20 Random Questions

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MTEL General Curriculum Mathematics Practice

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Question 1

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 1 Explanation:

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

Question 2

The chart below gives percentiles for the number of sit-ups that boys of various ages can do in 60 seconds (source , June 24, 2011)

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

A	95% of 12 year old boys can do 56 sit-ups in 60 seconds. Hint: The 95th percentile means that 95% of scores are less than or equal to 56, and 5% are greater than or equal to 56.
B	At most 25% of 7 year old boys can do 19 or more sit-ups in 60 seconds. Hint: The 25th percentile means that 25% of scores are less than or equal to 19, and 75% are greater than or equal to 19.
C	Half of all 13 year old boys can do less than 41 sit-ups in 60 seconds and half can do more than 41 sit-ups in 60 seconds. Hint: Close, but not quite. There's no accounting for boys who can do exactly 41 sit ups. Look at these data: 10, 20, 41, 41, 41, 41, 50, 60, 90. The median is 41, but more than half can do 41 or more.
D	At least 75% of 16 year old boys can only do 51 or fewer sit-ups in 60 seconds. Hint: The "at least" is necessary due to duplicates. Suppose the data were 10, 20, 51, 51. The 75th percentile is 51, but 100% of the boys can only do 51 or fewer situps.

Question 2 Explanation:

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

Question 3

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 3 Explanation:

Topic: Ordering Fractions (Objective 0017)

Question 4

Use the graph below to answer the question that follows:

The graph above best matches which of the following scenarios:

A	George left home at 10:00 and drove to work on a crooked path. He was stopped in traffic at 10:30 and 10:45. He drove 30 miles total. Hint: Just because he ended up 30 miles from home doesn't mean he drove 30 miles total.
B	George drove to work. On the way to work there is a little hill and a big hill. He slowed down for them. He made it to work at 11:15. Hint: The graph is not a picture of the roads.
C	George left home at 10:15. He drove 10 miles, then realized he‘d forgotten something at home. He turned back and got what he‘d forgotten. Then he drove in a straight line, at many different speeds, until he got to work around 11:15. Hint: A straight line on a distance versus time graph means constant speed.
D	George left home at 10:15. He drove 10 miles, then realized he‘d forgotten something at home. He turned back and got what he‘d forgotten. Then he drove at a constant speed until he got to work around 11:15.

Question 4 Explanation:

Topic: Use qualitative graphs to represent functional relationships in the real world (Objective 0021).

Question 5

Solve for x: $\large 4-\dfrac{2}{3}x=2x$

A	$ \large x=3$ Hint: Try plugging x=3 into the equation.
B	$ \large x=-3$ Hint: Left side is positive, right side is negative when you plug this in for x.
C	$ \large x=\dfrac{3}{2}$ Hint: One way to solve: $4=\dfrac{2}{3}x+2x$ $=\dfrac{8}{3}x$.$x=\dfrac{3 \times 4}{8}=\dfrac{3}{2}$. Another way is to just plug x=3/2 into the equation and see that each side equals 3 -- on a multiple choice test, you almost never have to actually solve for x.
D	$ \large x=-\dfrac{3}{2}$ Hint: Left side is positive, right side is negative when you plug this in for x.

Question 5 Explanation:

Topic: Solve linear equations (Objective 0020).

Question 6

Here is a mental math strategy for computing 26 x 16:

Step 1: 100 x 16 = 1600

Step 2: 25 x 16 = 1600 ÷· 4 = 400

Step 3: 26 x 16 = 400 + 16 = 416

Which property best justifies Step 3 in this strategy?

A	Commutative Property. Hint: For addition, the commutative property is $a+b=b+a$ and for multiplication it's $ a \times b = b \times a$.
B	Associative Property. Hint: For addition, the associative property is $(a+b)+c=a+(b+c)$ and for multiplication it's $(a \times b) \times c=a \times (b \times c)$
C	Identity Property. Hint: 0 is the additive identity, because $ a+0=a$ and 1 is the multiplicative identity because $a \times 1=a$. The phrase "identity property" is not standard.
D	Distributive Property. Hint: $ (25+1) \times 16 = 25 \times 16 + 1 \times 16 $. This is an example of the distributive property of multiplication over addition.

