Hints will display for most wrong answers; explanations for most right answers.   You can attempt a question multiple times; it will only be scored correct if you get it right the first time.

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


Your answers are highlighted below.
Question 1

Here are some statements:

I) 5 is an integer    II)\( -5 \)  is an integer    III) \(0\) is an integer

Which of the statements are true?

A

I only

B

I and II only

C

I and III only

D

I, II, and III

Hint:
The integers are ...-3, -2, -1, 0, 1, 2, 3, ....
Question 1 Explanation: 
Topic: Characteristics of Integers (Objective 0016)
Question 2

A map has a scale of 3 inches = 100 miles.  Cities A and B are 753 miles apart.  Let d be the distance between the two cities on the map.  Which of the following is not correct?

A
\( \large \dfrac{3}{100}=\dfrac{d}{753}\)
Hint:
Units on both side are inches/mile, and both numerators and denominators correspond -- this one is correct.
B
\( \large \dfrac{3}{100}=\dfrac{753}{d}\)
Hint:
Unit on the left is inches per mile, and on the right is miles per inch. The proportion is set up incorrectly (which is what we wanted). Another strategy is to notice that one of A or B has to be the answer because they cannot both be correct proportions. Then check that cross multiplying on A gives part D, so B is the one that is different from the other 3.
C
\( \large \dfrac{3}{d}=\dfrac{100}{753}\)
Hint:
Unitless on each side, as inches cancel on the left and miles on the right. Numerators correspond to the map, and denominators to the real life distances -- this one is correct.
D
\( \large 100d=3\cdot 753\)
Hint:
This is equivalent to part A.
Question 2 Explanation: 
Topic: Analyze the relationships among proportions, constant rates, and linear functions (Objective 0022).
Question 3

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 3 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 4

Which of the numbers below is not equivalent to 4%?

A
\( \large \dfrac{1}{25}\)
Hint:
1/25=4/100, so this is equal to 4% (be sure you read the question correctly).
B
\( \large \dfrac{4}{100}\)
Hint:
4/100=4% (be sure you read the question correctly).
C
\( \large 0.4\)
Hint:
0.4=40% so this is not equal to 4%
D
\( \large 0.04\)
Hint:
0.04=4/100, so this is equal to 4% (be sure you read the question correctly).
Question 4 Explanation: 
Converting between fractions, decimals, and percents (Objective 0017).
Question 5

The column below consists of two cubes and a cylinder.  The cylinder has diameter y, which is also the length of the sides of each cube.   The total height of the column is 5y.  Which of the formulas below gives the volume of the column?

 
A
\( \large 2{{y}^{3}}+\dfrac{3\pi {{y}^{3}}}{4}\)
Hint:
The cubes each have volume \(y^3\). The cylinder has radius \(\dfrac{y}{2}\) and height \(3y\). The volume of a cylinder is \(\pi r^2 h=\pi ({\dfrac{y}{2}})^2(3y)=\dfrac{3\pi {{y}^{3}}}{4}\). Note that the volume of a cylinder is analogous to that of a prism -- area of the base times height.
B
\( \large 2{{y}^{3}}+3\pi {{y}^{3}}\)
Hint:
y is the diameter of the circle, not the radius.
C
\( \large {{y}^{3}}+5\pi {{y}^{3}}\)
Hint:
Don't forget to count both cubes.
D
\( \large 2{{y}^{3}}+\dfrac{3\pi {{y}^{3}}}{8}\)
Hint:
Make sure you know how to find the volume of a cylinder.
Question 5 Explanation: 
Topic: Derive and use formulas for calculating the lengths, perimeters, areas, volumes, and surface areas of geometric shapes and figures (Objective 0023).
Question 6

On a map the distance from Boston to Detroit is 6 cm, and these two cities are 702 miles away from each other. Assuming the scale of the map is the same throughout, which answer below is closest to the distance between Boston and San Francisco on the map, given that they are 2,708 miles away from each other?

A

21 cm

Hint:
How many miles would correspond to 24 cm on the map? Try adjusting from there.
B

22 cm

Hint:
How many miles would correspond to 24 cm on the map? Try adjusting from there.
C

23 cm

Hint:
One way to solve this without a calculator is to note that 4 groups of 6 cm is 2808 miles, which is 100 miles too much. Then 100 miles would be about 1/7 th of 6 cm, or about 1 cm less than 24 cm.
D

24 cm

Hint:
4 groups of 6 cm is over 2800 miles on the map, which is too much.
Question 6 Explanation: 
Topic: Apply proportional thinking to estimate quantities in real world situations (Objective 0019).
Question 7

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 7 Explanation: 
Topic: Solve linear equations (Objective 0020).
Question 8

The "houses" below are made of toothpicks and gum drops.

