45 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

Please wait while the activity loads.
If this activity does not load, try refreshing your browser. Also, this page requires javascript. Please visit using a browser with javascript enabled.

If loading fails, click here to try again

Your answers are highlighted below.

Question 1

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 1 Explanation:

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

Question 2

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 2 Explanation:

Topic: Models of Fractions (Objective 0017)

Question 3

Use the table below to answer the question that follows:

Each number in the table above represents a value W that is determined by the values of x and y. For example, when x=3 and y=1, W=5. What is the value of W when x=9 and y=14? Assume that the patterns in the table continue as shown.

A	$ \large W=-5$ Hint: When y is even, W is even.
B	$ \large W=4$ Hint: Note that when x increases by 1, W increases by 2, and when y increases by 1, W decreases by 1. At x=y=0, W=0, so at x=9, y=14, W has increased by $9 \times 2$ and decreased by 14, or W=18-14=4.
C	$ \large W=6$ Hint: Try fixing x or y at 0, and start by finding W for x=0 y=14 or x=9, y=0.
D	$ \large W=32$ Hint: Try fixing x or y at 0, and start by finding W for x=0 y=14 or x=9, y=0.

Question 3 Explanation:

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

Question 4

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 4 Explanation:

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

Question 5

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

A	$ \large -0.044,\quad -0.04,\quad 0.04,\quad 0.044$ Hint: These are easier to compare if you add trailing zeroes (this is finding a common denominator) -- all in thousandths, -0.044, -0.040,0 .040, 0.044. The middle two numbers, -0.040 and 0.040 can be modeled as owing 4 cents and having 4 cents. The outer two numbers are owing or having a bit more.
B	$ \large -0.04,\quad -0.044,\quad 0.044,\quad 0.04$ Hint: 0.04=0.040, which is less than 0.044.
C	$ \large -0.04,\quad -0.044,\quad 0.04,\quad 0.044$ Hint: -0.04=-0.040, which is greater than $-0.044$.
D	$ \large -0.044,\quad -0.04,\quad 0.044,\quad 0.04$ Hint: 0.04=0.040, which is less than 0.044.

Question 5 Explanation:

Topic: Ordering decimals and integers (Objective 0017).

Question 6

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 6 Explanation:

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

Question 7

Below is a portion of a number line:

Point B is halfway between two tick marks. What number is represented by Point B?

A	$ \large 0.645$ Hint: That point is marked on the line, to the right.
B	$ \large 0.6421$ Hint: That point is to the left of point B.
C	$ \large 0.6422$ Hint: That point is to the left of point B.
D	$ \large 0.6425$

Question 7 Explanation:

Topic: Using Number Lines (Objective 0017)

Question 8

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 8 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 9

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 9 Explanation:

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

Question 10

Which of the following is not possible?

A	An equiangular triangle that is not equilateral. Hint: The AAA property of triangles states that all triangles with corresponding angles congruent are similar. Thus all triangles with three equal angles are similar, and are equilateral.
B	An equiangular quadrilateral that is not equilateral. Hint: A rectangle is equiangular (all angles the same measure), but if it's not a square, it's not equilateral (all sides the same length).
C	An equilateral quadrilateral that is not equiangular. Hint: This rhombus has equal sides, but it doesn't have equal angles:
D	An equiangular hexagon that is not equilateral. Hint: This hexagon has equal angles, but it doesn't have equal sides:

Question 10 Explanation:

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

Question 11

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 11 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 12

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 12 Explanation:

Topic: Integers (Objective 0016)

Question 13

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

A	a Hint: The slope of line a is negative.
B	b Hint: Wrong slope and wrong intercept.
C	c Hint: The intercept of line c is positive.
D	d Hint: Slope is 2 -- for every increase of 1 in x, y increases by 2. Intercept is -5 -- the point (0,-5) is on the line.

Question 13 Explanation:

Topic: Find a linear equation that represents a graph (Objective 0022).

Question 14

Which of the numbers below is the decimal equivalent of $ \dfrac{3}{8}?$

A	0.38 Hint: If you are just writing the numerator next to the denominator then your technique is way off, but by coincidence your answer is close; try with 2/3 and 0.23 is nowhere near correct.
B	0.125 Hint: This is 1/8, not 3/8.
C	0.375
D	0.83 Hint: 3/8 is less than a half, and 0.83 is more than a half, so they can't be equal.

