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

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Question 1

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 1 Explanation:

Topics: Scientific notation, exponents, simplifying fractions (Objective 0016, although overlaps with other objectives too).

Question 2

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 2 Explanation:

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

Question 3

Which of the graphs below represent functions?

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 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 4 Explanation:

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

Question 5

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 5 Explanation:

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

Question 6

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 6 Explanation:

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

Question 7

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 7 Explanation:

Topic: Scientific Notation (Objective 0016)

Question 8

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 8 Explanation:

Converting between fractions, decimals, and percents (Objective 0017).

Question 9

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 9 Explanation:

Topic: Models of Fractions (Objective 0017)

Question 10

A biology class requires a lab fee, which is a whole number of dollars, and the same amount for all students. On Monday the instructor collected $70 in fees, on Tuesday she collected $126, and on Wednesday she collected $266. What is the largest possible amount the fee could be?

A	$2 Hint: A possible fee, but not the largest possible fee. Check the other choices to see which are factors of all three numbers.
B	$7 Hint: A possible fee, but not the largest possible fee. Check the other choices to see which are factors of all three numbers.
C	$14 Hint: This is the greatest common factor of 70, 126, and 266.
D	$70 Hint: Not a factor of 126 or 266, so couldn't be correct.

Question 10 Explanation:

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

Question 11

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 11 Explanation:

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

Question 12

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 12 Explanation:

Topic: Classify and analyze three-dimensional figures using attributes of faces, edges, and vertices (Objective 0024).

Question 13

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 13 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 14

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 14 Explanation:

Topic: Using Number Lines (Objective 0017)

Question 15

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 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

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 16 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 17

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 17 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 18

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 18 Explanation:

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

Question 19

An above-ground swimming pool is in the shape of a regular hexagonal prism, is one meter high, and holds 65 cubic meters of water. A second pool has a base that is also a regular hexagon, but with sides twice as long as the sides in the first pool. This second pool is also one meter high. How much water will the second pool hold?

A	$ \large 65\text{ }{{\text{m}}^{3}}$ Hint: A bigger pool would hold more water.
B	$ \large 65\cdot 2\text{ }{{\text{m}}^{3}}$ Hint: Try a simpler example, say doubling the sides of the base of a 1 x 1 x 1 cube.
C	$ \large 65\cdot 4\text{ }{{\text{m}}^{3}}$ Hint: If we think of the pool as filled with 1 x 1 x 1 cubes (and some fractions of cubes), then scaling to the larger pool changes each 1 x 1 x 1 cube to a 2 x 2 x 1 prism, or multiplies volume by 4.
D	$ \large 65\cdot 8\text{ }{{\text{m}}^{3}}$ Hint: Try a simpler example, say doubling the sides of the base of a 1 x 1 x 1 cube.

Question 19 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 20

Which of the following inequalities describes all values of x with $\large \dfrac{x}{2}\le \dfrac{x}{3}$?

A	$ \large x < 0$ Hint: If x =0, then x/2 = x/3, so this answer can't be correct.
B	$ \large x \le 0$
C	$ \large x > 0$ Hint: If x =0, then x/2 = x/3, so this answer can't be correct.
D	$ \large x \ge 0$ Hint: Try plugging in x = 6.

Question 20 Explanation:

Topics: Inequalities, operations (Objective 0019) (not exactly sure how to classify, but this is like one of the problems on the official sample test).

Question 21

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 21 Explanation:

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

Question 22

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 22 Explanation:

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

Question 23

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 23 Explanation:

Topic: Converting between fraction and decimal representations (Objective 0017)

Question 24

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 24 Explanation:

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

Question 25

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 25 Explanation:

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

Question 26

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 26 Explanation:

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

Question 27

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 27 Explanation:

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

Question 28

Which of the following sets of polygons can be assembled to form a pentagonal pyramid?

A	2 pentagons and 5 rectangles. Hint: These can be assembled to form a pentagonal prism, not a pentagonal pyramid.
B	1 square and 5 equilateral triangles. Hint: You need a pentagon for a pentagonal pyramid.
C	1 pentagon and 5 isosceles triangles.
D	1 pentagon and 10 isosceles triangles.

Question 28 Explanation:

Topic:Classify and analyze three-dimensional figures using attributes of faces, edges, and vertices (Objective 0024).

Question 29

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 29 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 30

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

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

Question 30 Explanation:

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

Question 31

What is the perimeter of a right triangle with legs of lengths x and 2x?

