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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


Your answers are highlighted below.
Question 1

In March of 2012, 1 dollar was worth the same as 0.761 Euros, and 1 dollar was also worth the same as 83.03 Japanese Yen.  Which of the expressions below gives the number of Yen that are worth 1 Euro?

A
\( \large {83}.0{3}\cdot 0.{761}\)
Hint:
This equation gives less than the number of yen per dollar, but 1 Euro is worth more than 1 dollar.
B
\( \large \dfrac{0.{761}}{{83}.0{3}}\)
Hint:
Number is way too small.
C
\( \large \dfrac{{83}.0{3}}{0.{761}}\)
Hint:
One strategy here is to use easier numbers, say 1 dollar = .5 Euros and 100 yen, then 1 Euro would be 200 Yen (change the numbers in the equations and see what works). Another is to use dimensional analysis: we want # yen per Euro, or yen/Euro = yen/dollar \(\times\) dollar/Euro = \(83.03 \times \dfrac {1}{0.761}\)
D
\( \large \dfrac{1}{0.{761}}\cdot \dfrac{1}{{83}.0{3}}\)
Hint:
Number is way too small.
Question 1 Explanation: 
Topic: Analyze the relationships among proportions, constant rates, and linear functions (Objective 0022).
Question 2

Use the expression below to answer the question that follows.

                 \( \large \dfrac{\left( 4\times {{10}^{3}} \right)\times \left( 3\times {{10}^{4}} \right)}{6\times {{10}^{6}}}\)

Which of the following is equivalent to the expression above?

A

2

Hint:
\(10^3 \times 10^4=10^7\), and note that if you're guessing when the answers are so closely related, you're generally better off guessing one of the middle numbers.
B

20

Hint:
\( \dfrac{\left( 4\times {{10}^{3}} \right)\times \left( 3\times {{10}^{4}} \right)}{6\times {{10}^{6}}}=\dfrac {12 \times {{10}^{7}}}{6\times {{10}^{6}}}=\)\(2 \times {{10}^{1}}=20 \)
C

200

Hint:
\(10^3 \times 10^4=10^7\)
D

2000

Hint:
\(10^3 \times 10^4=10^7\), and note that if you're guessing when the answers are so closely related, you're generally better off guessing one of the middle numbers.
Question 2 Explanation: 
Topics: Scientific notation, exponents, simplifying fractions (Objective 0016, although overlaps with other objectives too).
Question 3

Which of the graphs below represent functions?

I. II. III. IV.   
A

I and IV only.

Hint:
There are vertical lines that go through 2 points in IV .
B

I and III only.

Hint:
Even though III is not continuous, it's still a function (assuming that vertical lines between the "steps" do not go through 2 points).
C

II and III only.

Hint:
Learn about the vertical line test.
D

I, II, and IV only.

Hint:
There are vertical lines that go through 2 points in II.
Question 3 Explanation: 
Understand the definition of function and various representations of functions (e.g., input/output machines, tables, graphs, mapping diagrams, formulas). (Objective 0021).
Question 4

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 4 Explanation: 
Topic: Understand models of operations on numbers (Objective 0019).
Question 5

The prime factorization of  n can be written as n=pqr, where p, q, and r are distinct prime numbers.  How many factors does n have, including 1 and itself?

A
\( \large3\)
Hint:
1, p, q, r, and pqr are already 5, so this isn't enough. You might try plugging in p=2, q=3, and r=5 to help with this problem.
B
\( \large5\)
Hint:
Don't forget pq, etc. You might try plugging in p=2, q=3, and r=5 to help with this problem.
C
\( \large6\)
Hint:
You might try plugging in p=2, q=3, and r=5 to help with this problem.
D
\( \large8\)
Hint:
1, p, q, r, pq, pr, qr, pqr.
Question 5 Explanation: 
Topic: Recognize uses of prime factorization of a number (Objective 0018).
Question 6

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 6 Explanation: 
Topic: Scientific Notation (Objective 0016)
Question 7

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 7 Explanation: 
Topic: Using number lines (Objective 0017)
Question 8

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 8 Explanation: 
Topic: Recognize and apply the concept of conditional probability (Objective 0026).
Question 9

Which of the following is equivalent to

\( \large A-B+C\div D\times E\)?