Question 6 Explanation:

Topic: Analyze and justify mental math techniques, by applying arithmetic properties such as commutative, distributive, and associative (Objective 0019). Note that it's hard to write a question like this as a multiple choice question -- worthwhile to understand why the other steps work too.

Question 7

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 7 Explanation:

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

Question 8

The letters A, B, and C represent digits (possibly equal) in the twelve digit number x=111,111,111,ABC. For which values of A, B, and C is x divisible by 40?

A	$ \large A = 3, B = 2, C=0$ Hint: Note that it doesn't matter what the first 9 digits are, since 1000 is divisible by 40, so DEF,GHI,JKL,000 is divisible by 40 - we need to check the last 3.
B	$ \large A = 0, B = 0, C=4$ Hint: Not divisible by 10, since it doesn't end in 0.
C	$ \large A = 4, B = 2, C=0$ Hint: Divisible by 10 and by 4, but not by 40, as it's not divisible by 8. Look at 40 as the product of powers of primes -- 8 x 5, and check each. To check 8, either check whether 420 is divisible by 8, or take ones place + twice tens place + 4 * hundreds place = 18, which is not divisible by 8.
D	$ \large A =1, B=0, C=0$ Hint: Divisible by 10 and by 4, but not by 40, as it's not divisible by 8. Look at 40 as the product of powers of primes -- 8 x 5, and check each. To check 8, either check whether 100 is divisible by 8, or take ones place + twice tens place + 4 * hundreds place = 4, which is not divisible by 8.

Question 8 Explanation:

Topic: Understand divisibility rules and why they work (Objective 018).

Question 9

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 9 Explanation:

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

Question 10

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 10 Explanation:

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

Question 11

Four children randomly line up, single file. What is the probability that they are in height order, with the shortest child in front? All of the children are different heights.

A	$ \large \dfrac{1}{4}$ Hint: Try a simpler question with 3 children -- call them big, medium, and small -- and list all the ways they could line up. Then see how to extend your logic to the problem with 4 children.
B	$ \large \dfrac{1}{256} $ Hint: Try a simpler question with 3 children -- call them big, medium, and small -- and list all the ways they could line up. Then see how to extend your logic to the problem with 4 children.
C	$ \large \dfrac{1}{16}$ Hint: Try a simpler question with 3 children -- call them big, medium, and small -- and list all the ways they could line up. Then see how to extend your logic to the problem with 4 children.
D	$ \large \dfrac{1}{24}$ Hint: The number of ways for the children to line up is $4!=4 \times 3 \times 2 \times 1 =24$ -- there are 4 choices for who is first in line, then 3 for who is second, etc. Only one of these lines has the children in the order specified.

Question 11 Explanation:

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

Question 12

Use the four figures below to answer the question that follows:

How many of the figures pictured above have at least one line of reflective symmetry?

A	$ \large 1$
B	$ \large 2$ Hint: The ellipse has 2 lines of reflective symmetry (horizontal and vertical, through the center) and the triangle has 3. The other two figures have rotational symmetry, but not reflective symmetry.
C	$ \large 3$
D	$ \large 4$ Hint: All four have rotational symmetry, but not reflective symmetry.

Question 12 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 13

Use the expression below to answer the question that follows.

$\large \dfrac{\left( 155 \right)\times \left( 6,124 \right)}{977}$

Which of the following is the best estimate of the expression above?

A	100 Hint: 6124/977 is approximately 6.
B	200 Hint: 6124/977 is approximately 6.
C	1,000 Hint: 6124/977 is approximately 6. 155 is approximately 150, and $ 6 \times 150 = 3 \times 300 = 900$, so this answer is closest.
D	2,000 Hint: 6124/977 is approximately 6.

Question 13 Explanation:

Topics: Estimation, simplifying fractions (Objective 0016).

Question 14

The column below consists of two cubes and a cylinder. The cylinder has diameter y, which is also the length of the sides of each cube. The total height of the column is 5y. Which of the formulas below gives the volume of the column?

