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

Question 1 |

#### At a school fundraising event, people can buy a ticket to spin a spinner like the one below. The region that the spinner lands in tells which, if any, prize the person wins.

#### If 240 people buy tickets to spin the spinner, what is the best estimate of the number of keychains that will be given away?

## 40Hint: "Keychain" appears on the spinner twice. | |

## 80Hint: The probability of getting a keychain is 1/3, and so about 1/3 of the time the spinner will win. | |

## 100Hint: What is the probability of winning a keychain? | |

## 120Hint: That would be the answer for getting any prize, not a keychain specifically. |

Question 2 |

#### 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?

\( \large 65\text{ }{{\text{m}}^{3}}\) Hint: A bigger pool would hold more water. | |

\( \large 65\cdot 2\text{ }{{\text{m}}^{3}}\) Hint: Try a simpler example, say doubling the sides of the base of a 1 x 1 x 1 cube. | |

\( \large 65\cdot 4\text{ }{{\text{m}}^{3}}\) 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. | |

\( \large 65\cdot 8\text{ }{{\text{m}}^{3}}\) Hint: Try a simpler example, say doubling the sides of the base of a 1 x 1 x 1 cube. |

Question 3 |

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

\( \large x=3\) Hint: Try plugging x=3 into the equation. | |

\( \large x=-3\) Hint: Left side is positive, right side is negative when you plug this in for x. | |

\( \large x=\dfrac{3}{2}\) Hint: One way to solve: \(4=\dfrac{2}{3}x+2x\) \(=\dfrac{8}{3}x\).\(x=\dfrac{3 \times 4}{8}=\dfrac{3}{2}\). Another way is to just plug x=3/2 into the equation and see that each side equals 3 -- on a multiple choice test, you almost never have to actually solve for x. | |

\( \large x=-\dfrac{3}{2}\) Hint: Left side is positive, right side is negative when you plug this in for x. |

Question 4 |

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

## 1.6 cmHint: This is more the height of a Lego toy college student -- less than an inch! | |

## 16 cmHint: Less than knee high on most college students. | |

## 160 cmHint: 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. | |

## 1600 cmHint: This college student might be taller than some campus buildings! |

Question 5 |

#### A teacher has a list of all the countries in the world and their populations in March 2012. She is going to have her students use technology to compute the mean and median of the numbers on the list. Which of the following statements is true?

## The teacher can be sure that the mean and median will be the same without doing any computation.Hint: Does this make sense? How likely is it that the mean and median of any large data set will be the same? | |

## 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). | |

## 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? | |

## 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 6 |

#### 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?

## Five millionHint: Pay attention to the exponents. Adding 3 and 2 doesn't work because they have different place values. | |

## Fifty thousandHint: Pay attention to the exponents. Adding 3 and 2 doesn't work because they have different place values. | |

## Three millionHint: Don't add the exponents. | |

## Thirty thousandHint: \( 3\times {{10}^{4}} = 30,000;\) the other term is much smaller and doesn't change the estimate. |

Question 7 |

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

\( \large 2\) Hint: Write \(8^3\) as a power of 2. | |

\( \large \dfrac{1}{2}\) Hint: \(8^3 \cdot {2}^{-10}={(2^3)}^3 \cdot {2}^{-10}\) =\(2^9 \cdot {2}^{-10} =2^{-1}\) | |

\( \large 16\) Hint: Write \(8^3\) as a power of 2. | |

\( \large \dfrac{1}{16}\) Hint: Write \(8^3\) as a power of 2. |

Question 8 |

#### A solution requires 4 ml of saline for every 7 ml of medicine. How much saline would be required for 50 ml of medicine?

\( \large 28 \dfrac{4}{7}\) ml Hint: 49 ml of medicine requires 28 ml of saline. The extra ml of saline requires 4 ml saline/ 7 ml medicine = 4/7 ml saline per 1 ml medicine. | |

\( \large 28 \dfrac{1}{4}\) ml Hint: 49 ml of medicine requires 28 ml of saline. How much saline does the extra ml require? | |

\( \large 28 \dfrac{1}{7}\) ml Hint: 49 ml of medicine requires 28 ml of saline. How much saline does the extra ml require? | |

\( \large 87.5\) ml Hint: 49 ml of medicine requires 28 ml of saline. How much saline does the extra ml require? |

Question 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.