Which of the following does not represent the number of gumdrops in a row of h houses?

A
\( \large 2+3h\)
Hint:
Think of this as start with 2 gumdrops on the left wall, and then add 3 gumdrops for each house.
B
\( \large 5+3(h-1)\)
Hint:
Think of this as start with one house, and then add 3 gumdrops for each of the other h-1 houses.
C
\( \large h+(h+1)+(h+1)\)
Hint:
Look at the gumdrops in 3 rows: h gumdrops for the "rooftops," h+1 for the tops of the vertical walls, and h+1 for the floors.
D
\( \large 5+3h\)
Hint:
This one is not a correct equation (which makes it the correct answer!). Compare to choice A. One of them has to be wrong, as they differ by 3.
Question 8 Explanation: 
Topic: Translate among different representations (e.g., tables, graphs, algebraic expressions, verbal descriptions) of functional relationships (Objective 0021).
Question 9

Use the graph below to answer the question that follows.

If the polygon shown above is reflected about the y axis and then rotated 90 degrees clockwise about the origin, which of the following graphs is the result?

A
Hint:
Try following the point (1,4) to see where it goes after each transformation.
B
C
Hint:
Make sure you're reflecting in the correct axis.
D
Hint:
Make sure you're rotating the correct direction.
Question 9 Explanation: 
Topic: Analyze and apply geometric transformations (e.g., translations, rotations, reflections, dilations); relate them to concepts of symmetry, similarity, and congruence; and use these concepts to solve problems (Objective 0024).
Question 10

Use the graph below to answer the question that follows:

The graph above represents the equation \( \large 3x+Ay=B\), where A and B are integers.  What are the values of A and B?

A
\( \large A = -2, B= 6\)
Hint:
Plug in (2,0) to get B=6, then plug in (0,-3) to get A=-2.
B
\( \large A = 2, B = 6\)
Hint:
Try plugging (0,-3) into this equation.
C
\( \large A = -1.5, B=-3\)
Hint:
The problem said that A and B were integers and -1.5 is not an integer. Don't try to use slope-intercept form.
D
\( \large A = 2, B = -3\)
Hint:
Try plugging (2,0) into this equation.
Question 10 Explanation: 
Topic: Find a linear equation that represents a graph (Objective 0022).
Question 11

Use the expression below to answer the question that follows:

                 \( \large \dfrac{\left( 7,154 \right)\times \left( 896 \right)}{216}\)

Which of the following is the best estimate of the expression above?

A

2,000

Hint:
The answer is bigger than 7,000.
B

20,000

Hint:
Estimate 896/216 first.
C

3,000

Hint:
The answer is bigger than 7,000.
D

30,000

Hint:
\( \dfrac{896}{216} \approx 4\) and \(7154 \times 4\) is over 28,000, so this answer is closest.
Question 11 Explanation: 
Topics: Estimation, simplifying fractions (Objective 0016, overlaps with other objectives).
Question 12

Which of the following is equal to eleven billion four hundred thousand?

A
\( \large 11,400,000\)
Hint:
That's eleven million four hundred thousand.
B
\(\large11,000,400,000\)
C
\( \large11,000,000,400,000\)
Hint:
That's eleven trillion four hundred thousand (although with British conventions; this answer is correct, but in the US, it isn't).
D
\( \large 11,400,000,000\)
Hint:
That's eleven billion four hundred million
Question 12 Explanation: 
Topic: Place Value (Objective 0016)
Question 13

The histogram below shows the number of pairs of footware owned by a group of college students.

Which of the following statements can be inferred from the graph above?

A

The median number of pairs of footware owned is between 50 and 60 pairs.

Hint:
The same number of data points are less than the median as are greater than the median -- but on this histogram, clearly more than half the students own less than 50 pairs of shoes, so the median is less than 50.
B

The mode of the number of pairs of footware owned is 20.

Hint:
The mode is the most common number of pairs of footwear owned. We can't tell it from this histogram because each bar represents 10 different numbers-- perhaps 8 students each own each number from 10 to 19, but 40 students own exactly 6 pairs of shoes.... or perhaps not....
C

The mean number of pairs of footware owned is less than the median number of pairs of footware owned.

