20 Random Questions

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

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Question 1

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 1 Explanation:

Topic: Converting between fraction and decimal representations (Objective 0017)

Question 2

A family on vacation drove the first 200 miles in 4 hours and the second 200 miles in 5 hours. Which expression below gives their average speed for the entire trip?

A	$ \large \dfrac{200+200}{4+5}$ Hint: Average speed is total distance divided by total time.
B	$ \large \left( \dfrac{200}{4}+\dfrac{200}{5} \right)\div 2$ Hint: This seems logical, but the problem is that it weights the first 4 hours and the second 5 hours equally, when each hour should get the same weight in computing the average speed.
C	$ \large \dfrac{200}{4}+\dfrac{200}{5} $ Hint: This would be an average of 90 miles per hour!
D	$ \large \dfrac{400}{4}+\dfrac{400}{5} $ Hint: This would be an average of 180 miles per hour! Even a family of race car drivers probably doesn't have that average speed on a vacation!

Question 2 Explanation:

Topic: Solve a variety of measurement problems (e.g., time, temperature, rates, average rates of change) in real-world situations (Objective 0023).

Question 3

Below are four inputs and outputs for a function machine representing the function A:

Which of the following equations could also represent A for the values shown?

A	$ \large A(n)=n+4$ Hint: For a question like this, you don't have to find the equation yourself, you can just try plugging the function machine inputs into the equation, and see if any values come out wrong. With this equation n= -1 would output 3, not 0 as the machine does.
B	$ \large A(n)=n+2$ Hint: For a question like this, you don't have to find the equation yourself, you can just try plugging the function machine inputs into the equation, and see if any values come out wrong. With this equation n= 2 would output 4, not 6 as the machine does.
C	$ \large A(n)=2n+2$ Hint: Simply plug in each of the four function machine input values, and see that the equation produces the correct output, e.g. A(2)=6, A(-1)=0, etc.
D	$ \large A(n)=2\left( n+2 \right)$ Hint: For a question like this, you don't have to find the equation yourself, you can just try plugging the function machine inputs into the equation, and see if any values come out wrong. With this equation n= 2 would output 8, not 6 as the machine does.

Question 3 Explanation:

Topics: Understand various representations of functions, and translate among different representations of functional relationships (Objective 0021).

Question 4

M is a multiple of 26. Which of the following cannot be true?

A	M is odd. Hint: All multiples of 26 are also multiples of 2, so they must be even.
B	M is a multiple of 3. Hint: 3 x 26 is a multiple of both 3 and 26.
C	M is 26. Hint: 1 x 26 is a multiple of 26.
D	M is 0. Hint: 0 x 26 is a multiple of 26.

Question 4 Explanation:

Topic: Characteristics of composite numbers (Objective 0018).

Question 5

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 5 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 6

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 6 Explanation:

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

Question 7

An above-ground swimming pool is in the shape of a regular hexagonal prism, is one meter high, and holds 65 cubic meters of water. A second pool has a base that is also a regular hexagon, but with sides twice as long as the sides in the first pool. This second pool is also one meter high. How much water will the second pool hold?

A	$ \large 65\text{ }{{\text{m}}^{3}}$ Hint: A bigger pool would hold more water.
B	$ \large 65\cdot 2\text{ }{{\text{m}}^{3}}$ Hint: Try a simpler example, say doubling the sides of the base of a 1 x 1 x 1 cube.
C	$ \large 65\cdot 4\text{ }{{\text{m}}^{3}}$ Hint: If we think of the pool as filled with 1 x 1 x 1 cubes (and some fractions of cubes), then scaling to the larger pool changes each 1 x 1 x 1 cube to a 2 x 2 x 1 prism, or multiplies volume by 4.
D	$ \large 65\cdot 8\text{ }{{\text{m}}^{3}}$ Hint: Try a simpler example, say doubling the sides of the base of a 1 x 1 x 1 cube.

Question 7 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 8

Which of the following is equal to one million three hundred thousand?