\( \large 60\dfrac{\text{miles}}{\text{hour}}\cdot 5280\dfrac{\text{feet}}{\text{mile}}\cdot 60\dfrac{\text{minutes}}{\text{hour}}\cdot 60\dfrac{\text{seconds}}{\text{minute}}
\) Hint: This answer is not in feet/second. | |

\( \large 60\dfrac{\text{miles}}{\text{hour}}\cdot 5280\dfrac{\text{feet}}{\text{mile}}\cdot \dfrac{1}{60}\dfrac{\text{hour}}{\text{minutes}}\cdot \dfrac{1}{60}\dfrac{\text{minute}}{\text{seconds}}
\) Hint: This is the only choice where the answer is in feet per second and the unit conversions are correct. | |

\( \large 60\dfrac{\text{miles}}{\text{hour}}\cdot \dfrac{1}{5280}\dfrac{\text{foot}}{\text{miles}}\cdot 60\dfrac{\text{hours}}{\text{minute}}\cdot \dfrac{1}{60}\dfrac{\text{minute}}{\text{seconds}}\) Hint: Are there really 60 hours in a minute? | |

\( \large 60\dfrac{\text{miles}}{\text{hour}}\cdot \dfrac{1}{5280}\dfrac{\text{mile}}{\text{feet}}\cdot 60\dfrac{\text{minutes}}{\text{hour}}\cdot \dfrac{1}{60}\dfrac{\text{minute}}{\text{seconds}}\) Hint: This answer is not in feet/second. |

Question 10 |

#### On a map the distance from Boston to Detroit is 6 cm, and these two cities are 702 miles away from each other. Assuming the scale of the map is the same throughout, which answer below is closest to the distance between Boston and San Francisco on the map, given that they are 2,708 miles away from each other?

## 21 cmHint: How many miles would correspond to 24 cm on the map? Try adjusting from there. | |

## 22 cmHint: How many miles would correspond to 24 cm on the map? Try adjusting from there. | |

## 23 cmHint: One way to solve this without a calculator is to note that 4 groups of 6 cm is 2808 miles, which is 100 miles too much. Then 100 miles would be about 1/7 th of 6 cm, or about 1 cm less than 24 cm. | |

## 24 cmHint: 4 groups of 6 cm is over 2800 miles on the map, which is too much. |

Question 11 |

#### A sales companies pays its representatives $2 for each item sold, plus 40% of the price of the item. The rest of the money that the representatives collect goes to the company. All transactions are in cash, and all items cost $4 or more. If the price of an item in dollars is p, which expression represents the amount of money the company collects when the item is sold?

\( \large \dfrac{3}{5}p-2\) Hint: The company gets 3/5=60% of the price, minus the $2 per item. | |

\( \large \dfrac{3}{5}\left( p-2 \right)\) Hint: This is sensible, but not what the problem states. | |

\( \large \dfrac{2}{5}p+2\) Hint: The company pays the extra $2; it doesn't collect it. | |

\( \large \dfrac{2}{5}p-2\) Hint: This has the company getting 2/5 = 40% of the price of each item, but that's what the representative gets. |

Question 12 |

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

## 2 pentagons and 5 rectangles.Hint: These can be assembled to form a pentagonal prism, not a pentagonal pyramid. | |

## 1 square and 5 equilateral triangles.Hint: You need a pentagon for a pentagonal pyramid. | |

## 1 pentagon and 5 isosceles triangles. | |

## 1 pentagon and 10 isosceles triangles. |

Question 13 |

#### 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?

## 4Hint: The card blocks more than half of the circles, so this number is too small. | |

## 5Hint: The card blocks more than half of the circles, so this number is too small. | |

## 8Hint: The card blocks more than half of the circles, so this number is too small. | |

## 12Hint: 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 14 |

## 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). | |

## 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. | |

## 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. | |

## 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 15 |

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

\( \large \dfrac{4}{6}\) Hint: \( 0.\bar{6}=\dfrac{2}{3}=\dfrac{4}{6}\) | |

\( \large \dfrac{3}{5}\) 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. | |

\( \large \dfrac{6}{10}\) 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. | |

\( \large \dfrac{1}{6}\) Hint: This is less than a half, and \( 0.\bar{6}\) is greater than a half. |

Question 16 |

#### Use the table below to answer the question that follows:

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

\( \large W=-5\) Hint: When y is even, W is even. | |

\( \large W=4\) Hint: Note that when x increases by 1, W increases by 2, and when y increases by 1, W decreases by 1. At x=y=0, W=0, so at x=9, y=14, W has increased by \(9 \times 2\) and decreased by 14, or W=18-14=4. | |

\( \large W=6\) Hint: Try fixing x or y at 0, and start by finding W for x=0 y=14 or x=9, y=0. | |

\( \large W=32\) Hint: Try fixing x or y at 0, and start by finding W for x=0 y=14 or x=9, y=0. |

