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

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 1 Explanation:

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

Question 2

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 2 Explanation:

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

Question 3

Which of the lists below contains only irrational numbers?

A	$ \large\pi , \quad \sqrt{6},\quad \sqrt{\dfrac{1}{2}}$
B	$ \large\pi , \quad \sqrt{9}, \quad \pi +1$ Hint: $ \sqrt{9}=3$
C	$ \large\dfrac{1}{3},\quad \dfrac{5}{4},\quad \dfrac{2}{9}$ Hint: These are all rational.
D	$ \large-3,\quad 14,\quad 0$ Hint: These are all rational.

Question 3 Explanation:

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

Question 4

Taxicab fares in Boston (Spring 2012) are $2.60 for the first $\dfrac{1}{7}$ of a mile or less and $0.40 for each $\dfrac{1}{7}$ of a mile after that.

Let d represent the distance a passenger travels in miles (with $d>\dfrac{1}{7}$). Which of the following expressions represents the total fare?

A	$ \large \$2.60+\$0.40d$ Hint: It's 40 cents for 1/7 of a mile, not per mile.
B	$ \large \$2.60+\$0.40\dfrac{d}{7}$ Hint: According to this equation, going 7 miles would cost $3; does that make sense?
C	$ \large \$2.20+\$2.80d$ Hint: You can think of the fare as $2.20 to enter the cab, and then $0.40 for each 1/7 of a mile, including the first 1/7 of a mile (or $2.80 per mile). Alternatively, you pay $2.60 for the first 1/7 of a mile, and then $2.80 per mile for d-1/7 miles. The total is 2.60+2.80(d-1/7) = 2.60+ 2.80d -.40 = 2.20+2.80d.
D	$ \large \$2.60+\$2.80d$ Hint: Don't count the first 1/7 of a mile twice.

Question 4 Explanation:

Topic: Identify variables and derive algebraic expressions that represent real-world situations (Objective 0020), and select the linear equation that best models a real-world situation (Objective 0022).

Question 5

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 5 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 6

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 6 Explanation:

Topic: Place Value (Objective 0016)

Question 7

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 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

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 8 Explanation:

Topics: Comparing fractions, and understanding the meaning of fractions (Objective 0017).

Question 9

What is the probability that two randomly selected people were born on the same day of the week? Assume that all days are equally probable.

A	$ \large \dfrac{1}{7}$ Hint: It doesn't matter what day the first person was born on. The probability that the second person will match is 1/7 (just designate one person the first and the other the second). Another way to look at it is that if you list the sample space of all possible pairs, e.g. (Wed, Sun), there are 49 such pairs, and 7 of them are repeats of the same day, and 7/49=1/7.
B	$ \large \dfrac{1}{14}$ Hint: What would be the sample space here? Ie, how would you list 14 things that you pick one from?
C	$ \large \dfrac{1}{42}$ Hint: If you wrote the seven days of the week on pieces of paper and put the papers in a jar, this would be the probability that the first person picked Sunday and the second picked Monday from the jar -- not the same situation.
D	$ \large \dfrac{1}{49}$ Hint: This is the probability that they are both born on a particular day, e.g. Sunday.

Question 9 Explanation:

Topic: Calculate the probabilities of simple and compound events and of independent and dependent events (Objective 0026).

Question 10

In which table below is y a function of x?

A	Hint: If x=3, y can have two different values, so it's not a function.
B	Hint: If x=3, y can have two different values, so it's not a function.
C	Hint: If x=1, y can have different values, so it's not a function.
D	Hint: Each value of x always corresponds to the same value of y.

Question 10 Explanation:

Topic: Understand the definition of function and various representations of functions (e.g., input/output machines, tables, graphs, mapping diagrams, formulas) (Objective 0021).

