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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


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Question 1

P is a prime number that divides 240.  Which of the following must be true?

A

P divides 30

Hint:
2, 3, and 5 are the prime factors of 240, and all divide 30.
B

P divides 48

Hint:
P=5 doesn't work.
C

P divides 75

Hint:
P=2 doesn't work.
D

P divides 80

Hint:
P=3 doesn't work.
Question 1 Explanation: 
Topic: Find the prime factorization of a number and recognize its uses (Objective 0018).
Question 2

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 2 Explanation: 
Topic: Venn Diagrams (Objective 0025)
Question 3

Which of the following is an irrational number?

A
\( \large \sqrt[3]{8}\)
Hint:
This answer is the cube root of 8. Since 2 x 2 x 2 =8, this is equal to 2, which is rational because 2 = 2/1.
B
\( \large \sqrt{8}\)
Hint:
It is not trivial to prove that this is irrational, but you can get this answer by eliminating the other choices.
C
\( \large \dfrac{1}{8}\)
Hint:
1/8 is the RATIO of two integers, so it is rational.
D
\( \large -8\)
Hint:
Negative integers are also rational, -8 = -8/1, a ratio of integers.
Question 3 Explanation: 
Topic: Identifying rational and irrational numbers (Objective 0016).
Question 4

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 4 Explanation: 
Topic: Apply proportional thinking to estimate quantities in real world situations (Objective 0019).
Question 5

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 5 Explanation: 
Topic: Characteristics of Integers (Objective 0016)
Question 6

Here is a student's work on several multiplication problems:

For which of the following problems is this student most likely to get the correct solution, even though he is using an incorrect algorithm?

A

58 x 22

Hint:
This problem involves regrouping, which the student does not do correctly.
B

16 x 24

Hint:
This problem involves regrouping, which the student does not do correctly.
C

31 x 23

Hint:
There is no regrouping with this problem.
D

141 x 32

Hint:
This problem involves regrouping, which the student does not do correctly.
Question 6 Explanation: 
Topic: Analyze computational algorithms (Objective 0019).
Question 7

What is the mathematical name of the three-dimensional polyhedron depicted below?

A

Tetrahedron

Hint:
All the faces of a tetrahedron are triangles.
B

Triangular Prism

Hint:
A prism has two congruent, parallel bases, connected by parallelograms (since this is a right prism, the parallelograms are rectangles).
C

Triangular Pyramid

Hint:
A pyramid has one base, not two.
D

Trigon

Hint:
A trigon is a triangle (this is not a common term).
Question 7 Explanation: 
Topic: Classify and analyze three-dimensional figures using attributes of faces, edges, and vertices (Objective 0024).
Question 8

How many lines of reflective symmetry and how many centers of rotational symmetry does the parallelogram depicted below have?

 
A

4 lines of reflective symmetry, 1 center of rotational symmetry.

Hint:
Try cutting out a shape like this one from paper, and fold where you think the lines of reflective symmetry are (or put a mirror there). Do things line up as you thought they would?
B

2 lines of reflective symmetry, 1 center of rotational symmetry.

Hint:
Try cutting out a shape like this one from paper, and fold where you think the lines of reflective symmetry are (or put a mirror there). Do things line up as you thought they would?
C

0 lines of reflective symmetry, 1 center of rotational symmetry.

Hint:
The intersection of the diagonals is a center of rotational symmetry. There are no lines of reflective symmetry, although many people get confused about this fact (best to play with hands on examples to get a feel). Just fyi, the letter S also has rotational, but not reflective symmetry, and it's one that kids often write backwards.
D

2 lines of reflective symmetry, 0 centers of rotational symmetry.

Hint:
Try cutting out a shape like this one from paper. Trace onto another sheet of paper. See if there's a way to rotate the cut out shape (less than a complete turn) so that it fits within the outlines again.
Question 8 Explanation: 
Topic: Analyze geometric transformations (e.g., translations, rotations, reflections, dilations); relate them to concepts of symmetry (Objective 0024).
Question 9

The expression \( \large {{7}^{-4}}\cdot {{8}^{-6}}\) is equal to which of the following?

