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

What is the least common multiple of 540 and 216?

A	$ \large{{2}^{5}}\cdot {{3}^{6}}\cdot 5$ Hint: This is the product of the numbers, not the LCM.
B	$ \large{{2}^{3}}\cdot {{3}^{3}}\cdot 5$ 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 for each prime that's a factor of either number, use the largest exponent that appears in one of the factorizations. You can also take the product of the two numbers divided by their GCD.
C	$ \large{{2}^{2}}\cdot {{3}^{3}}\cdot 5$ Hint: 216 is a multiple of 8.
D	$ \large{{2}^{2}}\cdot {{3}^{2}}\cdot {{5}^{2}}$ Hint: Not a multiple of 216 and not a multiple of 540.

Question 1 Explanation:

Topic: Find the least common multiple of a set of numbers (Objective 0018).

Question 2

In each expression below N represents a negative integer. Which expression could have a negative value?

A	$ \large {{N}^{2}}$ Hint: Squaring always gives a non-negative value.
B	$ \large 6-N$ Hint: A story problem for this expression is, if it was 6 degrees out at noon and N degrees out at sunrise, by how many degrees did the temperature rise by noon? Since N is negative, the answer to this question has to be positive, and more than 6.
C	$ \large -N$ Hint: If N is negative, then -N is positive
D	$ \large 6+N$ Hint: For example, if $N=-10$, then $6+N = -4$

Question 2 Explanation:

If you are stuck on a question like this, try a few examples to eliminate some choices and to help you understand what the question means. Topic: Characteristics of integers (Objective 0016).

Question 3

Below is a portion of a number line.

Point A is one-quarter of the distance from 0.26 to 0.28. What number is represented by point A?

A	$ \large0.26$ Hint: Please reread the question.
B	$ \large0.2625$ Hint: This is one-quarter of the distance between 0.26 and 0.27, which is not what the question asked.
C	$ \large0.265$
D	$ \large0.27$ Hint: Please read the question more carefully. This answer would be correct if Point A were halfway between the tick marks, but it's not.

Question 3 Explanation:

Topic: Using number lines (Objective 0017)

Question 4

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 4 Explanation:

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

Question 5

A homeowner is planning to tile the kitchen floor with tiles that measure 6 inches by 8 inches. The kitchen floor is a rectangle that measures 10 ft by 12 ft, and there are no gaps between the tiles. How many tiles does the homeowner need?

A	30 Hint: The floor is 120 sq feet, and the tiles are smaller than 1 sq foot. Also, remember that 1 sq foot is 12 $\times$ 12=144 sq inches.
B	120 Hint: The floor is 120 sq feet, and the tiles are smaller than 1 sq foot.
C	300 Hint: Recheck your calculations.
D	360 Hint: One way to do this is to note that 6 inches = 1/2 foot and 8 inches = 2/3 foot, so the area of each tile is 1/2 $\times$ 2/3=1/3 sq foot, or each square foot of floor requires 3 tiles. The area of the floor is 120 square feet. Note that the tiles would fit evenly oriented in either direction, parallel to the walls.

Question 5 Explanation:

Topic: Estimate and calculate measurements, use unit conversions to solve measurement problems, solve measurement problems in real-world situations (Objective 0023).

Question 6

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 6 Explanation:

Topic: Operations on Fractions, Order of Operations (Objective 0019).

Question 7

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 7 Explanation:

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

Question 8

What set of transformations will transform the leftmost image into the rightmost image?

A	A 90 degree clockwise rotation about (2,1) followed by a translation of two units to the right. Hint: Part of the figure would move below the x-axis with these transformations.
B	A translation 3 units up, followed by a reflection about the line y=x. Hint: See what happens to the point (5,1) under this set of transformations.
C	A 90 degree clockwise rotation about (5,1), followed by a translation of 2 units up.
D	A 90 degree clockwise rotation about (2,1) followed by a translation of 2 units to the right. Hint: See what happens to the point (3,3) under this set of transformations.

Question 8 Explanation:

Topic:Analyze and apply geometric transformations (e.g., translations, rotations, reflections, dilations) (Objective 0024).

