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MTEL General Curriculum Mathematics Practice

Question 1

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 1 Explanation: 
Topic: Interpret the meaning of the slope and the intercepts of a linear equation that models a real-world situation (Objective 0022).
Question 2

The chairs in a large room can be arranged in rows of 18, 25, or 60 with no chairs left over. If C is the smallest possible number of chairs in the room, which of the following inequalities does C satisfy?

A
\( \large C\le 300\)
Hint:
Find the LCM.
B
\( \large 300 < C \le 500 \)
Hint:
Find the LCM.
C
\( \large 500 < C \le 700 \)
Hint:
Find the LCM.
D
\( \large C>700\)
Hint:
The LCM is 900, which is the smallest number of chairs.
Question 2 Explanation: 
Topic: Apply LCM in "real-world" situations (according to standardized tests....) (Objective 0018).
Question 3

Which property is not shared by all rhombi?

A

4 congruent sides

Hint:
The most common definition of a rhombus is a quadrilateral with 4 congruent sides.
B

A center of rotational symmetry

Hint:
The diagonal of a rhombus separates it into two congruent isosceles triangles. The center of this line is a center of 180 degree rotational symmetry that switches the triangles.
C

4 congruent angles

Hint:
Unless the rhombus is a square, it does not have 4 congruent angles.
D

2 sets of parallel sides

Hint:
All rhombi are parallelograms.
Question 3 Explanation: 
Topic: Classify and analyze polygons using attributes of sides and angles, and symmetry (Objective 0024).
Question 4

A teacher has a list of all the countries in the world and their populations in March 2012.  She is going to have her students use technology to compute the mean and median of the numbers on the list.   Which of the following statements is true?

A

The teacher can be sure that the mean and median will be the same without doing any computation.

Hint:
Does this make sense? How likely is it that the mean and median of any large data set will be the same?
B

The teacher can be sure that the mean is bigger than the median without doing any computation.

Hint:
This is a skewed distribution, and very large countries like China and India contribute huge numbers to the mean, but are counted the same as small countries like Luxembourg in the median (the same thing happens w/data on salaries, where a few very high income people tilt the mean -- that's why such data is usually reported as medians).
C

The teacher can be sure that the median is bigger than the mean without doing any computation.

Hint:
Think about a set of numbers like 1, 2, 3, 4, 10,000 -- how do the mean/median compare? How might that relate to countries of the world?
D

There is no way for the teacher to know the relative size of the mean and median without computing them.

Hint:
Knowing the shape of the distribution of populations does give us enough info to know the relative size of the mean and median, even without computing them.
Question 4 Explanation: 
Topic: Use measures of central tendency (e.g., mean, median, mode) and spread to describe and interpret real-world data (Objective 0025).
Question 5

Some children explored the diagonals in 2 x 2 squares on pages of a calendar (where all four squares have numbers in them).  They conjectured that the sum of the diagonals is always equal; in the example below, 8+16=9+15.

 

Which of the equations below could best be used to explain why the children€™s conjecture is correct?

A
\( \large 8x+16x=9x+15x\)
Hint:
What would x represent in this case? Make sure you can describe in words what x represents.
B
\( \large x+(x+2)=(x+1)+(x+1)\)
Hint:
What would x represent in this case? Make sure you can describe in words what x represents.
C
\( \large x+(x+8)=(x+1)+(x+7)\)
Hint:
x is the number in the top left square, x+8 is one below and to the right, x+1 is to the right of x, and x+7 is below x.
D
\( \large x+8+16=x+9+15\)
Hint:
What would x represent in this case? Make sure you can describe in words what x represents.
Question 5 Explanation: 
Topic: Recognize and apply the concepts of variable, equality, and equation to express relationships algebraically (Objective 0020).
There are 5 questions to complete.

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