Question 14 Explanation:

Topic: Converting between fractions and decimals (Objective 0017)

Question 15

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 15 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 16

The letters A, and B represent digits (possibly equal) in the ten digit number x=1,438,152,A3B. For which values of A and B is x divisible by 12, but not by 9?

A	$ \large A = 0, B = 4$ Hint: Digits add to 31, so not divisible by 3, so not divisible by 12.
B	$ \large A = 7, B = 2$ Hint: Digits add to 36, so divisible by 9.
C	$ \large A = 0, B = 6$ Hint: Digits add to 33, divisible by 3, not 9. Last digits are 36, so divisible by 4, and hence by 12.
D	$ \large A = 4, B = 8$ Hint: Digits add to 39, divisible by 3, not 9. Last digits are 38, so not divisible by 4, so not divisible by 12.

Question 16 Explanation:

Topic: Demonstrate knowledge of divisibility rules (Objective 0018).

Question 17

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 17 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 18

The expression $ \large{{8}^{3}}\cdot {{2}^{-10}}$ is equal to which of the following?

A	$ \large 2$ Hint: Write $8^3$ as a power of 2.
B	$ \large \dfrac{1}{2}$ Hint: $8^3 \cdot {2}^{-10}={(2^3)}^3 \cdot {2}^{-10}$ =$2^9 \cdot {2}^{-10} =2^{-1}$
C	$ \large 16$ Hint: Write $8^3$ as a power of 2.
D	$ \large \dfrac{1}{16}$ Hint: Write $8^3$ as a power of 2.

Question 18 Explanation:

Topic: Laws of Exponents (Objective 0019).

Question 19

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 19 Explanation:

Topic: Apply knowledge of combinations and permutations to the computation of probabilities (Objective 0026).

Question 20

Use the table below to answer the question that follows:

Gordon wants to buy three pounds of nuts. Each of the stores above ordinarily sells the nuts for $4.99 a pound, but is offering a discount this week. At which store can he buy the nuts for the least amount of money?

A	Store A Hint: This would save about $2.50. You can quickly see that D saves more.
B	Store B Hint: This saves 15% and C saves 25%.
C	Store C
D	Store D Hint: This is about 20% off, which is less of a discount than C.

Question 20 Explanation:

Topic: Understand the meanings and models of integers, fractions, decimals,percents, and mixed numbers and apply them to the solution of word problems (Objective 0017).

Question 21

Which of the following is the equation of a linear function?

A	$ \large y={{x}^{2}}+2x+7$ Hint: This is a quadratic function.
B	$ \large y={{2}^{x}}$ Hint: This is an exponential function.
C	$ \large y=\dfrac{15}{x}$ Hint: This is an inverse function.
D	$ \large y=x+(x+4)$ Hint: This is a linear function, y=2x+4, it's graph is a straight line with slope 2 and y-intercept 4.

Question 21 Explanation:

Topic: Distinguish between linear and nonlinear functions (Objective 0022).

Question 22

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 22 Explanation:

Topic: Use measures of central tendency (e.g., mean, median, mode) and spread to describe and interpret real-world data (Objective 0025).

Question 23

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 23 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 24

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 24 Explanation:

Topic: Scientific Notation (Objective 0016)

Question 25

In the triangle below, $\overline{AC}\cong \overline{AD}\cong \overline{DE}$ and $m\angle CAD=100{}^\circ $. What is $m\angle DAE$?

A	$ \large 20{}^\circ $ Hint: Angles ACD and ADC are congruent since they are base angles of an isosceles triangle. Since the angles of a triangle sum to 180, they sum to 80, and they are 40 deg each. Thus angle ADE is 140 deg, since it makes a straight line with angle ADC. Angles DAE and DEA are base angles of an isosceles triangle and thus congruent-- they sum to 40 deg, so are 20 deg each.
B	$ \large 25{}^\circ $ Hint: If two sides of a triangle are congruent, then it's isosceles, and the base angles of an isosceles triangle are equal.
C	$ \large 30{}^\circ $ Hint: If two sides of a triangle are congruent, then it's isosceles, and the base angles of an isosceles triangle are equal.
D	$ \large 40{}^\circ $ Hint: Make sure you're calculating the correct angle.