A
\( \large \dfrac{8}{{{\left( 56 \right)}^{4}}}\)
Hint:
The bases are whole numbers, and the exponents are negative. How can the numerator be 8?
B
\( \large \dfrac{64}{{{\left( 56 \right)}^{4}}}\)
Hint:
The bases are whole numbers, and the exponents are negative. How can the numerator be 64?
C
\( \large \dfrac{1}{8\cdot {{\left( 56 \right)}^{4}}}\)
Hint:
\(8^{-6}=8^{-4} \times 8^{-2}\)
D
\( \large \dfrac{1}{64\cdot {{\left( 56 \right)}^{4}}}\)
Question 9 Explanation: 
Topics: Laws of exponents (Objective 0019).
Question 10

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 10 Explanation: 
Topic: Determine how the characteristics (e.g., area, volume) of geometric figures and shapes are affected by changes in their dimensions (Objective 0023).
Question 11

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 11 Explanation: 
Topics: Identify prime and composite numbers and demonstrate knowledge of divisibility rules (Objective 0018).
Question 12
I. \(\large \dfrac{1}{2}+\dfrac{1}{3}\) II. \( \large   .400000\)  III. \(\large\dfrac{1}{5}+\dfrac{1}{5}\)
     
IV. \( \large 40\% \) V. \( \large 0.25 \) VI. \(\large\dfrac{14}{35}\)

 

Which of the lists below includes all of the above expressions that are equivalent to \( \dfrac{2}{5}\)?

A

I, III, V, VI

Hint:
I and V are not at all how fractions and decimals work.
B

III, VI

Hint:
These are right, but there are more.
C

II, III, VI

Hint:
These are right, but there are more.
D

II, III, IV, VI

Question 12 Explanation: 
Topic: Converting between fractions, decimals, and percents (Objective 0017)
Question 13

The speed of sound in dry air at 68 degrees F is 343.2 meters per second.  Which of the expressions below could be used to compute the number of kilometers that a sound wave travels in 10 minutes (in dry air at 68 degrees F)?

A
\( \large 343.2\times 60\times 10\)
Hint:
In kilometers, not meters.
B
\( \large 343.2\times 60\times 10\times \dfrac{1}{1000}\)
Hint:
Units are meters/sec \(\times\) seconds/minute \(\times\) minutes \(\times\) kilometers/meter, and the answer is in kilometers.
C
\( \large 343.2\times \dfrac{1}{60}\times 10\)
Hint:
Include units and make sure answer is in kilometers.
D
\( \large 343.2\times \dfrac{1}{60}\times 10\times \dfrac{1}{1000}\)
Hint:
Include units and make sure answer is in kilometers.
Question 13 Explanation: 
Topic: Use unit conversions and dimensional analysis to solve measurement problems (Objective 0023).
Question 14

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 14 Explanation: 
Topic: Identify and analyze direct and inverse relationships in tables, graphs, algebraic expressions and real-world situations (Objective 0021)
Question 15

Which of the lines depicted below is a graph of \( \large y=2x-5\)?

A

a

Hint:
The slope of line a is negative.
B

b

Hint:
Wrong slope and wrong intercept.
C

c

Hint:
The intercept of line c is positive.
D

d

Hint:
Slope is 2 -- for every increase of 1 in x, y increases by 2. Intercept is -5 -- the point (0,-5) is on the line.
Question 15 Explanation: 
Topic: Find a linear equation that represents a graph (Objective 0022).
Question 16

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 16 Explanation: 
Topic: Understand meaning and models of operations on fractions (Objective 0019).
Question 17

Which of the numbers below is a fraction equivalent to \( 0.\bar{6}\)?