A	$ \large 6x$ Hint: Use the Pythagorean Theorem.
B	$ \large 3x+5{{x}^{2}}$ Hint: Don't forget to take square roots when you use the Pythagorean Theorem.
C	$ \large 3x+\sqrt{5}{{x}^{2}}$ Hint: $\sqrt {5 x^2}$ is not $\sqrt {5}x^2$.
D	$ \large 3x+\sqrt{5}{{x}^{{}}}$ Hint: To find the hypotenuse, h, use the Pythagorean Theorem: $x^2+(2x)^2=h^2.$ $5x^2=h^2,h=\sqrt{5}x$. The perimeter is this plus x plus 2x.

Question 31 Explanation:

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

Question 32

Exactly one of the numbers below is a prime number. Which one is it?

A	$ \large511 $ Hint: Divisible by 7.
B	$ \large517$ Hint: Divisible by 11.
C	$ \large519$ Hint: Divisible by 3.
D	$ \large521$

Question 32 Explanation:

Topics: Identify prime and composite numbers and demonstrate knowledge of divisibility rules (Objective 0018).

Question 33

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 33 Explanation:

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

Question 34

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 34 Explanation:

Topic: Converting between fractions and decimals (Objective 0017)

Question 35

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 35 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 36

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 36 Explanation:

Topic: Place Value (Objective 0016)

Question 37

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 37 Explanation:

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

Question 38

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 38 Explanation:

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

Question 39

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 39 Explanation:

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

Question 40

A map has a scale of 3 inches = 100 miles. Cities A and B are 753 miles apart. Let d be the distance between the two cities on the map. Which of the following is not correct?

A	$ \large \dfrac{3}{100}=\dfrac{d}{753}$ Hint: Units on both side are inches/mile, and both numerators and denominators correspond -- this one is correct.
B	$ \large \dfrac{3}{100}=\dfrac{753}{d}$ Hint: Unit on the left is inches per mile, and on the right is miles per inch. The proportion is set up incorrectly (which is what we wanted). Another strategy is to notice that one of A or B has to be the answer because they cannot both be correct proportions. Then check that cross multiplying on A gives part D, so B is the one that is different from the other 3.
C	$ \large \dfrac{3}{d}=\dfrac{100}{753}$ Hint: Unitless on each side, as inches cancel on the left and miles on the right. Numerators correspond to the map, and denominators to the real life distances -- this one is correct.
D	$ \large 100d=3\cdot 753$ Hint: This is equivalent to part A.

Question 40 Explanation:

Topic: Analyze the relationships among proportions, constant rates, and linear functions (Objective 0022).

Question 41

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 41 Explanation:

Topic: Characteristics of composite numbers (Objective 0018).

Question 42

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 42 Explanation:

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

Question 43

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 43 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 44

The first histogram shows the average life expectancies for women in different countries in Africa in 1998; the second histogram gives similar data for Europe:

How much bigger is the range of the data for Africa than the range of the data for Europe?

A	0 years Hint: Range is the maximum life expectancy minus the minimum life expectancy.
B	12 years Hint: Are you subtracting frequencies? Range is about values of the data, not frequency.
C	18 years Hint: It's a little hard to read the graph, but it doesn't matter if you're consistent. It looks like the range for Africa is 80-38= 42 years and for Europe is 88-64 = 24; 42-24=18.
D	42 years Hint: Read the question more carefully.

Question 44 Explanation:

Topic: Compare different data sets (Objective 0025).

Question 45

Use the expression below to answer the question that follows.

$ \large 3\times {{10}^{4}}+2.2\times {{10}^{2}}$

Which of the following is closest to the expression above?

A	Five million Hint: Pay attention to the exponents. Adding 3 and 2 doesn't work because they have different place values.
B	Fifty thousand Hint: Pay attention to the exponents. Adding 3 and 2 doesn't work because they have different place values.
C	Three million Hint: Don't add the exponents.
D	Thirty thousand Hint: $ 3\times {{10}^{4}} = 30,000;$ the other term is much smaller and doesn't change the estimate.

Question 45 Explanation:

Topics: Place value, scientific notation, estimation (Objective 0016)

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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.

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	\(\large1.3\times {{10}^{6}}\)
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	\( \large \dfrac{1}{25}\) 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).

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	\( \large \$2.60+\$0.40d\) 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	\( \large 0.645\) 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	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.

A	\( \large 6g\) Hint: You must scale in all three dimensions.
B	\( \large 12g\) Hint: Height is multiplied by 3, and diameter and radius are multiplied by 2. Since the radius is squared, final result is multiplied by \(2^2\times 3=12\).
C	\( \large 18g\) Hint: Don't square the height scale factor.
D	\( \large 36g\) Hint: Don't square the height scale factor.