A	$ \large 2{{y}^{3}}+\dfrac{3\pi {{y}^{3}}}{4}$ Hint: The cubes each have volume $y^3$. The cylinder has radius $\dfrac{y}{2}$ and height $3y$. The volume of a cylinder is $\pi r^2 h=\pi ({\dfrac{y}{2}})^2(3y)=\dfrac{3\pi {{y}^{3}}}{4}$. Note that the volume of a cylinder is analogous to that of a prism -- area of the base times height.
B	$ \large 2{{y}^{3}}+3\pi {{y}^{3}}$ Hint: y is the diameter of the circle, not the radius.
C	$ \large {{y}^{3}}+5\pi {{y}^{3}}$ Hint: Don't forget to count both cubes.
D	$ \large 2{{y}^{3}}+\dfrac{3\pi {{y}^{3}}}{8}$ Hint: Make sure you know how to find the volume of a cylinder.

Question 14 Explanation:

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

Question 15

The equation $ \large F=\frac{9}{5}C+32$ is used to convert a temperature measured in Celsius to the equivalent Farentheit temperature.

A patient's temperature increased by 1.5° Celcius. By how many degrees Fahrenheit did her temperature increase?

A	1.5° Hint: Celsius and Fahrenheit don't increase at the same rate.
B	1.8° Hint: That's how much the Fahrenheit temp increases when the Celsius temp goes up by 1 degree.
C	2.7° Hint: Each degree increase in Celsius corresponds to a $\dfrac{9}{5}=1.8$ degree increase in Fahrenheit. Thus the increase is 1.8+0.9=2.7.
D	Not enough information. Hint: A linear equation has constant slope, which means that every increase of the same amount in one variable, gives a constant increase in the other variable. It doesn't matter what temperature the patient started out at.

Question 15 Explanation:

Topic: Interpret the meaning of the slope and the intercepts of a linear equation that models a real-world situation (Objective 0022).

Question 16

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 16 Explanation:

Topic: Integers (Objective 0016)

Question 17

Which of the following is an irrational number?

A	$ \large \sqrt[3]{8}$ Hint: This answer is the cube root of 8. Since 2 x 2 x 2 =8, this is equal to 2, which is rational because 2 = 2/1.
B	$ \large \sqrt{8}$ Hint: It is not trivial to prove that this is irrational, but you can get this answer by eliminating the other choices.
C	$ \large \dfrac{1}{8}$ Hint: 1/8 is the RATIO of two integers, so it is rational.
D	$ \large -8$ Hint: Negative integers are also rational, -8 = -8/1, a ratio of integers.

Question 17 Explanation:

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

Question 18

The window glass below has the shape of a semi-circle on top of a square, where the side of the square has length x. It was cut from one piece of glass.

What is the perimeter of the window glass?

A	$ \large 3x+\dfrac{\pi x}{2}$ Hint: By definition, $\pi$ is the ratio of the circumference of a circle to its diameter; thus the circumference is $\pi d$. Since we have a semi-circle, its perimeter is $ \dfrac{1}{2} \pi x$. Only 3 sides of the square contribute to the perimeter.
B	$ \large 3x+2\pi x$ Hint: Make sure you know how to find the circumference of a circle.
C	$ \large 3x+\pi x$ Hint: Remember it's a semi-circle, not a circle.
D	$ \large 4x+2\pi x$ Hint: Only 3 sides of the square contribute to the perimeter.

Question 18 Explanation:

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

Question 19

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 19 Explanation:

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

Question 20

Which of the following is closest to the height of a college student in centimeters?

A	1.6 cm Hint: This is more the height of a Lego toy college student -- less than an inch!
B	16 cm Hint: Less than knee high on most college students.
C	160 cm Hint: Remember, a meter stick (a little bigger than a yard stick) is 100 cm. Also good to know is that 4 inches is approximately 10 cm.
D	1600 cm Hint: This college student might be taller than some campus buildings!

Question 20 Explanation:

Topic: Estimate and calculate measurements using customary, metric, and nonstandard units of measurement (Objective 0023).

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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.