A
\( \large \dfrac{4}{6}\)
Hint:
\( 0.\bar{6}=\dfrac{2}{3}=\dfrac{4}{6}\)
B
\( \large \dfrac{3}{5}\)
Hint:
This is equal to 0.6, without the repeating decimal. Answer is equivalent to choice c, which is another way to tell that it's wrong.
C
\( \large \dfrac{6}{10}\)
Hint:
This is equal to 0.6, without the repeating decimal. Answer is equivalent to choice b, which is another way to tell that it's wrong.
D
\( \large \dfrac{1}{6}\)
Hint:
This is less than a half, and \( 0.\bar{6}\) is greater than a half.
Question 17 Explanation: 
Topic: Converting between fraction and decimal representations (Objective 0017)
Question 18

Given that 10 cm is approximately equal to 4 inches, which of the following expressions models a way to find out approximately how many inches are equivalent to 350 cm?

A
\( \large 350\times \left( \dfrac{10}{4} \right)\)
Hint:
The final result should be smaller than 350, and this answer is bigger.
B
\( \large 350\times \left( \dfrac{4}{10} \right)\)
Hint:
Dimensional analysis can help here: \(350 \text{cm} \times \dfrac{4 \text{in}}{10 \text{cm}}\). The cm's cancel and the answer is in inches.
C
\( \large (10-4) \times 350 \)
Hint:
This answer doesn't make much sense. Try with a simpler example (e.g. 20 cm not 350 cm) to make sure that your logic makes sense.
D
\( \large (350-10) \times 4\)
Hint:
This answer doesn't make much sense. Try with a simpler example (e.g. 20 cm not 350 cm) to make sure that your logic makes sense.
Question 18 Explanation: 
Topic: Applying fractions to word problems (Objective 0017) This problem is similar to one on the official sample test for that objective, but it might fit better into unit conversion and dimensional analysis (Objective 0023: Measurement)
Question 19

Which of the following is equivalent to \(  \dfrac{3}{4}-\dfrac{1}{8}+\dfrac{2}{8}\times \dfrac{1}{2}?\)

A
\( \large \dfrac{7}{16}\)
Hint:
Multiplication comes before addition and subtraction in the order of operations.
B
\( \large \dfrac{1}{2}\)
Hint:
Addition and subtraction are of equal priority in the order of operations -- do them left to right.
C
\( \large \dfrac{3}{4}\)
Hint:
\( \dfrac{3}{4}-\dfrac{1}{8}+\dfrac{2}{8}\times \dfrac{1}{2}\)=\( \dfrac{3}{4}-\dfrac{1}{8}+\dfrac{1}{8}\)=\( \dfrac{3}{4}+-\dfrac{1}{8}+\dfrac{1}{8}\)=\( \dfrac{3}{4}\)
D
\( \large \dfrac{3}{16}\)
Hint:
Multiplication comes before addition and subtraction in the order of operations.
Question 19 Explanation: 
Topic: Operations on Fractions, Order of Operations (Objective 0019).
Question 20

The chart below gives percentiles for the number of sit-ups that boys of various ages can do in 60 seconds (source , June 24, 2011)

 

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

A

95% of 12 year old boys can do 56 sit-ups in 60 seconds.

Hint:
The 95th percentile means that 95% of scores are less than or equal to 56, and 5% are greater than or equal to 56.
B

At most 25% of 7 year old boys can do 19 or more sit-ups in 60 seconds.

Hint:
The 25th percentile means that 25% of scores are less than or equal to 19, and 75% are greater than or equal to 19.
C

Half of all 13 year old boys can do less than 41 sit-ups in 60 seconds and half can do more than 41 sit-ups in 60 seconds.

Hint:
Close, but not quite. There's no accounting for boys who can do exactly 41 sit ups. Look at these data: 10, 20, 41, 41, 41, 41, 50, 60, 90. The median is 41, but more than half can do 41 or more.
D

At least 75% of 16 year old boys can only do 51 or fewer sit-ups in 60 seconds.

Hint:
The "at least" is necessary due to duplicates. Suppose the data were 10, 20, 51, 51. The 75th percentile is 51, but 100% of the boys can only do 51 or fewer situps.
Question 20 Explanation: 
Topic: Analyze and interpret various graphic and nongraphic data representations (e.g., frequency distributions, percentiles) (Objective 0025).
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