Question 25 Explanation:

Topic: Classify and analyze polygons using attributes of sides and angles, including real-world applications. (Objective 0024).

Question 26

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 26 Explanation:

Topics: Laws of exponents (Objective 0019).

Question 27

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 27 Explanation:

Topic: Converting between fractions, decimals, and percents (Objective 0017)

Question 28

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 28 Explanation:

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

Question 29

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 29 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 30

Here is a method that a student used for subtraction:

Which of the following is correct?

A	The student used a method that worked for this problem and can be generalized to any subtraction problem. Hint: Note that this algorithm is taught as the "standard" algorithm in much of Europe (it's where the term "borrowing" came from -- you borrow on top and "pay back" on the bottom).
B	The student used a method that worked for this problem and that will work for any subtraction problem that only requires one regrouping; it will not work if more regrouping is required. Hint: Try some more examples.
C	The student used a method that worked for this problem and will work for all three-digit subtraction problems, but will not work for larger problems. Hint: Try some more examples.
D	The student used a method that does not work. The student made two mistakes that cancelled each other out and was lucky to get the right answer for this problem. Hint: Remember, there are many ways to do subtraction; there is no one "right" algorithm.

Question 30 Explanation:

Topic: Analyze and justify standard and non-standard computational techniques (Objective 0019).

Question 31

A car is traveling at 60 miles per hour. Which of the expressions below could be used to compute how many feet the car travels in 1 second? Note that 1 mile = 5,280 feet.

A	$ \large 60\dfrac{\text{miles}}{\text{hour}}\cdot 5280\dfrac{\text{feet}}{\text{mile}}\cdot 60\dfrac{\text{minutes}}{\text{hour}}\cdot 60\dfrac{\text{seconds}}{\text{minute}} $ Hint: This answer is not in feet/second.
B	$ \large 60\dfrac{\text{miles}}{\text{hour}}\cdot 5280\dfrac{\text{feet}}{\text{mile}}\cdot \dfrac{1}{60}\dfrac{\text{hour}}{\text{minutes}}\cdot \dfrac{1}{60}\dfrac{\text{minute}}{\text{seconds}} $ Hint: This is the only choice where the answer is in feet per second and the unit conversions are correct.
C	$ \large 60\dfrac{\text{miles}}{\text{hour}}\cdot \dfrac{1}{5280}\dfrac{\text{foot}}{\text{miles}}\cdot 60\dfrac{\text{hours}}{\text{minute}}\cdot \dfrac{1}{60}\dfrac{\text{minute}}{\text{seconds}}$ Hint: Are there really 60 hours in a minute?
D	$ \large 60\dfrac{\text{miles}}{\text{hour}}\cdot \dfrac{1}{5280}\dfrac{\text{mile}}{\text{feet}}\cdot 60\dfrac{\text{minutes}}{\text{hour}}\cdot \dfrac{1}{60}\dfrac{\text{minute}}{\text{seconds}}$ Hint: This answer is not in feet/second.

Question 31 Explanation:

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

Question 32

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 32 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 33

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 33 Explanation:

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

Question 34

The picture below shows identical circles drawn on a piece of paper. The rectangle represents an index card that is blocking your view of $ \dfrac{3}{5}$ of the circles on the paper. How many circles are covered by the rectangle?

$q22 fraction dots covered$

A	4 Hint: The card blocks more than half of the circles, so this number is too small.
B	5 Hint: The card blocks more than half of the circles, so this number is too small.
C	8 Hint: The card blocks more than half of the circles, so this number is too small.
D	12 Hint: 2/5 of the circles or 8 circles are showing. Thus 4 circles represent 1/5 of the circles, and $4 \times 5=20$ circles represent 5/5 or all the circles. Thus 12 circles are hidden.

Question 34 Explanation:

Topic: Models of Fractions (Objective 0017)

Question 35

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 35 Explanation:

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

Question 36

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 36 Explanation:

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

Question 37

The least common multiple of 60 and N is 1260. Which of the following could be the prime factorization of N?

