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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


Your answers are highlighted below.
Question 1

Here is a mental math strategy for computing 26 x 16:

Step 1: 100 x 16 = 1600

Step 2: 25 x 16 = 1600 ÷· 4 = 400

Step 3: 26 x 16 = 400 + 16 = 416

Which property best justifies Step 3 in this strategy?

A

Commutative Property.

Hint:
For addition, the commutative property is \(a+b=b+a\) and for multiplication it's \( a \times b = b \times a\).
B

Associative Property.

Hint:
For addition, the associative property is \((a+b)+c=a+(b+c)\) and for multiplication it's \((a \times b) \times c=a \times (b \times c)\)
C

Identity Property.

Hint:
0 is the additive identity, because \( a+0=a\) and 1 is the multiplicative identity because \(a \times 1=a\). The phrase "identity property" is not standard.
D

Distributive Property.

Hint:
\( (25+1) \times 16 = 25 \times 16 + 1 \times 16 \). This is an example of the distributive property of multiplication over addition.
Question 1 Explanation: 
Topic: Analyze and justify mental math techniques, by applying arithmetic properties such as commutative, distributive, and associative (Objective 0019). Note that it's hard to write a question like this as a multiple choice question -- worthwhile to understand why the other steps work too.
Question 2

The function d(x) gives the result when 12 is divided by x.  Which of the following is a graph of d(x)?

 
A
Hint:
d(x) is 12 divided by x, not x divided by 12.
B
Hint:
When x=2, what should d(x) be?
C
Hint:
When x=2, what should d(x) be?
D
Question 2 Explanation: 
Topic: Identify and analyze direct and inverse relationships in tables, graphs, algebraic expressions and real-world situations (Objective 0021)
Question 3

Which of the following points is closest to \( \dfrac{34}{135} \times \dfrac{53}{86}\)?

A

A

Hint:
\(\frac{34}{135} \approx \frac{1}{4}\) and \( \frac{53}{86} \approx \frac {2}{3}\). \(\frac {1}{4}\) of \(\frac {2}{3}\) is small and closest to A.
B

B

Hint:
Estimate with simpler fractions.
C

C

Hint:
Estimate with simpler fractions.
D

D

Hint:
Estimate with simpler fractions.
Question 3 Explanation: 
Topic: Understand meaning and models of operations on fractions (Objective 0019).
Question 4

What fraction of the area of the picture below is shaded?

A
\( \large \dfrac{17}{24}\)
Hint:
You might try adding segments so each quadrant is divided into 6 pieces with equal area -- there will be 24 regions, not all the same shape, but all the same area, with 17 of them shaded (for the top left quarter, you could also first change the diagonal line to a horizontal or vertical line that divides the square in two equal pieces and shade one) .
B
\( \large \dfrac{3}{4}\)
Hint:
Be sure you're taking into account the different sizes of the pieces.
C
\( \large \dfrac{2}{3}\)
Hint:
The bottom half of the picture is 2/3 shaded, and the top half is more than 2/3 shaded, so this answer is too small.
D
\( \large \dfrac{17}{6} \)
Hint:
This answer is bigger than 1, so doesn't make any sense. Be sure you are using the whole picture, not one quadrant, as the unit.
Question 4 Explanation: 
Topic: Models of Fractions (Objective 0017)
Question 5

A solution requires 4 ml of saline for every 7 ml of medicine. How much saline would be required for 50 ml of medicine?

A
\( \large 28 \dfrac{4}{7}\) ml
Hint:
49 ml of medicine requires 28 ml of saline. The extra ml of saline requires 4 ml saline/ 7 ml medicine = 4/7 ml saline per 1 ml medicine.
B
\( \large 28 \dfrac{1}{4}\) ml
Hint:
49 ml of medicine requires 28 ml of saline. How much saline does the extra ml require?
C
\( \large 28 \dfrac{1}{7}\) ml
Hint:
49 ml of medicine requires 28 ml of saline. How much saline does the extra ml require?
D
\( \large 87.5\) ml
Hint:
49 ml of medicine requires 28 ml of saline. How much saline does the extra ml require?
Question 5 Explanation: 
Topic: Apply proportional thinking to estimate quantities in real world situations (Objective 0019).
Question 6

Which of the following is not possible?

A

An equiangular triangle that is not equilateral.

Hint:
The AAA property of triangles states that all triangles with corresponding angles congruent are similar. Thus all triangles with three equal angles are similar, and are equilateral.
B

An equiangular quadrilateral that is not equilateral.

Hint:
A rectangle is equiangular (all angles the same measure), but if it's not a square, it's not equilateral (all sides the same length).
C

An equilateral quadrilateral that is not equiangular.

Hint:
This rhombus has equal sides, but it doesn't have equal angles:
D

An equiangular hexagon that is not equilateral.

Hint:
This hexagon has equal angles, but it doesn't have equal sides:
Question 6 Explanation: 
Topic: Classify and analyze polygons using attributes of sides and angles (Objective 0024).
Question 7

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 7 Explanation: 
Topic: Match three-dimensional figures and their two-dimensional representations (e.g., nets, projections, perspective drawings) (Objective 0024).
Question 8

Which of the following is closest to the height of a college student in centimeters?