A
\( \large A-B-\dfrac{C}{DE} \)
Hint:
In the order of operations, multiplication and division have the same priority, so do them left to right; same with addition and subtraction.
B
\( \large A-B+\dfrac{CE}{D}\)
Hint:
In practice, you're better off using parentheses than writing an expression like the one in the question. The PEMDAS acronym that many people memorize is misleading. Multiplication and division have equal priority and are done left to right. They have higher priority than addition and subtraction. Addition and subtraction also have equal priority and are done left to right.
C
\( \large \dfrac{AE-BE+CE}{D}\)
Hint:
Use order of operations, don't just compute left to right.
D
\( \large A-B+\dfrac{C}{DE}\)
Hint:
In the order of operations, multiplication and division have the same priority, so do them left to right
Question 9 Explanation: 
Topic: Justify algebraic manipulations by application of the properties of order of operations (Objective 0020).
Question 10

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

A
\( \large 11,400,000\)
Hint:
That's eleven million four hundred thousand.
B
\(\large11,000,400,000\)
C
\( \large11,000,000,400,000\)
Hint:
That's eleven trillion four hundred thousand (although with British conventions; this answer is correct, but in the US, it isn't).
D
\( \large 11,400,000,000\)
Hint:
That's eleven billion four hundred million
Question 10 Explanation: 
Topic: Place Value (Objective 0016)
Question 11

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 11 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 12

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 12 Explanation: 
Topics: Estimation, Scientific Notation in the real world (Objective 0016).
Question 13

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 13 Explanation: 
Topics: Laws of exponents (Objective 0019).
Question 14

Here are some statements:

I) 5 is an integer    II)\( -5 \)  is an integer    III) \(0\) is an integer

Which of the statements are true?

A

I only

B

I and II only

C

I and III only

D

I, II, and III

Hint:
The integers are ...-3, -2, -1, 0, 1, 2, 3, ....
Question 14 Explanation: 
Topic: Characteristics of Integers (Objective 0016)
Question 15

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 15 Explanation: 
Topic: Apply knowledge of combinations and permutations to the computation of probabilities (Objective 0026).
Question 16

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

A
\( \large \dfrac{4}{6}\)
Hint:
\( 0.\bar{6}=\dfrac{2}{3}=\dfrac{4}{6}\)
B
\( \large \dfrac{3}{5}\)
Hint:
This is equal to 0.6, without the repeating decimal. Answer is equivalent to choice c, which is another way to tell that it's wrong.
C
\( \large \dfrac{6}{10}\)
Hint:
This is equal to 0.6, without the repeating decimal. Answer is equivalent to choice b, which is another way to tell that it's wrong.
D
\( \large \dfrac{1}{6}\)
Hint:
This is less than a half, and \( 0.\bar{6}\) is greater than a half.
Question 16 Explanation: 
Topic: Converting between fraction and decimal representations (Objective 0017)
Question 17

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 17 Explanation: 
Topic: Converting between fractions and decimals (Objective 0017)
Question 18

Each individual cube that makes up the rectangular solid depicted below has 6 inch sides.  What is the surface area of the solid in square feet?

 
A
\( \large 11\text{ f}{{\text{t}}^{2}}\)
Hint:
Check your units and make sure you're using feet and inches consistently.
B
\( \large 16.5\text{ f}{{\text{t}}^{2}}\)
Hint:
Each square has surface area \(\dfrac{1}{2} \times \dfrac {1}{2}=\dfrac {1}{4}\) sq feet. There are 9 squares on the top and bottom, and 12 on each of 4 sides, for a total of 66 squares. 66 squares \(\times \dfrac {1}{4}\) sq feet/square =16.5 sq feet.
C
\( \large 66\text{ f}{{\text{t}}^{2}}\)
Hint:
The area of each square is not 1.
D
\( \large 2376\text{ f}{{\text{t}}^{2}}\)
Hint:
Read the question more carefully -- the answer is supposed to be in sq feet, not sq inches.
Question 18 Explanation: 
Topics: Use unit conversions to solve measurement problems, and derive and use formulas for calculating surface areas of geometric shapes and figures (Objective 0023).
Question 19

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 19 Explanation: 
Topic: Recognize and apply the concept of conditional probability (Objective 0026).
Question 20

Kendra is trying to decide which fraction is greater, \(  \dfrac{4}{7}\) or \(  \dfrac{5}{8}\). Which of the following answers shows the best reasoning?