A	$ \large2\cdot 5\cdot 7$ Hint: 1260 is divisible by 9 and 60 is not, so N must be divisible by 9 for 1260 to be the LCM.
B	$ \large{{2}^{3}}\cdot {{3}^{2}}\cdot 5 \cdot 7$ Hint: 1260 is not divisible by 8, so it isn't a multiple of this N.
C	$ \large3 \cdot 5 \cdot 7$ Hint: 1260 is divisible by 9 and 60 is not, so N must be divisible by 9 for 1260 to be the LCM.
D	$ \large{{3}^{2}}\cdot 5\cdot 7$ Hint: $1260=2^2 \cdot 3^2 \cdot 5 \cdot 7$ and $60=2^2 \cdot 3 \cdot 5$. In order for 1260 to be the LCM, N has to be a multiple of $3^2$ and of 7 (because 60 is not a multiple of either of these). N also cannot introduce a factor that would require the LCM to be larger (as in choice b).

Question 37 Explanation:

Topic: Least Common Multiple (Objective 0018)

Question 38

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 38 Explanation:

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

Question 39

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 39 Explanation:

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

Question 40

Below are front, side, and top views of a three-dimensional solid.

Which of the following could be the solid shown above?

A	A sphere Hint: All views would be circles.
B	A cylinder
C	A cone Hint: Two views would be triangles, not rectangles.
D	A pyramid Hint: How would one view be a circle?

Question 40 Explanation:

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

Question 41

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 41 Explanation:

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

Question 42

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 42 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 43

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

A	4 lines of reflective symmetry, 1 center of rotational symmetry. Hint: Try cutting out a shape like this one from paper, and fold where you think the lines of reflective symmetry are (or put a mirror there). Do things line up as you thought they would?
B	2 lines of reflective symmetry, 1 center of rotational symmetry. Hint: Try cutting out a shape like this one from paper, and fold where you think the lines of reflective symmetry are (or put a mirror there). Do things line up as you thought they would?
C	0 lines of reflective symmetry, 1 center of rotational symmetry. Hint: The intersection of the diagonals is a center of rotational symmetry. There are no lines of reflective symmetry, although many people get confused about this fact (best to play with hands on examples to get a feel). Just fyi, the letter S also has rotational, but not reflective symmetry, and it's one that kids often write backwards.
D	2 lines of reflective symmetry, 0 centers of rotational symmetry. Hint: Try cutting out a shape like this one from paper. Trace onto another sheet of paper. See if there's a way to rotate the cut out shape (less than a complete turn) so that it fits within the outlines again.

Question 43 Explanation:

Topic: Analyze geometric transformations (e.g., translations, rotations, reflections, dilations); relate them to concepts of symmetry (Objective 0024).

Question 44

The following story situations model $ 12\div 3$:

I) Jack has 12 cookies, which he wants to share equally between himself and two friends. How many cookies does each person get?

II) Trent has 12 cookies, which he wants to put into bags of 3 cookies each. How many bags can he make?

III) Cicely has $12. Cookies cost $3 each. How many cookies can she buy?

Which of these questions illustrate the same model of division, either partitive (partioning) or measurement (quotative)?

A	I and II
B	I and III
C	II and III Hint: Problem I is partitive (or partitioning or sharing) -- we put 12 objects into 3 groups. Problems II and III are quotative (or measurement) -- we put 12 objects in groups of 3.
D	All three problems model the same meaning of division

Question 44 Explanation:

Topic: Understand models of operations on numbers (Objective 0019).

Question 45

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 45 Explanation:

Topic: Using number lines (Objective 0017)

Once you are finished, click the button below. Any items you have not completed will be marked incorrect. Get Results

There are 45 questions to complete.

←

List

→

Return

Shaded items are complete.

1	2	3	4	5
6	7	8	9	10
11	12	13	14	15
16	17	18	19	20
21	22	23	24	25
26	27	28	29	30
31	32	33	34	35
36	37	38	39	40
41	42	43	44	45
End

Return

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	\( \large \dfrac{17}{24}\) 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	\( \large W=-5\) Hint: When y is even, W is even.
B	\( \large W=4\) Hint: Note that when x increases by 1, W increases by 2, and when y increases by 1, W decreases by 1. At x=y=0, W=0, so at x=9, y=14, W has increased by \(9 \times 2\) and decreased by 14, or W=18-14=4.
C	\( \large W=6\) Hint: Try fixing x or y at 0, and start by finding W for x=0 y=14 or x=9, y=0.
D	\( \large W=32\) Hint: Try fixing x or y at 0, and start by finding W for x=0 y=14 or x=9, y=0.