Question 9

The Americans with Disabilties Act (ADA) regulations state that the maximum slope for a wheelchair ramp in new construction is 1:12, although slopes between 1:16 and 1:20 are preferred. The maximum rise for any run is 30 inches. The graph below shows the rise and runs of four different wheelchair ramps. Which ramp is in compliance with the ADA regulations for new construction?

A	A Hint: Rise is more than 30 inches.
B	B Hint: Run is almost 24 feet, so rise can be almost 2 feet.
C	C Hint: Run is 12 feet, so rise can be at most 1 foot.
D	D Hint: Slope is 1:10 -- too steep.

Question 9 Explanation:

Topic: Interpret meaning of slope in a real world situation (Objective 0022).

Question 10

The histogram below shows the number of pairs of footware owned by a group of college students.

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

A	The median number of pairs of footware owned is between 50 and 60 pairs. Hint: The same number of data points are less than the median as are greater than the median -- but on this histogram, clearly more than half the students own less than 50 pairs of shoes, so the median is less than 50.
B	The mode of the number of pairs of footware owned is 20. Hint: The mode is the most common number of pairs of footwear owned. We can't tell it from this histogram because each bar represents 10 different numbers-- perhaps 8 students each own each number from 10 to 19, but 40 students own exactly 6 pairs of shoes.... or perhaps not....
C	The mean number of pairs of footware owned is less than the median number of pairs of footware owned. Hint: This is a right skewed distribution, and so the mean is bigger than the median -- the few large values on the right pull up the mean, but have little effect on the median.
D	The median number of pairs of footware owned is between 10 and 20. Hint: There are approximately 230 students represented in this survey, and the 41st through 120th lowest values are between 10 and 20 -- thus the middle value is in that range.

Question 10 Explanation:

Topics: Analyze and interpret various graphic and data representations, and use measures of central tendency (e.g., mean, median, mode) and spread to describe and interpret real-world data (Objective 0025).

Question 11

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

$q21 fraction area$

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 11 Explanation:

Topic: Models of Fractions (Objective 0017)

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

If x is an integer, which of the following must also be an integer?

A	$ \large \dfrac{x}{2}$ Hint: If x is odd, then $ \dfrac{x}{2} $ is not an integer, e.g. 3/2 = 1.5.
B	$ \large \dfrac{2}{x}$ Hint: Only an integer if x = -2, -1, 1, or 2.
C	$ \large-x$ Hint: -1 times any integer is still an integer.
D	$\large\sqrt{x}$ Hint: Usually not an integer, e.g. $ \sqrt{2} \approx 1.414 $.

Question 13 Explanation:

Topic: Integers (Objective 0016)

Question 14

The table below gives the result of a survey at a college, asking students whether they were residents or commuters:

Based on the above data, what is the probability that a randomly chosen commuter student is a junior or a senior?

A	$ \large \dfrac{34}{43}$
B	$ \large \dfrac{34}{71}$ Hint: This is the probability that a randomly chosen junior or senior is a commuter student.
C	$ \large \dfrac{34}{147}$ Hint: This is the probability that a randomly chosen student is a junior or senior who is a commuter.
D	$ \large \dfrac{71}{147}$ Hint: This is the probability that a randomly chosen student is a junior or a senior.

Question 14 Explanation:

Topic: Recognize and apply the concept of conditional probability (Objective 0026).

Question 15

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 15 Explanation:

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

Question 16

The histogram below shows the frequency of a class's scores on a 4 question quiz.

What was the mean score on the quiz?

A	$ \large 2.75$ Hint: There were 20 students who took the quiz. Total points earned: $2 \times 1+6 \times 2+ 7\times 3+5 \times 4=55$, and 55/20 = 2.75.
B	$ \large 2$ Hint: How many students are there total? Did you count them all?
C	$ \large 3$ Hint: How many students are there total? Did you count them all? Be sure you're finding the mean, not the median or the mode.
D	$ \large 2.5$ Hint: How many students are there total? Did you count them all? Don't just take the mean of 1, 2, 3, 4 -- you have to weight them properly.