Question 11

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 11 Explanation:

Topic: Place Value (Objective 0016)

Question 12

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 12 Explanation:

Topic: Venn Diagrams (Objective 0025)

Question 13

In January 2011, the national debt was about 14 trillion dollars and the US population was about 300 million people. Someone reading these figures estimated that the national debt was about $5,000 per person. Which of these statements best describes the reasonableness of this estimate?

A	It is too low by a factor of 10 Hint: 14 trillion $ \approx 15 \times {{10}^{12}} $ and 300 million $ \approx 3 \times {{10}^{8}}$, so the true answer is about $ 5 \times {{10}^{4}} $ or $50,000.
B	It is too low by a factor of 100
C	It is too high by a factor of 10
D	It is too high by a factor of 100

Question 13 Explanation:

Topics: Estimation, Scientific Notation in the real world (Objective 0016).

Question 14

If two fair coins are flipped, what is the probability that one will come up heads and the other tails?

A	$ \large \dfrac{1}{4}$ Hint: Think of the coins as a penny and a dime, and list all possibilities.
B	$ \large \dfrac{1}{3} $ Hint: This is a very common misconception. There are three possible outcomes -- both heads, both tails, and one of each -- but they are not equally likely. Think of the coins as a penny and a dime, and list all possibilities.
C	$ \large \dfrac{1}{2}$ Hint: The possibilities are HH, HT, TH, TT, and all are equally likely. Two of the four have one of each coin, so the probability is 2/4=1/2.
D	$ \large \dfrac{3}{4}$ Hint: Think of the coins as a penny and a dime, and list all possibilities.

Question 14 Explanation:

Topic: Calculate the probabilities of simple and compound events and of independent and dependent events (Objective 0026).

Question 15

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 15 Explanation:

Topic: Understand meaning and models of operations on fractions (Objective 0019).

Question 16

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 16 Explanation:

Topic: Scientific Notation (Objective 0016)

Question 17

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 17 Explanation:

Topic: Recognize and extend patterns using a variety of representations (e.g., verbal, numeric, pictorial, algebraic) (Objective 0021).

Question 18

The polygon depicted below is drawn on dot paper, with the dots spaced 1 unit apart. What is the perimeter of the polygon?

A	$ \large 18+\sqrt{2} \text{ units}$ Hint: Be careful with the Pythagorean Theorem.
B	$ \large 18+2\sqrt{2}\text{ units}$ Hint: There are 13 horizontal or vertical 1 unit segments. The longer diagonal is the hypotenuse of a 3-4-5 right triangle, so its length is 5 units. The shorter diagonal is the hypotenuse of a 45-45-90 right triangle with side 2, so its hypotenuse has length $2 \sqrt{2}$.
C	$ \large 18 \text{ units} $ Hint: Use the Pythagorean Theorem to find the lengths of the diagonal segments.
D	$ \large 20 \text{ units}$ Hint: Use the Pythagorean Theorem to find the lengths of the diagonal segments.

Question 18 Explanation:

Topic: Recognize and apply connections between algebra and geometry (e.g., the use of coordinate systems, the Pythagorean theorem) (Objective 0024).

Question 19

Which of the lists below is in order from least to greatest value?

A	$ \large \dfrac{1}{2},\quad \dfrac{1}{3},\quad \dfrac{1}{4},\quad \dfrac{1}{5}$ Hint: This is ordered from greatest to least.
B	$ \large \dfrac{1}{3},\quad \dfrac{2}{7},\quad \dfrac{3}{8},\quad \dfrac{4}{11}$ Hint: 1/3 = 2/6 is bigger than 2/7.
C	$ \large \dfrac{1}{4},\quad \dfrac{2}{5},\quad \dfrac{2}{3},\quad \dfrac{4}{5}$ Hint: One way to look at this: 1/4 and 2/5 are both less than 1/2, and 2/3 and 4/5 are both greater than 1/2. 1/4 is 25% and 2/5 is 40%, so 2/5 is greater. The distance from 2/3 to 1 is 1/3 and from 4/5 to 1 is 1/5, and 1/5 is less than 1/3, so 4/5 is bigger.
D	$ \large \dfrac{7}{8},\quad \dfrac{6}{7},\quad \dfrac{5}{6},\quad \dfrac{4}{5}$ Hint: This is in order from greatest to least.