A	\( \large -0.044,\quad -0.04,\quad 0.04,\quad 0.044\) Hint: These are easier to compare if you add trailing zeroes (this is finding a common denominator) -- all in thousandths, -0.044, -0.040,0 .040, 0.044. The middle two numbers, -0.040 and 0.040 can be modeled as owing 4 cents and having 4 cents. The outer two numbers are owing or having a bit more.
B	\( \large -0.04,\quad -0.044,\quad 0.044,\quad 0.04\) Hint: 0.04=0.040, which is less than 0.044.
C	\( \large -0.04,\quad -0.044,\quad 0.04,\quad 0.044\) Hint: -0.04=-0.040, which is greater than \(-0.044\).
D	\( \large -0.044,\quad -0.04,\quad 0.044,\quad 0.04\) Hint: 0.04=0.040, which is less than 0.044.

A	\( \large 0.645\) Hint: That point is marked on the line, to the right.
B	\( \large 0.6421\) Hint: That point is to the left of point B.
C	\( \large 0.6422\) Hint: That point is to the left of point B.
D	\( \large 0.6425\)

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	\( \large 343.2\times 60\times 10\) 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.

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	\( \large 0.8p=\$8.73\) 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	\( \large A = 0, B = 4\) Hint: Digits add to 31, so not divisible by 3, so not divisible by 12.
B	\( \large A = 7, B = 2\) Hint: Digits add to 36, so divisible by 9.
C	\( \large A = 0, B = 6\) Hint: Digits add to 33, divisible by 3, not 9. Last digits are 36, so divisible by 4, and hence by 12.
D	\( \large A = 4, B = 8\) Hint: Digits add to 39, divisible by 3, not 9. Last digits are 38, so not divisible by 4, so not divisible by 12.

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	\( \large 2\) Hint: Write \(8^3\) as a power of 2.
B	\( \large \dfrac{1}{2}\) Hint: \(8^3 \cdot {2}^{-10}={(2^3)}^3 \cdot {2}^{-10}\) =\(2^9 \cdot {2}^{-10} =2^{-1}\)
C	\( \large 16\) Hint: Write \(8^3\) as a power of 2.
D	\( \large \dfrac{1}{16}\) Hint: Write \(8^3\) as a power of 2.

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.

A	\( \large y={{x}^{2}}+2x+7\) Hint: This is a quadratic function.
B	\( \large y={{2}^{x}}\) Hint: This is an exponential function.
C	\( \large y=\dfrac{15}{x}\) Hint: This is an inverse function.
D	\( \large y=x+(x+4)\) Hint: This is a linear function, y=2x+4, it's graph is a straight line with slope 2 and y-intercept 4.

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	\( \large 20{}^\circ \) Hint: Angles ACD and ADC are congruent since they are base angles of an isosceles triangle. Since the angles of a triangle sum to 180, they sum to 80, and they are 40 deg each. Thus angle ADE is 140 deg, since it makes a straight line with angle ADC. Angles DAE and DEA are base angles of an isosceles triangle and thus congruent-- they sum to 40 deg, so are 20 deg each.
B	\( \large 25{}^\circ \) Hint: If two sides of a triangle are congruent, then it's isosceles, and the base angles of an isosceles triangle are equal.
C	\( \large 30{}^\circ \) Hint: If two sides of a triangle are congruent, then it's isosceles, and the base angles of an isosceles triangle are equal.
D	\( \large 40{}^\circ \) Hint: Make sure you're calculating the correct angle.