A	\( \large x=3\) Hint: Try plugging x=3 into the equation.
B	\( \large x=-3\) Hint: Left side is positive, right side is negative when you plug this in for x.
C	\( \large x=\dfrac{3}{2}\) Hint: One way to solve: \(4=\dfrac{2}{3}x+2x\) \(=\dfrac{8}{3}x\).\(x=\dfrac{3 \times 4}{8}=\dfrac{3}{2}\). Another way is to just plug x=3/2 into the equation and see that each side equals 3 -- on a multiple choice test, you almost never have to actually solve for x.
D	\( \large x=-\dfrac{3}{2}\) Hint: Left side is positive, right side is negative when you plug this in for x.

A	Commutative Property. Hint: For addition, the commutative property is \(a+b=b+a\) and for multiplication it's \( a \times b = b \times a\).
B	Associative Property. Hint: For addition, the associative property is \((a+b)+c=a+(b+c)\) and for multiplication it's \((a \times b) \times c=a \times (b \times c)\)
C	Identity Property. Hint: 0 is the additive identity, because \( a+0=a\) and 1 is the multiplicative identity because \(a \times 1=a\). The phrase "identity property" is not standard.
D	Distributive Property. Hint: \( (25+1) \times 16 = 25 \times 16 + 1 \times 16 \). This is an example of the distributive property of multiplication over addition.

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	\( \large A = 3, B = 2, C=0\) Hint: Note that it doesn't matter what the first 9 digits are, since 1000 is divisible by 40, so DEF,GHI,JKL,000 is divisible by 40 - we need to check the last 3.
B	\( \large A = 0, B = 0, C=4\) Hint: Not divisible by 10, since it doesn't end in 0.
C	\( \large A = 4, B = 2, C=0\) Hint: Divisible by 10 and by 4, but not by 40, as it's not divisible by 8. Look at 40 as the product of powers of primes -- 8 x 5, and check each. To check 8, either check whether 420 is divisible by 8, or take ones place + twice tens place + 4 * hundreds place = 18, which is not divisible by 8.
D	\( \large A =1, B=0, C=0\) Hint: Divisible by 10 and by 4, but not by 40, as it's not divisible by 8. Look at 40 as the product of powers of primes -- 8 x 5, and check each. To check 8, either check whether 100 is divisible by 8, or take ones place + twice tens place + 4 * hundreds place = 4, which is not divisible by 8.

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	\( \large \dfrac{1}{4}\) Hint: Try a simpler question with 3 children -- call them big, medium, and small -- and list all the ways they could line up. Then see how to extend your logic to the problem with 4 children.
B	\( \large \dfrac{1}{256} \) Hint: Try a simpler question with 3 children -- call them big, medium, and small -- and list all the ways they could line up. Then see how to extend your logic to the problem with 4 children.
C	\( \large \dfrac{1}{16}\) Hint: Try a simpler question with 3 children -- call them big, medium, and small -- and list all the ways they could line up. Then see how to extend your logic to the problem with 4 children.
D	\( \large \dfrac{1}{24}\) Hint: The number of ways for the children to line up is \(4!=4 \times 3 \times 2 \times 1 =24\) -- there are 4 choices for who is first in line, then 3 for who is second, etc. Only one of these lines has the children in the order specified.

A	\( \large 1\)
B	\( \large 2\) Hint: The ellipse has 2 lines of reflective symmetry (horizontal and vertical, through the center) and the triangle has 3. The other two figures have rotational symmetry, but not reflective symmetry.
C	\( \large 3\)
D	\( \large 4\) Hint: All four have rotational symmetry, but not reflective symmetry.

A	\( \large 2{{y}^{3}}+\dfrac{3\pi {{y}^{3}}}{4}\) Hint: The cubes each have volume \(y^3\). The cylinder has radius \(\dfrac{y}{2}\) and height \(3y\). The volume of a cylinder is \(\pi r^2 h=\pi ({\dfrac{y}{2}})^2(3y)=\dfrac{3\pi {{y}^{3}}}{4}\). Note that the volume of a cylinder is analogous to that of a prism -- area of the base times height.
B	\( \large 2{{y}^{3}}+3\pi {{y}^{3}}\) Hint: y is the diameter of the circle, not the radius.
C	\( \large {{y}^{3}}+5\pi {{y}^{3}}\) Hint: Don't forget to count both cubes.
D	\( \large 2{{y}^{3}}+\dfrac{3\pi {{y}^{3}}}{8}\) Hint: Make sure you know how to find the volume of a cylinder.