A

\( \dfrac{4}{7}\) is \( \dfrac{3}{7}\)away from 1, and \( \dfrac{5}{8}\) is \( \dfrac{3}{8}\)away from 1. Since eighth‘s are smaller than seventh‘s, \( \dfrac{5}{8}\) is closer to 1, and is the greater of the two fractions.

B

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

Hint:
Not how to compare fractions. By this logic, 1/2 and 3/4 are equal, but 1/2 and 2/4 are not.
C

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

Hint:
Starts out as something that works, but the conclusion is wrong. 4/7 = 32/56 and 5/8 = 35/56. The cross multiplication gives the numerators, and 35/56 is bigger.
D

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

Hint:
Conclusion is correct, logic is wrong. With this reasoning, 1/2 would be less than 2/100,000.
Question 20 Explanation: 
Topics: Comparing fractions, and understanding the meaning of fractions (Objective 0017).
Question 21

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 21 Explanation: 
Topic: Estimate and calculate measurements using customary, metric, and nonstandard units of measurement (Objective 0023).
Question 22

What is the mathematical name of the three-dimensional polyhedron depicted below?

A

Tetrahedron

Hint:
All the faces of a tetrahedron are triangles.
B

Triangular Prism

Hint:
A prism has two congruent, parallel bases, connected by parallelograms (since this is a right prism, the parallelograms are rectangles).
C

Triangular Pyramid

Hint:
A pyramid has one base, not two.
D

Trigon

Hint:
A trigon is a triangle (this is not a common term).
Question 22 Explanation: 
Topic: Classify and analyze three-dimensional figures using attributes of faces, edges, and vertices (Objective 0024).
Question 23

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

A
\( \large \dfrac{1}{7}\)
Hint:
It doesn't matter what day the first person was born on. The probability that the second person will match is 1/7 (just designate one person the first and the other the second). Another way to look at it is that if you list the sample space of all possible pairs, e.g. (Wed, Sun), there are 49 such pairs, and 7 of them are repeats of the same day, and 7/49=1/7.
B
\( \large \dfrac{1}{14}\)
Hint:
What would be the sample space here? Ie, how would you list 14 things that you pick one from?
C
\( \large \dfrac{1}{42}\)
Hint:
If you wrote the seven days of the week on pieces of paper and put the papers in a jar, this would be the probability that the first person picked Sunday and the second picked Monday from the jar -- not the same situation.
D
\( \large \dfrac{1}{49}\)
Hint:
This is the probability that they are both born on a particular day, e.g. Sunday.
Question 23 Explanation: 
Topic: Calculate the probabilities of simple and compound events and of independent and dependent events (Objective 0026).
Question 24

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 24 Explanation: 
Topics: Laws of exponents, order of operations, interpret absolute value (Objective 0019).
Question 25

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

A
\( \large \dfrac{1}{25}\)
Hint:
1/25=4/100, so this is equal to 4% (be sure you read the question correctly).
B
\( \large \dfrac{4}{100}\)
Hint:
4/100=4% (be sure you read the question correctly).
C
\( \large 0.4\)
Hint:
0.4=40% so this is not equal to 4%
D
\( \large 0.04\)
Hint:
0.04=4/100, so this is equal to 4% (be sure you read the question correctly).
Question 25 Explanation: 
Converting between fractions, decimals, and percents (Objective 0017).
Question 26

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

A

M is odd.

Hint:
All multiples of 26 are also multiples of 2, so they must be even.
B

M is a multiple of 3.

Hint:
3 x 26 is a multiple of both 3 and 26.
C

M is 26.

Hint:
1 x 26 is a multiple of 26.
D

M is 0.

Hint:
0 x 26 is a multiple of 26.
Question 26 Explanation: 
Topic: Characteristics of composite numbers (Objective 0018).
Question 27

A publisher prints a series of books with covers made of identical material and using the same thickness of paper for each page.  The covers of the book together are 0.4 cm thick, and 125 pieces of the paper used together are 1 cm thick.

The publisher uses a linear function to determine the total thickness, T(n) of a book made with n sheets of paper.   What are the slope and intercept of T(n)?