Question 19 Explanation:

Topic: Ordering Fractions (Objective 0017)

Question 20

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

$ \large \dfrac{2}{3}\times \dfrac{3}{4}=\dfrac{4\times 2}{3\times 3}=\dfrac{8}{9}$ $ \large \dfrac{2}{5}\times \dfrac{7}{7}=\dfrac{7\times 2}{5\times 7}=\dfrac{2}{5}$ $ \large \dfrac{7}{6}\times \dfrac{3}{4}=\dfrac{4\times 7}{6\times 3}=\dfrac{28}{18}=\dfrac{14}{9}$

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

A	It is not valid. It never produces the correct answer. Hint: In the middle example,the answer is correct.
B	It is not valid. It produces the correct answer in a few special cases, but it‘s still not a valid algorithm. Hint: Note that this algorithm gives a/b divided by c/d, not a/b x c/d, but some students confuse multiplication and cross-multiplication. If a=0 or if c/d =1, division and multiplication give the same answer.
C	It is valid if the rational numbers in the multiplication problem are in lowest terms. Hint: Lowest terms is irrelevant.
D	It is valid for all rational numbers. Hint: Can't be correct as the first and last examples have the wrong answers.

Question 20 Explanation:

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

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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	\( \large\pi , \quad \sqrt{6},\quad \sqrt{\dfrac{1}{2}}\)
B	\( \large\pi , \quad \sqrt{9}, \quad \pi +1\) Hint: \( \sqrt{9}=3\)
C	\( \large\dfrac{1}{3},\quad \dfrac{5}{4},\quad \dfrac{2}{9}\) Hint: These are all rational.
D	\( \large-3,\quad 14,\quad 0\) Hint: These are all rational.

A	\( \large \$2.60+\$0.40d\) Hint: It's 40 cents for 1/7 of a mile, not per mile.
B	\( \large \$2.60+\$0.40\dfrac{d}{7}\) Hint: According to this equation, going 7 miles would cost $3; does that make sense?
C	\( \large \$2.20+\$2.80d\) Hint: You can think of the fare as $2.20 to enter the cab, and then $0.40 for each 1/7 of a mile, including the first 1/7 of a mile (or $2.80 per mile). Alternatively, you pay $2.60 for the first 1/7 of a mile, and then $2.80 per mile for d-1/7 miles. The total is 2.60+2.80(d-1/7) = 2.60+ 2.80d -.40 = 2.20+2.80d.
D	\( \large \$2.60+\$2.80d\) Hint: Don't count the first 1/7 of a mile twice.

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	\( \large 11,400,000\) 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

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.

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.

A	\( \large \dfrac{1}{7}\) Hint: It doesn't matter what day the first person was born on. The probability that the second person will match is 1/7 (just designate one person the first and the other the second). Another way to look at it is that if you list the sample space of all possible pairs, e.g. (Wed, Sun), there are 49 such pairs, and 7 of them are repeats of the same day, and 7/49=1/7.
B	\( \large \dfrac{1}{14}\) Hint: What would be the sample space here? Ie, how would you list 14 things that you pick one from?
C	\( \large \dfrac{1}{42}\) Hint: If you wrote the seven days of the week on pieces of paper and put the papers in a jar, this would be the probability that the first person picked Sunday and the second picked Monday from the jar -- not the same situation.
D	\( \large \dfrac{1}{49}\) Hint: This is the probability that they are both born on a particular day, e.g. Sunday.

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.