Hint:
This is a right skewed distribution, and so the mean is bigger than the median -- the few large values on the right pull up the mean, but have little effect on the median.
D

The median number of pairs of footware owned is between 10 and 20.

Hint:
There are approximately 230 students represented in this survey, and the 41st through 120th lowest values are between 10 and 20 -- thus the middle value is in that range.
Question 13 Explanation: 
Topics: Analyze and interpret various graphic and data representations, and use measures of central tendency (e.g., mean, median, mode) and spread to describe and interpret real-world data (Objective 0025).
Question 14

Which of the following nets will not fold into a cube?

A
Hint:
If you have trouble visualizing, cut them out and fold (during the test, you can tear paper to approximate).
B
C
Hint:
If you have trouble visualizing, cut them out and fold (during the test, you can tear paper to approximate).
D
Hint:
If you have trouble visualizing, cut them out and fold (during the test, you can tear paper to approximate).
Question 14 Explanation: 
Topic: Match three-dimensional figures and their two-dimensional representations (e.g., nets, projections, perspective drawings) (Objective 0024).
Question 15

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 15 Explanation: 
Topic: Match three-dimensional figures and their two-dimensional representations (e.g., nets, projections, perspective drawings) (Objective 0024).
Question 16

Use the expression below to answer the question that follows.

                 \(\large \dfrac{\left( 155 \right)\times \left( 6,124 \right)}{977}\)

Which of the following is the best estimate of the expression above?

A

100

Hint:
6124/977 is approximately 6.
B

200

Hint:
6124/977 is approximately 6.
C

1,000

Hint:
6124/977 is approximately 6. 155 is approximately 150, and \( 6 \times 150 = 3 \times 300 = 900\), so this answer is closest.
D

2,000

Hint:
6124/977 is approximately 6.
Question 16 Explanation: 
Topics: Estimation, simplifying fractions (Objective 0016).
Question 17

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 17 Explanation: 
Topic: Use measures of central tendency (e.g., mean, median, mode) and spread to describe and interpret real-world data (Objective 0025).
Question 18

Which of the numbers below is the decimal equivalent of \( \dfrac{3}{8}?\)

A

0.38

Hint:
If you are just writing the numerator next to the denominator then your technique is way off, but by coincidence your answer is close; try with 2/3 and 0.23 is nowhere near correct.
B

0.125

Hint:
This is 1/8, not 3/8.
C

0.375

D

0.83

Hint:
3/8 is less than a half, and 0.83 is more than a half, so they can't be equal.
Question 18 Explanation: 
Topic: Converting between fractions and decimals (Objective 0017)
Question 19

The Venn Diagram below gives data on the number of seniors, athletes, and vegetarians in the student body at a college:

How many students at the college are seniors who are not vegetarians?

A
\( \large 137\)
Hint:
Doesn't include the senior athletes who are not vegetarians.
B
\( \large 167\)
C
\( \large 197\)
Hint:
That's all seniors, including vegetarians.
D
\( \large 279\)
Hint:
Includes all athletes who are not vegetarians, some of whom are not seniors.
Question 19 Explanation: 
Topic: Venn Diagrams (Objective 0025)
Question 20

The pattern below consists of a row of black squares surrounded by white squares.

 How many white squares would surround a row of 157 black squares?

A

314

Hint:
Try your procedure on a smaller number that you can count to see where you made a mistake.
B

317

Hint:
Are there ever an odd number of white squares?
C

320

Hint:
One way to see this is that there are 6 tiles on the left and right ends, and the rest of the white tiles are twice the number of black tiles (there are many other ways to look at it too).
D

322

Hint:
Try your procedure on a smaller number that you can count to see where you made a mistake.
Question 20 Explanation: 
Topic: Recognize and extend patterns using a variety of representations (e.g., verbal, numeric, pictorial, algebraic) (Objective 0021).
Once you are finished, click the button below. Any items you have not completed will be marked incorrect. Get Results
There are 20 questions to complete.
List
Return
Shaded items are complete.
12345
678910
1112131415
1617181920
End
Return

If you found a mistake or have comments on a particular question, please contact me (please copy and paste at least part of the question into the form, as the numbers change depending on how quizzes are displayed).   General comments can be left here.