathematics Practice

Question 1

Which of the graphs below represent functions?

I. II. III. IV.   
A

I and IV only.

Hint:
There are vertical lines that go through 2 points in IV .
B

I and III only.

Hint:
Even though III is not continuous, it's still a function (assuming that vertical lines between the "steps" do not go through 2 points).
C

II and III only.

Hint:
Learn about the vertical line test.
D

I, II, and IV only.

Hint:
There are vertical lines that go through 2 points in II.
Question 1 Explanation: 
Understand the definition of function and various representations of functions (e.g., input/output machines, tables, graphs, mapping diagrams, formulas). (Objective 0021).
Question 2

Which of the following is the equation of a linear function?

A
\( \large y={{x}^{2}}+2x+7\)
Hint:
This is a quadratic function.
B
\( \large y={{2}^{x}}\)
Hint:
This is an exponential function.
C
\( \large y=\dfrac{15}{x}\)
Hint:
This is an inverse function.
D
\( \large y=x+(x+4)\)
Hint:
This is a linear function, y=2x+4, it's graph is a straight line with slope 2 and y-intercept 4.
Question 2 Explanation: 
Topic: Distinguish between linear and nonlinear functions (Objective 0022).
Question 3

A family has four children.  What is the probability that two children are girls and two are boys?  Assume the the probability of having a boy (or a girl) is 50%.

A
\( \large \dfrac{1}{2}\)
Hint:
How many different configurations are there from oldest to youngest, e.g. BGGG? How many of them have 2 boys and 2 girls?
B
\( \large \dfrac{1}{4}\)
Hint:
How many different configurations are there from oldest to youngest, e.g. BGGG? How many of them have 2 boys and 2 girls?
C
\( \large \dfrac{1}{5}\)
Hint:
Some configurations are more probable than others -- i.e. it's more likely to have two boys and two girls than all boys. Be sure you are weighting properly.
D
\( \large \dfrac{3}{8}\)
Hint:
There are two possibilities for each child, so there are \(2 \times 2 \times 2 \times 2 =16\) different configurations, e.g. from oldest to youngest BBBG, BGGB, GBBB, etc. Of these configurations, there are 6 with two boys and two girls (this is the combination \(_{4}C_{2}\) or "4 choose 2"): BBGG, BGBG, BGGB, GGBB, GBGB, and GBBG. Thus the probability is 6/16=3/8.
Question 3 Explanation: 
Topic: Apply knowledge of combinations and permutations to the computation of probabilities (Objective 0026).
Question 4

At a school fundraising event, people can buy a ticket to spin a spinner like the one below.  The region that the spinner lands in tells which, if any, prize the person wins.

If 240 people buy tickets to spin the spinner, what is the best estimate of the number of keychains that will be given away?

A

40

Hint:
"Keychain" appears on the spinner twice.
B

80

Hint:
The probability of getting a keychain is 1/3, and so about 1/3 of the time the spinner will win.
C

100

Hint:
What is the probability of winning a keychain?
D

120

Hint:
That would be the answer for getting any prize, not a keychain specifically.
Question 4 Explanation: 
Topic: I would call this topic expected value, which is not listed on the objectives. This question is very similar to one on the sample test. It's not a good question in that it's oversimplified (a more difficult and interesting question would be something like, "The school bought 100 keychains for prizes, what is the probability that they will run out before 240 people play?"). In any case, I believe the objective this is meant for is, "Recognize the difference between experimentally and theoretically determined probabilities in real-world situations. (Objective 0026)." This is not something easily assessed with multiple choice .
Question 5

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 5 Explanation: 
Topic: Calculate the probabilities of simple and compound events and of independent and dependent events (Objective 0026).
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