A	\( \large y={{x}^{2}}+2x+7\) 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	\( \large 65\text{ }{{\text{m}}^{3}}\) Hint: A bigger pool would hold more water.
B	\( \large 65\cdot 2\text{ }{{\text{m}}^{3}}\) Hint: Try a simpler example, say doubling the sides of the base of a 1 x 1 x 1 cube.
C	\( \large 65\cdot 4\text{ }{{\text{m}}^{3}}\) Hint: If we think of the pool as filled with 1 x 1 x 1 cubes (and some fractions of cubes), then scaling to the larger pool changes each 1 x 1 x 1 cube to a 2 x 2 x 1 prism, or multiplies volume by 4.
D	\( \large 65\cdot 8\text{ }{{\text{m}}^{3}}\) Hint: Try a simpler example, say doubling the sides of the base of a 1 x 1 x 1 cube.

A	\( \large x < 0\) Hint: If x =0, then x/2 = x/3, so this answer can't be correct.
B	\( \large x \le 0\)
C	\( \large x > 0\) Hint: If x =0, then x/2 = x/3, so this answer can't be correct.
D	\( \large x \ge 0\) Hint: Try plugging in x = 6.

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	\( \large 60\dfrac{\text{miles}}{\text{hour}}\cdot 5280\dfrac{\text{feet}}{\text{mile}}\cdot 60\dfrac{\text{minutes}}{\text{hour}}\cdot 60\dfrac{\text{seconds}}{\text{minute}} \) 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	\( \large \dfrac{4}{6}\) 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.

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

A	\( \large 6x\) Hint: Use the Pythagorean Theorem.
B	\( \large 3x+5{{x}^{2}}\) Hint: Don't forget to take square roots when you use the Pythagorean Theorem.
C	\( \large 3x+\sqrt{5}{{x}^{2}}\) Hint: \(\sqrt {5 x^2}\) is not \(\sqrt {5}x^2\).
D	\( \large 3x+\sqrt{5}{{x}^{{}}}\) Hint: To find the hypotenuse, h, use the Pythagorean Theorem: \(x^2+(2x)^2=h^2.\) \(5x^2=h^2,h=\sqrt{5}x\). The perimeter is this plus x plus 2x.

A	\( \large511 \) Hint: Divisible by 7.
B	\( \large517\) Hint: Divisible by 11.
C	\( \large519\) Hint: Divisible by 3.
D	\( \large521\)

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

A	\( \large 343.2\times 60\times 10\) 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	\( \large{{2}^{5}}\cdot {{3}^{6}}\cdot 5\) 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	\( \large \dfrac{3}{100}=\dfrac{d}{753}\) Hint: Units on both side are inches/mile, and both numerators and denominators correspond -- this one is correct.
B	\( \large \dfrac{3}{100}=\dfrac{753}{d}\) Hint: Unit on the left is inches per mile, and on the right is miles per inch. The proportion is set up incorrectly (which is what we wanted). Another strategy is to notice that one of A or B has to be the answer because they cannot both be correct proportions. Then check that cross multiplying on A gives part D, so B is the one that is different from the other 3.
C	\( \large \dfrac{3}{d}=\dfrac{100}{753}\) Hint: Unitless on each side, as inches cancel on the left and miles on the right. Numerators correspond to the map, and denominators to the real life distances -- this one is correct.
D	\( \large 100d=3\cdot 753\) Hint: This is equivalent to part A.

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 \(6+N = -4\)

MTEL General Curriculum Mathematics Practice

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?

2

20

200

2000

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

30

120

300

360

Which of the graphs below represent functions?

I and IV only.

I and III only.

II and III only.

I, II, and IV only.

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.

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

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

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

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

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

It is valid for all rational numbers.

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?

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

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

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?

4

5

8

12

A biology class requires a lab fee, which is a whole number of dollars, and the same amount for all students. On Monday the instructor collected $70 in fees, on Tuesday she collected $126, and on Wednesday she collected $266. What is the largest possible amount the fee could be?

$2

$7

$14

$70

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%.

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

Tetrahedron

Triangular Prism

Triangular Pyramid

Trigon

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?

Below is a portion of a number line:

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

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)?

Intercept = 0.4 cm, Slope = 125 cm/page

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

Intercept = 125 cm, Slope = 0.4 cm

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

In which table below is y a function of x?

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?

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

Which of the following inequalities describes all values of x with \(\large \dfrac{x}{2}\le \dfrac{x}{3}\)?

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 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.

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

Here is a method that a student used for subtraction:

Which of the following is correct?

The student used a method that worked for this problem and can be generalized to any subtraction problem.

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.

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.

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.

Which property is not shared by all rhombi?

4 congruent sides

A center of rotational symmetry

4 congruent angles

2 sets of parallel sides

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?

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