Question 16 Explanation:

Topics: Analyze and interpret various graphic representations, and use measures of central tendency (e.g., mean, median, mode) and spread to describe and interpret real-world data (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

Which property is not shared by all rhombi?

A	4 congruent sides Hint: The most common definition of a rhombus is a quadrilateral with 4 congruent sides.
B	A center of rotational symmetry Hint: The diagonal of a rhombus separates it into two congruent isosceles triangles. The center of this line is a center of 180 degree rotational symmetry that switches the triangles.
C	4 congruent angles Hint: Unless the rhombus is a square, it does not have 4 congruent angles.
D	2 sets of parallel sides Hint: All rhombi are parallelograms.

Question 18 Explanation:

Topic: Classify and analyze polygons using attributes of sides and angles, and symmetry (Objective 0024).

Question 19

Use the problem below to answer the question that follows:

T shirts are on sale for 20% off. Tasha paid $8.73 for a shirt. What is the regular price of the shirt? There is no tax on clothing purchases under $175.

Let p represent the regular price of these t-shirt. Which of the following equations is correct?

A	$ \large 0.8p=\$8.73$ Hint: 80% of the regular price = $8.73.
B	$ \large \$8.73+0.2*\$8.73=p$ Hint: The 20% off was off of the ORIGINAL price, not off the $8.73 (a lot of people make this mistake). Plus this is the same equation as in choice c.
C	$ \large 1.2*\$8.73=p$ Hint: The 20% off was off of the ORIGINAL price, not off the $8.73 (a lot of people make this mistake). Plus this is the same equation as in choice b.
D	$ \large p-0.2*\$8.73=p$ Hint: Subtract p from both sides of this equation, and you have -.2 x 8.73 =0.

Question 19 Explanation:

Topics: Use algebra to solve word problems involving percents and identify variables, and derive algebraic expressions that represent real-world situations (Objective 0020).

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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If you found a mistake or have comments on a particular question, please contact me (please copy and paste at least part of the question into the form, as the numbers change depending on how quizzes are displayed). General comments can be left here.

A	\( \large{{2}^{5}}\cdot {{3}^{6}}\cdot 5\) Hint: This is the product of the numbers, not the LCM.
B	\( \large{{2}^{3}}\cdot {{3}^{3}}\cdot 5\) 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 for each prime that's a factor of either number, use the largest exponent that appears in one of the factorizations. You can also take the product of the two numbers divided by their GCD.
C	\( \large{{2}^{2}}\cdot {{3}^{3}}\cdot 5\) Hint: 216 is a multiple of 8.
D	\( \large{{2}^{2}}\cdot {{3}^{2}}\cdot {{5}^{2}}\) Hint: Not a multiple of 216 and not a multiple of 540.

A	\( \large {{N}^{2}}\) Hint: Squaring always gives a non-negative value.
B	\( \large 6-N\) Hint: A story problem for this expression is, if it was 6 degrees out at noon and N degrees out at sunrise, by how many degrees did the temperature rise by noon? Since N is negative, the answer to this question has to be positive, and more than 6.
C	\( \large -N\) Hint: If N is negative, then -N is positive
D	\( \large 6+N\) Hint: For example, if \(N=-10\), then \(6+N = -4\)

A	\( \large0.26\) Hint: Please reread the question.
B	\( \large0.2625\) Hint: This is one-quarter of the distance between 0.26 and 0.27, which is not what the question asked.
C	\( \large0.265\)
D	\( \large0.27\) Hint: Please read the question more carefully. This answer would be correct if Point A were halfway between the tick marks, but it's not.

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	\( \large \dfrac{7}{16}\) 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.

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.

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?

A	\( \large \dfrac{x}{2}\) Hint: If x is odd, then \( \dfrac{x}{2} \) is not an integer, e.g. 3/2 = 1.5.
B	\( \large \dfrac{2}{x}\) Hint: Only an integer if x = -2, -1, 1, or 2.
C	\( \large-x\) Hint: -1 times any integer is still an integer.
D	\(\large\sqrt{x}\) Hint: Usually not an integer, e.g. \( \sqrt{2} \approx 1.414 \).