A

1.6 cm

Hint:
This is more the height of a Lego toy college student -- less than an inch!
B

16 cm

Hint:
Less than knee high on most college students.
C

160 cm

Hint:
Remember, a meter stick (a little bigger than a yard stick) is 100 cm. Also good to know is that 4 inches is approximately 10 cm.
D

1600 cm

Hint:
This college student might be taller than some campus buildings!
Question 8 Explanation: 
Topic: Estimate and calculate measurements using customary, metric, and nonstandard units of measurement (Objective 0023).
Question 9

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 9 Explanation: 
Topic: Find a linear equation that represents a graph (Objective 0022).
Question 10

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 10 Explanation: 
Topic: Translate among different representations (e.g., tables, graphs, algebraic expressions, verbal descriptions) of functional relationships (Objective 0021).
Question 11

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 11 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 12

How many factors does 80 have?

A
\( \large8\)
Hint:
Don't forget 1 and 80.
B
\( \large9\)
Hint:
Only perfect squares have an odd number of factors -- otherwise factors come in pairs.
C
\( \large10\)
Hint:
1,2,4,5,8,10,16,20,40,80
D
\( \large12\)
Hint:
Did you count a number twice? Include a number that isn't a factor?
Question 12 Explanation: 
Topic: Understand and apply principles of number theory (Objective 0018).
Question 13

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 13 Explanation: 
Topics: Estimation, simplifying fractions (Objective 0016, overlaps with other objectives).
Question 14

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 14 Explanation: 
Topics: Identify prime and composite numbers and demonstrate knowledge of divisibility rules (Objective 0018).
Question 15

Kendra is trying to decide which fraction is greater, \(  \dfrac{4}{7}\) or \(  \dfrac{5}{8}\). Which of the following answers shows the best reasoning?

A

\( \dfrac{4}{7}\) is \( \dfrac{3}{7}\)away from 1, and \( \dfrac{5}{8}\) is \( \dfrac{3}{8}\)away from 1. Since eighth‘s are smaller than seventh‘s, \( \dfrac{5}{8}\) is closer to 1, and is the greater of the two fractions.

B

\( 7-4=3\) and \( 8-5=3\), so the fractions are equal.

Hint:
Not how to compare fractions. By this logic, 1/2 and 3/4 are equal, but 1/2 and 2/4 are not.
C

\( 4\times 8=32\) and \( 7\times 5=35\). Since \( 32<35\) , \( \dfrac{5}{8}<\dfrac{4}{7}\)

Hint:
Starts out as something that works, but the conclusion is wrong. 4/7 = 32/56 and 5/8 = 35/56. The cross multiplication gives the numerators, and 35/56 is bigger.
D

\( 4<5\) and \( 7<8\), so \( \dfrac{4}{7}<\dfrac{5}{8}\)

Hint:
Conclusion is correct, logic is wrong. With this reasoning, 1/2 would be less than 2/100,000.
Question 15 Explanation: 
Topics: Comparing fractions, and understanding the meaning of fractions (Objective 0017).
Question 16

The first histogram shows the average life expectancies for women in different countries in Africa in 1998; the second histogram gives similar data for Europe:

  

How much bigger is the range of the data for Africa than the range of the data for Europe?

A

0 years

Hint:
Range is the maximum life expectancy minus the minimum life expectancy.
B

12 years

Hint:
Are you subtracting frequencies? Range is about values of the data, not frequency.
C

18 years

Hint:
It's a little hard to read the graph, but it doesn't matter if you're consistent. It looks like the range for Africa is 80-38= 42 years and for Europe is 88-64 = 24; 42-24=18.
D

42 years

Hint:
Read the question more carefully.
Question 16 Explanation: 
Topic: Compare different data sets (Objective 0025).
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

Use the graph below to answer the question that follows.

 

Which of the following is a correct equation for the graph of the line depicted above?

 
A
\( \large y=-\dfrac{1}{2}x+2\)
Hint:
The slope is -1/2 and the y-intercept is 2. You can also try just plugging in points. For example, this is the only choice that gives y=1 when x=2.
B
\( \large 4x=2y\)
Hint:
This line goes through (0,0); the graph above does not.
C
\( \large y=x+2\)
Hint:
The line pictured has negative slope.
D
\( \large y=-x+2\)
Hint:
Try plugging x=4 into this equation and see if that point is on the graph above.
Question 18 Explanation: 
Topic: Find a linear equation that represents a graph (Objective 0022).
Question 19

Below is a portion of a number line:

 Point B is halfway between two tick marks.  What number is represented by Point B?

 
A
\( \large 0.645\)
Hint:
That point is marked on the line, to the right.
B
\( \large 0.6421\)
Hint:
That point is to the left of point B.
C
\( \large 0.6422\)
Hint:
That point is to the left of point B.
D
\( \large 0.6425\)
Question 19 Explanation: 
Topic: Using Number Lines (Objective 0017)
Question 20

A cylindrical soup can has diameter 7 cm and height 11 cm. The can holds g grams of soup.   How many grams of the same soup could a cylindrical can with diameter 14 cm and height 33 cm hold?

A
\( \large 6g\)
Hint:
You must scale in all three dimensions.
B
\( \large 12g\)
Hint:
Height is multiplied by 3, and diameter and radius are multiplied by 2. Since the radius is squared, final result is multiplied by \(2^2\times 3=12\).
C
\( \large 18g\)
Hint:
Don't square the height scale factor.
D
\( \large 36g\)
Hint:
Don't square the height scale factor.
Question 20 Explanation: 
Topic: Determine how the characteristics (e.g., area, volume) of geometric figures and shapes are affected by changes in their dimensions (Objective 0023).
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