A	\( \large \dfrac{x}{2}\) 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	\( \large \sqrt[3]{8}\) Hint: This answer is the cube root of 8. Since 2 x 2 x 2 =8, this is equal to 2, which is rational because 2 = 2/1.
B	\( \large \sqrt{8}\) Hint: It is not trivial to prove that this is irrational, but you can get this answer by eliminating the other choices.
C	\( \large \dfrac{1}{8}\) Hint: 1/8 is the RATIO of two integers, so it is rational.
D	\( \large -8\) Hint: Negative integers are also rational, -8 = -8/1, a ratio of integers.

A	\( \large 3x+\dfrac{\pi x}{2}\) Hint: By definition, \(\pi\) is the ratio of the circumference of a circle to its diameter; thus the circumference is \(\pi d\). Since we have a semi-circle, its perimeter is \( \dfrac{1}{2} \pi x\). Only 3 sides of the square contribute to the perimeter.
B	\( \large 3x+2\pi x\) Hint: Make sure you know how to find the circumference of a circle.
C	\( \large 3x+\pi x\) Hint: Remember it's a semi-circle, not a circle.
D	\( \large 4x+2\pi x\) Hint: Only 3 sides of the square contribute to the perimeter.

MTEL General Curriculum Mathematics Practice

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

Which of the following could be the solid shown above?

A sphere

A cylinder

A cone

A pyramid

The chart below gives percentiles for the number of sit-ups that boys of various ages can do in 60 seconds (source , June 24, 2011)

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

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

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

Half of all 13 year old boys can do less than 41 sit-ups in 60 seconds and half can do more than 41 sit-ups in 60 seconds.

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

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

Use the graph below to answer the question that follows:

The graph above best matches which of the following scenarios:

George left home at 10:00 and drove to work on a crooked path. He was stopped in traffic at 10:30 and 10:45. He drove 30 miles total.

George drove to work. On the way to work there is a little hill and a big hill. He slowed down for them. He made it to work at 11:15.

George left home at 10:15. He drove 10 miles, then realized he‘d forgotten something at home. He turned back and got what he‘d forgotten. Then he drove in a straight line, at many different speeds, until he got to work around 11:15.

George left home at 10:15. He drove 10 miles, then realized he‘d forgotten something at home. He turned back and got what he‘d forgotten. Then he drove at a constant speed until he got to work around 11:15.

Solve for x: \(\large 4-\dfrac{2}{3}x=2x\)

Here is a mental math strategy for computing 26 x 16:

Step 1: 100 x 16 = 1600

Step 2: 25 x 16 = 1600 ÷· 4 = 400

Step 3: 26 x 16 = 400 + 16 = 416

Which property best justifies Step 3 in this strategy?

Commutative Property.

Associative Property.

Identity Property.

Distributive Property.

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

The letters A, B, and C represent digits (possibly equal) in the twelve digit number x=111,111,111,ABC. For which values of A, B, and C is x divisible by 40?

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 is the least common multiple of 540 and 216?

Four children randomly line up, single file. What is the probability that they are in height order, with the shortest child in front? All of the children are different heights.

Use the four figures below to answer the question that follows:

How many of the figures pictured above have at least one line of reflective symmetry?

Use the expression below to answer the question that follows.

\(\large \dfrac{\left( 155 \right)\times \left( 6,124 \right)}{977}\)

Which of the following is the best estimate of the expression above?

100

200

1,000

2,000

The column below consists of two cubes and a cylinder. The cylinder has diameter y, which is also the length of the sides of each cube. The total height of the column is 5y. Which of the formulas below gives the volume of the column?

The equation \( \large F=\frac{9}{5}C+32\) is used to convert a temperature measured in Celsius to the equivalent Farentheit temperature.

A patient's temperature increased by 1.5° Celcius. By how many degrees Fahrenheit did her temperature increase?

1.5°

1.8°

2.7°

Not enough information.

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

Which of the following is an irrational number?

The window glass below has the shape of a semi-circle on top of a square, where the side of the square has length x. It was cut from one piece of glass.

What is the perimeter of the window glass?

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.

Which of the following is closest to the height of a college student in centimeters?

1.6 cm

16 cm

160 cm

1600 cm