A	\( \large \dfrac{34}{43}\)
B	\( \large \dfrac{34}{71}\) Hint: This is the probability that a randomly chosen junior or senior is a commuter student.
C	\( \large \dfrac{34}{147}\) Hint: This is the probability that a randomly chosen student is a junior or senior who is a commuter.
D	\( \large \dfrac{71}{147}\) Hint: This is the probability that a randomly chosen student is a junior or a senior.

A	\( \large 2.75\) Hint: There were 20 students who took the quiz. Total points earned: \(2 \times 1+6 \times 2+ 7\times 3+5 \times 4=55\), and 55/20 = 2.75.
B	\( \large 2\) Hint: How many students are there total? Did you count them all?
C	\( \large 3\) Hint: How many students are there total? Did you count them all? Be sure you're finding the mean, not the median or the mode.
D	\( \large 2.5\) Hint: How many students are there total? Did you count them all? Don't just take the mean of 1, 2, 3, 4 -- you have to weight them properly.

A	\( \large 0.8p=\$8.73\) Hint: 80% of the regular price = $8.73.
B	\( \large \$8.73+0.2*\$8.73=p\) Hint: The 20% off was off of the ORIGINAL price, not off the $8.73 (a lot of people make this mistake). Plus this is the same equation as in choice c.
C	\( \large 1.2*\$8.73=p\) Hint: The 20% off was off of the ORIGINAL price, not off the $8.73 (a lot of people make this mistake). Plus this is the same equation as in choice b.
D	\( \large p-0.2*\$8.73=p\) Hint: Subtract p from both sides of this equation, and you have -.2 x 8.73 =0.

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.

MTEL General Curriculum Mathematics Practice

What is the least common multiple of 540 and 216?

In each expression below N represents a negative integer. Which expression could have a negative value?

Below is a portion of a number line.

Point A is one-quarter of the distance from 0.26 to 0.28. What number is represented by point A?

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

A homeowner is planning to tile the kitchen floor with tiles that measure 6 inches by 8 inches. The kitchen floor is a rectangle that measures 10 ft by 12 ft, and there are no gaps between the tiles. How many tiles does the homeowner need?

30

120

300

360

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

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

What set of transformations will transform the leftmost image into the rightmost image?

A 90 degree clockwise rotation about (2,1) followed by a translation of two units to the right.

A translation 3 units up, followed by a reflection about the line y=x.

A 90 degree clockwise rotation about (5,1), followed by a translation of 2 units up.

A 90 degree clockwise rotation about (2,1) followed by a translation of 2 units to the right.

A

B

C

D

The histogram below shows the number of pairs of footware owned by a group of college students.

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

The median number of pairs of footware owned is between 50 and 60 pairs.

The mode of the number of pairs of footware owned is 20.

The mean number of pairs of footware owned is less than the median number of pairs of footware owned.

The median number of pairs of footware owned is between 10 and 20.

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

How many factors does 80 have?

If x is an integer, which of the following must also be an integer?

The table below gives the result of a survey at a college, asking students whether they were residents or commuters:

Based on the above data, what is the probability that a randomly chosen commuter student is a junior or a senior?

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

The histogram below shows the frequency of a class's scores on a 4 question quiz.

What was the mean score on the quiz?

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?

The teacher can be sure that the mean and median will be the same without doing any computation.

The teacher can be sure that the mean is bigger than the median without doing any computation.

The teacher can be sure that the median is bigger than the mean without doing any computation.

There is no way for the teacher to know the relative size of the mean and median without computing them.

Which property is not shared by all rhombi?

4 congruent sides

A center of rotational symmetry

4 congruent angles

2 sets of parallel sides

Use the problem below to answer the question that follows:

T shirts are on sale for 20% off. Tasha paid $8.73 for a shirt. What is the regular price of the shirt? There is no tax on clothing purchases under $175.

Let p represent the regular price of these t-shirt. Which of the following equations is correct?

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