A	$\large1.3\times {{10}^{6}}$
B	$\large1.3\times {{10}^{9}}$ Hint: That's one billion three hundred million.
C	$\large1.03\times {{10}^{6}}$ Hint: That's one million thirty thousand.
D	$\large1.03\times {{10}^{9}}$ Hint: That's one billion thirty million

Question 8 Explanation:

Topic: Scientific Notation (Objective 0016)

Question 9

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 9 Explanation:

Topic: Identifying rational and irrational numbers (Objective 0016).

Question 10

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 10 Explanation:

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

Question 11

Which of the following values of x satisfies the inequality $ \large \left| {{(x+2)}^{3}} \right|<3?$

A	$ \large x=-3$ Hint: $ \left\| {{(-3+2)}^{3}} \right\|$=$ \left \| {(-1)}^3 \right \| $=$ \left \| -1 \right \|=1 $ .
B	$ \large x=0$ Hint: $ \left\| {{(0+2)}^{3}} \right\|$=$ \left \| {2}^3 \right \| $=$ \left \| 8 \right \| $ =$ 8$
C	$ \large x=-4$ Hint: $ \left\| {{(-4+2)}^{3}} \right\|$=$ \left \| {(-2)}^3 \right \| $=$ \left \| -8 \right \| $ =$ 8$
D	$ \large x=1$ Hint: $ \left\| {{(1+2)}^{3}} \right\|$=$ \left \| {3}^3 \right \| $=$ \left \| 27 \right \| $ = $27$

Question 11 Explanation:

Topics: Laws of exponents, order of operations, interpret absolute value (Objective 0019).

Question 12

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 12 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 13

A class is using base-ten block to represent numbers. A large cube represents 1000, a flat represents 100, a rod represents 10, and a little cube represents 1. Which of these is not a correct representation for 2,347?

A	23 flats, 4 rods, 7 little cubes Hint: Be sure you read the question carefully: 2300+40+7=2347
B	2 large cubes, 3 flats, 47 rods Hint: 2000+300+470 $ \neq$ 2347
C	2 large cubes, 34 rods, 7 little cubes Hint: Be sure you read the question carefully: 2000+340+7=2347
D	2 large cubes, 3 flats, 4 rods, 7 little cubes Hint: Be sure you read the question carefully: 2000+300+40+7=2347

Question 13 Explanation:

Topic: Place Value (Objective 0016)

Question 14

Use the samples of a student's work below to answer the question that follows:

This student divides fractions by first finding a common denominator, then dividing the numerators.

$ \large \dfrac{2}{3} \div \dfrac{3}{4} \longrightarrow \dfrac{8}{12} \div \dfrac{9}{12} \longrightarrow 8 \div 9 = \dfrac {8}{9}$ $ \large \dfrac{2}{5} \div \dfrac{7}{20} \longrightarrow \dfrac{8}{20} \div \dfrac{7}{20} \longrightarrow 8 \div 7 = \dfrac {8}{7}$ $ \large \dfrac{7}{6} \div \dfrac{3}{4} \longrightarrow \dfrac{14}{12} \div \dfrac{9}{12} \longrightarrow 14 \div 9 = \dfrac {14}{9}$

Which of the following best describes the mathematical validity of the algorithm the student is using?

A	It is not valid. Common denominators are for adding and subtracting fractions, not for dividing them. Hint: Don't be so rigid! Usually there's more than one way to do something in math.
B	It got the right answer in these three cases, but it isn‘t valid for all rational numbers. Hint: Did you try some other examples? What makes you say it's not valid?
C	It is valid if the rational numbers in the division problem are in lowest terms and the divisor is not zero. Hint: Lowest terms doesn't affect this problem at all.
D	It is valid for all rational numbers, as long as the divisor is not zero. Hint: When we have common denominators, the problem is in the form a/b divided by c/b, and the answer is a/c, as the student's algorithm predicts.

Question 14 Explanation:

Topic: Analyze Non-Standard Computational Algorithms (Objective 0019).

Question 15

There are 15 students for every teacher. Let t represent the number of teachers and let s represent the number of students. Which of the following equations is correct?

