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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

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 1 Explanation: 
Identify variables and derive algebraic expressions that represent real-world situations (Objective 0020).
Question 2
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 2 Explanation: 
Topic: Converting between fractions, decimals, and percents (Objective 0017)
Question 3

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 3 Explanation: 
Topic: Analyze the relationships among proportions, constant rates, and linear functions (Objective 0022).
Question 4

A family has four children.  What is the probability that two children are girls and two are boys?  Assume the the probability of having a boy (or a girl) is 50%.

A
\( \large \dfrac{1}{2}\)
Hint:
How many different configurations are there from oldest to youngest, e.g. BGGG? How many of them have 2 boys and 2 girls?
B
\( \large \dfrac{1}{4}\)
Hint:
How many different configurations are there from oldest to youngest, e.g. BGGG? How many of them have 2 boys and 2 girls?
C
\( \large \dfrac{1}{5}\)
Hint:
Some configurations are more probable than others -- i.e. it's more likely to have two boys and two girls than all boys. Be sure you are weighting properly.
D
\( \large \dfrac{3}{8}\)
Hint:
There are two possibilities for each child, so there are \(2 \times 2 \times 2 \times 2 =16\) different configurations, e.g. from oldest to youngest BBBG, BGGB, GBBB, etc. Of these configurations, there are 6 with two boys and two girls (this is the combination \(_{4}C_{2}\) or "4 choose 2"): BBGG, BGBG, BGGB, GGBB, GBGB, and GBBG. Thus the probability is 6/16=3/8.
Question 4 Explanation: 
Topic: Apply knowledge of combinations and permutations to the computation of probabilities (Objective 0026).
Question 5

A sales companies pays its representatives $2 for each item sold, plus 40% of the price of the item.   The rest of the money that the representatives collect goes to the company.  All transactions are in cash, and all items cost $4 or more.   If the price of an item in dollars is p, which expression represents the amount of money the company collects when the item is sold?

A
\( \large \dfrac{3}{5}p-2\)
Hint:
The company gets 3/5=60% of the price, minus the $2 per item.
B
\( \large \dfrac{3}{5}\left( p-2 \right)\)
Hint:
This is sensible, but not what the problem states.
C
\( \large \dfrac{2}{5}p+2\)
Hint:
The company pays the extra $2; it doesn't collect it.
D
\( \large \dfrac{2}{5}p-2\)
Hint:
This has the company getting 2/5 = 40% of the price of each item, but that's what the representative gets.
Question 5 Explanation: 
Topic: Use algebra to solve word problems involving fractions, ratios, proportions, and percents (Objective 0020).
Question 6

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 6 Explanation: 
Topics: Laws of exponents (Objective 0019).
Question 7

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 7 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 8

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 8 Explanation: 
Topic: Use unit conversions and dimensional analysis to solve measurement problems (Objective 0023).
Question 9

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 9 Explanation: 
Topic: Match three-dimensional figures and their two-dimensional representations (e.g., nets, projections, perspective drawings) (Objective 0024).
Question 10

What is the greatest common factor of 540 and 216?

A
\( \large{{2}^{2}}\cdot {{3}^{3}}\)
Hint:
One way to solve this is to factor both numbers: \(540=2^2 \cdot 3^3 \cdot 5\) and \(216=2^3 \cdot 3^3\). Then take the smaller power for each prime that is a factor of both numbers.
B
\( \large2\cdot 3\)
Hint:
This is a common factor of both numbers, but it's not the greatest common factor.
C
\( \large{{2}^{3}}\cdot {{3}^{3}}\)
Hint:
\(2^3 = 8\) is not a factor of 540.
D
\( \large{{2}^{2}}\cdot {{3}^{2}}\)
Hint:
This is a common factor of both numbers, but it's not the greatest common factor.
Question 10 Explanation: 
Topic: Find the greatest common factor of a set of numbers (Objective 0018).
Question 11

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 11 Explanation: 
Converting between fractions, decimals, and percents (Objective 0017).
Question 12

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 12 Explanation: 
Topic: Find the prime factorization of a number and recognize its uses (Objective 0018).
Question 13

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 13 Explanation: 
Topic: Compare different data sets (Objective 0025).
Question 14

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 14 Explanation: 
Topic: Find a linear equation that represents a graph (Objective 0022).
Question 15

Use the expression below to answer the question that follows.

                 \( \large \dfrac{\left( 4\times {{10}^{3}} \right)\times \left( 3\times {{10}^{4}} \right)}{6\times {{10}^{6}}}\)

Which of the following is equivalent to the expression above?