A	\( \large \dfrac{1}{4}\) Hint: Think of the coins as a penny and a dime, and list all possibilities.
B	\( \large \dfrac{1}{3} \) Hint: This is a very common misconception. There are three possible outcomes -- both heads, both tails, and one of each -- but they are not equally likely. Think of the coins as a penny and a dime, and list all possibilities.
C	\( \large \dfrac{1}{2}\) Hint: The possibilities are HH, HT, TH, TT, and all are equally likely. Two of the four have one of each coin, so the probability is 2/4=1/2.
D	\( \large \dfrac{3}{4}\) Hint: Think of the coins as a penny and a dime, and list all possibilities.

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.

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	\( \large 18+\sqrt{2} \text{ units}\) Hint: Be careful with the Pythagorean Theorem.
B	\( \large 18+2\sqrt{2}\text{ units}\) Hint: There are 13 horizontal or vertical 1 unit segments. The longer diagonal is the hypotenuse of a 3-4-5 right triangle, so its length is 5 units. The shorter diagonal is the hypotenuse of a 45-45-90 right triangle with side 2, so its hypotenuse has length \(2 \sqrt{2}\).
C	\( \large 18 \text{ units} \) Hint: Use the Pythagorean Theorem to find the lengths of the diagonal segments.
D	\( \large 20 \text{ units}\) Hint: Use the Pythagorean Theorem to find the lengths of the diagonal segments.

A	\( \large \dfrac{1}{2},\quad \dfrac{1}{3},\quad \dfrac{1}{4},\quad \dfrac{1}{5}\) Hint: This is ordered from greatest to least.
B	\( \large \dfrac{1}{3},\quad \dfrac{2}{7},\quad \dfrac{3}{8},\quad \dfrac{4}{11}\) Hint: 1/3 = 2/6 is bigger than 2/7.
C	\( \large \dfrac{1}{4},\quad \dfrac{2}{5},\quad \dfrac{2}{3},\quad \dfrac{4}{5}\) Hint: One way to look at this: 1/4 and 2/5 are both less than 1/2, and 2/3 and 4/5 are both greater than 1/2. 1/4 is 25% and 2/5 is 40%, so 2/5 is greater. The distance from 2/3 to 1 is 1/3 and from 4/5 to 1 is 1/5, and 1/5 is less than 1/3, so 4/5 is bigger.
D	\( \large \dfrac{7}{8},\quad \dfrac{6}{7},\quad \dfrac{5}{6},\quad \dfrac{4}{5}\) Hint: This is in order from greatest to least.

MTEL General Curriculum Mathematics Practice

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

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

Which of the lists below contains only irrational numbers?

Taxicab fares in Boston (Spring 2012) are $2.60 for the first \(\dfrac{1}{7}\) of a mile or less and $0.40 for each \(\dfrac{1}{7}\) of a mile after that.

Let d represent the distance a passenger travels in miles (with \(d>\dfrac{1}{7}\)). Which of the following expressions represents the total fare?

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

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?

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?

\( \dfrac{4}{7}\) 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.

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

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

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

What is the probability that two randomly selected people were born on the same day of the week? Assume that all days are equally probable.

In which table below is y a function of x?

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

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?

In January 2011, the national debt was about 14 trillion dollars and the US population was about 300 million people. Someone reading these figures estimated that the national debt was about $5,000 per person. Which of these statements best describes the reasonableness of this estimate?

It is too low by a factor of 10

It is too low by a factor of 100

It is too high by a factor of 10

It is too high by a factor of 100

If two fair coins are flipped, what is the probability that one will come up heads and the other tails?

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

A

B

C

D

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

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?

314

317

320

322

The polygon depicted below is drawn on dot paper, with the dots spaced 1 unit apart. What is the perimeter of the polygon?

Which of the lists below is in order from least to greatest value?

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

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

It is not valid. It never produces the correct answer.

It is not valid. It produces the correct answer in a few special cases, but it‘s still not a valid algorithm.

It is valid if the rational numbers in the multiplication problem are in lowest terms.

It is valid for all rational numbers.