A	$ \large t=s+15$ Hint: When there are 2 teachers, how many students should there be? Do those values satisfy this equation?
B	$ \large s=t+15$ Hint: When there are 2 teachers, how many students should there be? Do those values satisfy this equation?
C	$ \large t=15s$ Hint: This is a really easy mistake to make, which comes from transcribing directly from English, "1 teachers equals 15 students." To see that it's wrong, plug in s=2; do you really need 30 teachers for 2 students? To avoid this mistake, insert the word "number," "Number of teachers equals 15 times number of students" is more clearly problematic.
D	$ \large s=15t$

Question 15 Explanation:

Topic: Select the linear equation that best models a real-world situation (Objective 0022).

Question 16

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 16 Explanation:

Topic: Derive and use formulas for calculating the lengths, perimeters, areas, volumes, and surface areas of geometric shapes and figures (Objective 0023).

Question 17

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 17 Explanation:

Topic: Analyze and interpret various graphic and nongraphic data representations (e.g., frequency distributions, percentiles) (Objective 0025).

Question 18

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 18 Explanation:

Converting between fractions, decimals, and percents (Objective 0017).

Question 19

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 19 Explanation:

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

Question 20

A biology class requires a lab fee, which is a whole number of dollars, and the same amount for all students. On Monday the instructor collected $70 in fees, on Tuesday she collected $126, and on Wednesday she collected $266. What is the largest possible amount the fee could be?

A	$2 Hint: A possible fee, but not the largest possible fee. Check the other choices to see which are factors of all three numbers.
B	$7 Hint: A possible fee, but not the largest possible fee. Check the other choices to see which are factors of all three numbers.
C	$14 Hint: This is the greatest common factor of 70, 126, and 266.
D	$70 Hint: Not a factor of 126 or 266, so couldn't be correct.

Question 20 Explanation:

Topic: Use GCF in real-world context (Objective 0018)

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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.

A	\( \large \dfrac{200+200}{4+5}\) Hint: Average speed is total distance divided by total time.
B	\( \large \left( \dfrac{200}{4}+\dfrac{200}{5} \right)\div 2\) Hint: This seems logical, but the problem is that it weights the first 4 hours and the second 5 hours equally, when each hour should get the same weight in computing the average speed.
C	\( \large \dfrac{200}{4}+\dfrac{200}{5} \) Hint: This would be an average of 90 miles per hour!
D	\( \large \dfrac{400}{4}+\dfrac{400}{5} \) Hint: This would be an average of 180 miles per hour! Even a family of race car drivers probably doesn't have that average speed on a vacation!

A	\( \large A(n)=n+4\) Hint: For a question like this, you don't have to find the equation yourself, you can just try plugging the function machine inputs into the equation, and see if any values come out wrong. With this equation n= -1 would output 3, not 0 as the machine does.
B	\( \large A(n)=n+2\) Hint: For a question like this, you don't have to find the equation yourself, you can just try plugging the function machine inputs into the equation, and see if any values come out wrong. With this equation n= 2 would output 4, not 6 as the machine does.
C	\( \large A(n)=2n+2\) Hint: Simply plug in each of the four function machine input values, and see that the equation produces the correct output, e.g. A(2)=6, A(-1)=0, etc.
D	\( \large A(n)=2\left( n+2 \right)\) Hint: For a question like this, you don't have to find the equation yourself, you can just try plugging the function machine inputs into the equation, and see if any values come out wrong. With this equation n= 2 would output 8, not 6 as the machine does.

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?

A	\( \large 65\text{ }{{\text{m}}^{3}}\) Hint: A bigger pool would hold more water.
B	\( \large 65\cdot 2\text{ }{{\text{m}}^{3}}\) Hint: Try a simpler example, say doubling the sides of the base of a 1 x 1 x 1 cube.
C	\( \large 65\cdot 4\text{ }{{\text{m}}^{3}}\) Hint: If we think of the pool as filled with 1 x 1 x 1 cubes (and some fractions of cubes), then scaling to the larger pool changes each 1 x 1 x 1 cube to a 2 x 2 x 1 prism, or multiplies volume by 4.
D	\( \large 65\cdot 8\text{ }{{\text{m}}^{3}}\) Hint: Try a simpler example, say doubling the sides of the base of a 1 x 1 x 1 cube.

