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I used the official objectives and sample test to construct these questions, but cannot promise that they accurately reflect what’s on the real test.   Some of the sample questions were more convoluted than I could bear to write.   See terms of use.   See the MTEL Practice Test main page to view questions on a particular topic or to download paper practice tests.

MTEL General Curriculum Mathematics Practice

Question 1

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 1 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 2

A publisher prints a series of books with covers made of identical material and using the same thickness of paper for each page.  The covers of the book together are 0.4 cm thick, and 125 pieces of the paper used together are 1 cm thick.

The publisher uses a linear function to determine the total thickness, T(n) of a book made with n sheets of paper.   What are the slope and intercept of T(n)?

A

Intercept = 0.4 cm, Slope = 125 cm/page

Hint:
This would mean that each page of the book was 125 cm thick.
B

Intercept =0.4 cm, Slope = \(\dfrac{1}{125}\)cm/page

Hint:
The intercept is how thick the book would be with no pages in it. The slope is how much 1 extra page adds to the thickness of the book.
C

Intercept = 125 cm, Slope = 0.4 cm

Hint:
This would mean that with no pages in the book, it would be 125 cm thick.
D

Intercept = \(\dfrac{1}{125}\)cm, Slope = 0.4 pages/cm

Hint:
This would mean that each new page of the book made it 0.4 cm thicker.
Question 2 Explanation: 
Topic: Interpret the meaning of the slope and the intercepts of a linear equation that models a real-world situation (Objective 0022).
Question 3

Solve for x: \(\large 4-\dfrac{2}{3}x=2x\)

A
\( \large x=3\)
Hint:
Try plugging x=3 into the equation.
B
\( \large x=-3\)
Hint:
Left side is positive, right side is negative when you plug this in for x.
C
\( \large x=\dfrac{3}{2}\)
Hint:
One way to solve: \(4=\dfrac{2}{3}x+2x\) \(=\dfrac{8}{3}x\).\(x=\dfrac{3 \times 4}{8}=\dfrac{3}{2}\). Another way is to just plug x=3/2 into the equation and see that each side equals 3 -- on a multiple choice test, you almost never have to actually solve for x.
D
\( \large x=-\dfrac{3}{2}\)
Hint:
Left side is positive, right side is negative when you plug this in for x.
Question 3 Explanation: 
Topic: Solve linear equations (Objective 0020).
Question 4

The picture below shows identical circles drawn on a piece of paper.  The rectangle represents an index card that is blocking your view of \( \dfrac{3}{5}\) of the circles on the paper.  How many circles are covered by the rectangle?

A

4

Hint:
The card blocks more than half of the circles, so this number is too small.
B

5

Hint:
The card blocks more than half of the circles, so this number is too small.
C

8

Hint:
The card blocks more than half of the circles, so this number is too small.
D

12

Hint:
2/5 of the circles or 8 circles are showing. Thus 4 circles represent 1/5 of the circles, and \(4 \times 5=20\) circles represent 5/5 or all the circles. Thus 12 circles are hidden.
Question 4 Explanation: 
Topic: Models of Fractions (Objective 0017)
Question 5

Cell phone plan A charges $3 per month plus $0.10 per minute. Cell phone plan B charges $29.99 per month, with no fee for the first 400 minutes and then $0.20 for each additional minute.

Which equation can be used to solve for the number of minutes, m (with m>400) that a person would have to spend on the phone each month in order for the bills for plan A and plan B to be equal?

A
\( \large 3.10m=400+0.2m\)
Hint:
These are the numbers in the problem, but this equation doesn't make sense. If you don't know how to make an equation, try plugging in an easy number like m=500 minutes to see if each side equals what it should.
B
\( \large 3+0.1m=29.99+.20m\)
Hint:
Doesn't account for the 400 free minutes.
C
\( \large 3+0.1m=400+29.99+.20(m-400)\)
Hint:
Why would you add 400 minutes and $29.99? If you don't know how to make an equation, try plugging in an easy number like m=500 minutes to see if each side equals what it should.
D
\( \large 3+0.1m=29.99+.20(m-400)\)
Hint:
The left side is $3 plus $0.10 times the number of minutes. The right is $29.99 plus $0.20 times the number of minutes over 400.
Question 5 Explanation: 
Identify variables and derive algebraic expressions that represent real-world situations (Objective 0020).
There are 5 questions to complete.

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