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	\( \large \dfrac{1}{64\cdot {{\left( 56 \right)}^{4}}}\)

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. \(\large\dfrac{14}{35}\)

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	\( \large 60\dfrac{\text{miles}}{\text{hour}}\cdot 5280\dfrac{\text{feet}}{\text{mile}}\cdot 60\dfrac{\text{minutes}}{\text{hour}}\cdot 60\dfrac{\text{seconds}}{\text{minute}} \) Hint: This answer is not in feet/second.
B	\( \large 60\dfrac{\text{miles}}{\text{hour}}\cdot 5280\dfrac{\text{feet}}{\text{mile}}\cdot \dfrac{1}{60}\dfrac{\text{hour}}{\text{minutes}}\cdot \dfrac{1}{60}\dfrac{\text{minute}}{\text{seconds}} \) Hint: This is the only choice where the answer is in feet per second and the unit conversions are correct.
C	\( \large 60\dfrac{\text{miles}}{\text{hour}}\cdot \dfrac{1}{5280}\dfrac{\text{foot}}{\text{miles}}\cdot 60\dfrac{\text{hours}}{\text{minute}}\cdot \dfrac{1}{60}\dfrac{\text{minute}}{\text{seconds}}\) Hint: Are there really 60 hours in a minute?
D	\( \large 60\dfrac{\text{miles}}{\text{hour}}\cdot \dfrac{1}{5280}\dfrac{\text{mile}}{\text{feet}}\cdot 60\dfrac{\text{minutes}}{\text{hour}}\cdot \dfrac{1}{60}\dfrac{\text{minute}}{\text{seconds}}\) Hint: This answer is not in feet/second.

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	\( \large \dfrac{502}{1222}\) 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.

A	\( \large2\cdot 5\cdot 7\) Hint: 1260 is divisible by 9 and 60 is not, so N must be divisible by 9 for 1260 to be the LCM.
B	\( \large{{2}^{3}}\cdot {{3}^{2}}\cdot 5 \cdot 7\) Hint: 1260 is not divisible by 8, so it isn't a multiple of this N.
C	\( \large3 \cdot 5 \cdot 7\) Hint: 1260 is divisible by 9 and 60 is not, so N must be divisible by 9 for 1260 to be the LCM.
D	\( \large{{3}^{2}}\cdot 5\cdot 7\) Hint: \(1260=2^2 \cdot 3^2 \cdot 5 \cdot 7\) and \(60=2^2 \cdot 3 \cdot 5\). In order for 1260 to be the LCM, N has to be a multiple of \(3^2\) and of 7 (because 60 is not a multiple of either of these). N also cannot introduce a factor that would require the LCM to be larger (as in choice b).

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	\( \large 6g\) 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.

MTEL General Curriculum Mathematics Practice

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

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

Use the table below to answer the question that follows:

Each number in the table above represents a value W that is determined by the values of x and y. For example, when x=3 and y=1, W=5. What is the value of W when x=9 and y=14? Assume that the patterns in the table continue as shown.

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

P divides 30

P divides 48

P divides 75

P divides 80

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

Which property is not shared by all rhombi?

4 congruent sides

A center of rotational symmetry

4 congruent angles

2 sets of parallel sides

Below is a portion of a number line:

Point B is halfway between two tick marks. What number is represented by Point B?

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

What was the mean score on the quiz?

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)?

Which of the following is not possible?

An equiangular triangle that is not equilateral.

An equiangular quadrilateral that is not equilateral.

An equilateral quadrilateral that is not equiangular.

An equiangular hexagon that is not equilateral.

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.

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

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

a

b

c

d

Which of the numbers below is the decimal equivalent of \( \dfrac{3}{8}?\)

0.38

0.125

0.375

0.83

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?

The letters A, and B represent digits (possibly equal) in the ten digit number x=1,438,152,A3B. For which values of A and B is x divisible by 12, but not by 9?

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?

The expression \( \large{{8}^{3}}\cdot {{2}^{-10}}\) is equal to which of the following?

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%.

Use the table below to answer the question that follows:

Gordon wants to buy three pounds of nuts. Each of the stores above ordinarily sells the nuts for $4.99 a pound, but is offering a discount this week. At which store can he buy the nuts for the least amount of money?

Store A

Store B

Store C

Store D

Which of the following is the equation of a linear function?

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.

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?

The student‘s solution is correct.

The student did not correctly use properties of equality.

The student did not correctly use the distributive property.

The student did not correctly use the commutative property.

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.

1	2	3	4	5
6	7	8	9	10
11	12	13	14	15
16	17	18	19	20
21	22	23	24	25
26	27	28	29	30
31	32	33	34	35
36	37	38	39	40
41	42	43	44	45
End