A	\(\large1.3\times {{10}^{6}}\)
B	\(\large1.3\times {{10}^{9}}\) Hint: That's one billion three hundred million.
C	\(\large1.03\times {{10}^{6}}\) Hint: That's one million thirty thousand.
D	\(\large1.03\times {{10}^{9}}\) Hint: That's one billion thirty million

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.

A	\( \large x=-3\) Hint: \( \left\| {{(-3+2)}^{3}} \right\|\)=\( \left \| {(-1)}^3 \right \| \)=\( \left \| -1 \right \|=1 \) .
B	\( \large x=0\) Hint: \( \left\| {{(0+2)}^{3}} \right\|\)=\( \left \| {2}^3 \right \| \)=\( \left \| 8 \right \| \) =\( 8\)
C	\( \large x=-4\) Hint: \( \left\| {{(-4+2)}^{3}} \right\|\)=\( \left \| {(-2)}^3 \right \| \)=\( \left \| -8 \right \| \) =\( 8\)
D	\( \large x=1\) Hint: \( \left\| {{(1+2)}^{3}} \right\|\)=\( \left \| {3}^3 \right \| \)=\( \left \| 27 \right \| \) = \(27\)

A	\( \large t=s+15\) Hint: When there are 2 teachers, how many students should there be? Do those values satisfy this equation?
B	\( \large s=t+15\) Hint: When there are 2 teachers, how many students should there be? Do those values satisfy this equation?
C	\( \large t=15s\) Hint: This is a really easy mistake to make, which comes from transcribing directly from English, "1 teachers equals 15 students." To see that it's wrong, plug in s=2; do you really need 30 teachers for 2 students? To avoid this mistake, insert the word "number," "Number of teachers equals 15 times number of students" is more clearly problematic.
D	\( \large s=15t\)

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.

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).

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.

MTEL General Curriculum Mathematics Practice

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

A family on vacation drove the first 200 miles in 4 hours and the second 200 miles in 5 hours. Which expression below gives their average speed for the entire trip?

Below are four inputs and outputs for a function machine representing the function A:

Which of the following equations could also represent A for the values shown?

M is a multiple of 26. Which of the following cannot be true?

M is odd.

M is a multiple of 3.

M is 26.

M is 0.

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?

40

80

100

120

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

Which of the following is equal to one million three hundred thousand?

Which of the following is an irrational number?

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

2 pentagons and 5 rectangles.

1 square and 5 equilateral triangles.

1 pentagon and 5 isosceles triangles.

1 pentagon and 10 isosceles triangles.

Which of the following values of x satisfies the inequality \( \large \left| {{(x+2)}^{3}} \right|<3?\)

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?

Commutative Property.

Associative Property.

Identity Property.

Distributive Property.

A class is using base-ten block to represent numbers. A large cube represents 1000, a flat represents 100, a rod represents 10, and a little cube represents 1. Which of these is not a correct representation for 2,347?

23 flats, 4 rods, 7 little cubes

2 large cubes, 3 flats, 47 rods

2 large cubes, 34 rods, 7 little cubes

2 large cubes, 3 flats, 4 rods, 7 little cubes

Use the samples of a student's work below to answer the question that follows:

This student divides fractions by first finding a common denominator, then dividing the numerators.

Which of the following best describes the mathematical validity of the algorithm the student is using?

It is not valid. Common denominators are for adding and subtracting fractions, not for dividing them.

It got the right answer in these three cases, but it isn‘t valid for all rational numbers.

It is valid if the rational numbers in the division problem are in lowest terms and the divisor is not zero.

It is valid for all rational numbers, as long as the divisor is not zero.

There are 15 students for every teacher. Let t represent the number of teachers and let s represent the number of students. Which of the following equations is correct?

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?

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?

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

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

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.

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

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

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 biology class requires a lab fee, which is a whole number of dollars, and the same amount for all students. On Monday the instructor collected $70 in fees, on Tuesday she collected $126, and on Wednesday she collected $266. What is the largest possible amount the fee could be?

$2

$7

$14

$70