A

2

Hint:
\(10^3 \times 10^4=10^7\), and note that if you're guessing when the answers are so closely related, you're generally better off guessing one of the middle numbers.
B

20

Hint:
\( \dfrac{\left( 4\times {{10}^{3}} \right)\times \left( 3\times {{10}^{4}} \right)}{6\times {{10}^{6}}}=\dfrac {12 \times {{10}^{7}}}{6\times {{10}^{6}}}=\)\(2 \times {{10}^{1}}=20 \)
C

200

Hint:
\(10^3 \times 10^4=10^7\)
D

2000

Hint:
\(10^3 \times 10^4=10^7\), and note that if you're guessing when the answers are so closely related, you're generally better off guessing one of the middle numbers.
Question 15 Explanation: 
Topics: Scientific notation, exponents, simplifying fractions (Objective 0016, although overlaps with other objectives too).
Question 16

The table below gives data from various years on how many young girls drank milk.

Based on the data given above, what was the probability that a randomly chosen girl in 1990 drank milk?

A
\( \large \dfrac{502}{1222}\)
Hint:
This is the probability that a randomly chosen girl who drinks milk was in the 1989-1991 food survey.
B
\( \large \dfrac{502}{2149}\)
Hint:
This is the probability that a randomly chosen girl from the whole survey drank milk and was also surveyed in 1989-1991.
C
\( \large \dfrac{502}{837}\)
D
\( \large \dfrac{1222}{2149}\)
Hint:
This is the probability that a randomly chosen girl from any year of the survey drank milk.
Question 16 Explanation: 
Topic: Recognize and apply the concept of conditional probability (Objective 0026).
Question 17

Here is a student's work solving an equation:

\( x-4=-2x+6\)

\( x-4+4=-2x+6+4\)

\( x=-2x+10\)

\( x-2x=10\)

\( x=10\)

Which of the following statements is true?

A

The student‘s solution is correct.

Hint:
Try plugging into the original solution.
B

The student did not correctly use properties of equality.

Hint:
After \( x=-2x+10\), the student subtracted 2x on the left and added 2x on the right.
C

The student did not correctly use the distributive property.

Hint:
Distributive property is \(a(b+c)=ab+ac\).
D

The student did not correctly use the commutative property.

Hint:
Commutative property is \(a+b=b+a\) or \(ab=ba\).
Question 17 Explanation: 
Topic: Justify algebraic manipulations by application of the properties of equality, the order of operations, the number properties, and the order properties (Objective 0020).
Question 18

Which of the following sets of polygons can be assembled to form a pentagonal pyramid?

A

2 pentagons and 5 rectangles.

Hint:
These can be assembled to form a pentagonal prism, not a pentagonal pyramid.
B

1 square and 5 equilateral triangles.

Hint:
You need a pentagon for a pentagonal pyramid.
C

1 pentagon and 5 isosceles triangles.

D

1 pentagon and 10 isosceles triangles.

Question 18 Explanation: 
Topic:Classify and analyze three-dimensional figures using attributes of faces, edges, and vertices (Objective 0024).
Question 19

Elena is going to use a calculator to check whether or not 267 is prime. She will pick certain divisors, and then find 267 divided by each, and see if she gets a whole number. If she never gets a whole number, then she's found a prime. Which numbers does Elena NEED to check before she can stop checking and be sure she has a prime?

A

All natural numbers from 2 to 266.

Hint:
She only needs to check primes -- checking the prime factors of any composite is enough to look for divisors. As a test taking strategy, the other three choices involve primes, so worth thinking about.
B

All primes from 2 to 266 .

Hint:
Remember, factors come in pairs (except for square root factors), so she would first find the smaller of the pair and wouldn't need to check the larger.
C

All primes from 2 to 133 .

Hint:
She doesn't need to check this high. Factors come in pairs, and something over 100 is going to be paired with something less than 3, so she will find that earlier.
D

All primes from \( \large 2\) to \( \large \sqrt{267}\).

Hint:
\(\sqrt{267} \times \sqrt{267}=267\). Any other pair of factors will have one factor less than \( \sqrt{267}\) and one greater, so she only needs to check up to \( \sqrt{267}\).
Question 19 Explanation: 
Topic: Identify prime and composite numbers (Objective 0018).
Question 20

What is the length of side \(\overline{BD}\) in the triangle below, where \(\angle DBA\) is a right angle?

A
\( \large 1\)
Hint:
Use the Pythagorean Theorem.
B
\( \large \sqrt{5}\)
Hint:
\(2^2+e^2=3^2\) or \(4+e^2=9;e^2=5; e=\sqrt{5}\).
C
\( \large \sqrt{13}\)
Hint:
e is not the hypotenuse.
D
\( \large 5\)
Hint:
Use the Pythagorean Theorem.
Question 20 Explanation: 
Topic: Derive and use formulas for calculating the lengths, perimeters, areas, volumes, and surface areas of geometric shapes and figures (Objective 0023), and recognize and apply connections between algebra and geometry (e.g., the use of coordinate systems, the Pythagorean theorem) (Objective 0024).
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