A

Intercept = 0.4 cm, Slope = 125 cm/page

Hint:
This would mean that each page of the book was 125 cm thick.
B

Intercept =0.4 cm, Slope = \(\dfrac{1}{125}\)cm/page

Hint:
The intercept is how thick the book would be with no pages in it. The slope is how much 1 extra page adds to the thickness of the book.
C

Intercept = 125 cm, Slope = 0.4 cm

Hint:
This would mean that with no pages in the book, it would be 125 cm thick.
D

Intercept = \(\dfrac{1}{125}\)cm, Slope = 0.4 pages/cm

Hint:
This would mean that each new page of the book made it 0.4 cm thicker.
Question 27 Explanation: 
Topic: Interpret the meaning of the slope and the intercepts of a linear equation that models a real-world situation (Objective 0022).
Question 28

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

Use the solution procedure below to answer the question that follows:

\( \large {\left( x+3 \right)}^{2}=10\)

\( \large \left( x+3 \right)\left( x+3 \right)=10\)

\( \large {x}^{2}+9=10\)

\( \large {x}^{2}+9-9=10-9\)

\( \large {x}^{2}=1\)

\( \large x=1\text{ or }x=-1\)

Which of the following is incorrect in the procedure shown above?

A

The commutative property is used incorrectly.

Hint:
The commutative property is \(a+b=b+a\) or \(ab=ba\).
B

The associative property is used incorrectly.

Hint:
The associative property is \(a+(b+c)=(a+b)+c\) or \(a \times (b \times c)=(a \times b) \times c\).
C

Order of operations is done incorrectly.

D

The distributive property is used incorrectly.

Hint:
\((x+3)(x+3)=x(x+3)+3(x+3)\)=\(x^2+3x+3x+9.\)
Question 30 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 31

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 31 Explanation: 
Topic:Analyze and apply geometric transformations (e.g., translations, rotations, reflections, dilations) (Objective 0024).
Question 32

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 32 Explanation: 
Topic: Match three-dimensional figures and their two-dimensional representations (e.g., nets, projections, perspective drawings) (Objective 0024).
Question 33

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 33 Explanation: 
Topic: Recognize and extend patterns using a variety of representations (e.g., verbal, numeric, pictorial, algebraic) (Objective 0021).
Question 34

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 34 Explanation: 
Topic: Analyze and interpret various graphic and nongraphic data representations (e.g., frequency distributions, percentiles) (Objective 0025).
Question 35

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 35 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 36

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

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

A
\( \large A(n)=n+4\)
Hint:
For a question like this, you don't have to find the equation yourself, you can just try plugging the function machine inputs into the equation, and see if any values come out wrong. With this equation n= -1 would output 3, not 0 as the machine does.
B
\( \large A(n)=n+2\)
Hint:
For a question like this, you don't have to find the equation yourself, you can just try plugging the function machine inputs into the equation, and see if any values come out wrong. With this equation n= 2 would output 4, not 6 as the machine does.
C
\( \large A(n)=2n+2\)
Hint:
Simply plug in each of the four function machine input values, and see that the equation produces the correct output, e.g. A(2)=6, A(-1)=0, etc.
D
\( \large A(n)=2\left( n+2 \right)\)
Hint:
For a question like this, you don't have to find the equation yourself, you can just try plugging the function machine inputs into the equation, and see if any values come out wrong. With this equation n= 2 would output 8, not 6 as the machine does.
Question 36 Explanation: 
Topics: Understand various representations of functions, and translate among different representations of functional relationships (Objective 0021).
Question 37

The function d(x) gives the result when 12 is divided by x.  Which of the following is a graph of d(x)?

 
A
Hint:
d(x) is 12 divided by x, not x divided by 12.
B
Hint:
When x=2, what should d(x) be?
C
Hint:
When x=2, what should d(x) be?
D
Question 37 Explanation: 
Topic: Identify and analyze direct and inverse relationships in tables, graphs, algebraic expressions and real-world situations (Objective 0021)
Question 38

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 38 Explanation: 
Topic: Classify and analyze polygons using attributes of sides and angles, and symmetry (Objective 0024).
Question 39

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?

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 39 Explanation: 
Topic: Models of Fractions (Objective 0017)
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

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 41 Explanation: 
Topic: Interpret the meaning of the slope and the intercepts of a linear equation that models a real-world situation (Objective 0022).
Question 42

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 42 Explanation: 
Topic: Use unit conversions and dimensional analysis to solve measurement problems (Objective 0023).
Question 43

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 43 Explanation: 
Topics: Estimation, simplifying fractions (Objective 0016).
Question 44

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 44 Explanation: 
Topic: Use measures of central tendency (e.g., mean, median, mode) and spread to describe and interpret real-world data (Objective 0025).
Question 45

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