Question 17 |

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

\( \large y={{x}^{2}}+2x+7\) Hint: This is a quadratic function. | |

\( \large y={{2}^{x}}\) Hint: This is an exponential function. | |

\( \large y=\dfrac{15}{x}\) Hint: This is an inverse function. | |

\( \large y=x+(x+4)\) 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 |

#### Use the graph below to answer the question that follows:

#### The graph above best matches which of the following scenarios:

## George left home at 10:00 and drove to work on a crooked path. He was stopped in traffic at 10:30 and 10:45. He drove 30 miles total.Hint: Just because he ended up 30 miles from home doesn't mean he drove 30 miles total. | |

## George drove to work. On the way to work there is a little hill and a big hill. He slowed down for them. He made it to work at 11:15.Hint: The graph is not a picture of the roads. | |

## 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. | |

## 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 19 |

#### Which of the following is not possible?

## An equiangular triangle that is not equilateral.Hint: The AAA property of triangles states that all triangles with corresponding angles congruent are similar. Thus all triangles with three equal angles are similar, and are equilateral. | |

## An equiangular quadrilateral that is not equilateral.Hint: A rectangle is equiangular (all angles the same measure), but if it's not a square, it's not equilateral (all sides the same length). | |

## An equilateral quadrilateral that is not equiangular.Hint: This rhombus has equal sides, but it doesn't have equal angles: | |

## An equiangular hexagon that is not equilateral.Hint: This hexagon has equal angles, but it doesn't have equal sides: |

Question 20 |

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

## M is odd.Hint: All multiples of 26 are also multiples of 2, so they must be even. | |

## M is a multiple of 3.Hint: 3 x 26 is a multiple of both 3 and 26. | |

## M is 26.Hint: 1 x 26 is a multiple of 26. | |

## M is 0.Hint: 0 x 26 is a multiple of 26. |

Question 21 |

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

\( \large {{N}^{2}}\) Hint: Squaring always gives a non-negative value. | |

\( \large 6-N\) 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. | |

\( \large -N\) Hint: If N is negative, then -N is positive | |

\( \large 6+N\) Hint: For example, if \(N=-10\), then \(6+N = -4\) |

Question 22 |

#### Use the samples of a student€™s work below to answer the question that follows:

#### This student divides fractions by first finding a common denominator, then dividing the numerators.

\( \large \dfrac{2}{3} \div \dfrac{3}{4} \longrightarrow \dfrac{8}{12} \div \dfrac{9}{12} \longrightarrow 8 \div 9 = \dfrac {8}{9}\)\( \large \dfrac{2}{5} \div \dfrac{7}{20} \longrightarrow \dfrac{8}{20} \div \dfrac{7}{20} \longrightarrow 8 \div 7 = \dfrac {8}{7}\)

\( \large \dfrac{7}{6} \div \dfrac{3}{4} \longrightarrow \dfrac{14}{12} \div \dfrac{9}{12} \longrightarrow 14 \div 9 = \dfrac {14}{9}\)

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

## It is not valid. Common denominators are for adding and subtracting fractions, not for dividing them.Hint: Don't be so rigid! Usually there's more than one way to do something in math. | |

## It got the right answer in these three cases, but it isn‘t valid for all rational numbers.Hint: Did you try some other examples? What makes you say it's not valid? | |

## It is valid if the rational numbers in the division problem are in lowest terms and the divisor is not zero.Hint: Lowest terms doesn't affect this problem at all. | |

## It is valid for all rational numbers, as long as the divisor is not zero.Hint: When we have common denominators, the problem is in the form a/b divided by c/b, and the answer is a/c, as the student's algorithm predicts. |

Question 23 |

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

## AHint: Rise is more than 30 inches. | |

## BHint: Run is almost 24 feet, so rise can be almost 2 feet. | |

## CHint: Run is 12 feet, so rise can be at most 1 foot. | |

## DHint: Slope is 1:10 -- too steep. |

Question 24 |

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

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

## 1.5°Hint: Celsius and Fahrenheit don't increase at the same rate. | |

## 1.8°Hint: That's how much the Fahrenheit temp increases when the Celsius temp goes up by 1 degree. | |

## 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. | |

## 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 25 |

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

\( \large 2{{y}^{3}}+\dfrac{3\pi {{y}^{3}}}{4}\) Hint: The cubes each have volume \(y^3\). The cylinder has radius \(\dfrac{y}{2}\) and height \(3y\). The volume of a cylinder is \(\pi r^2 h=\pi ({\dfrac{y}{2}})^2(3y)=\dfrac{3\pi {{y}^{3}}}{4}\). Note that the volume of a cylinder is analogous to that of a prism -- area of the base times height. | |

\( \large 2{{y}^{3}}+3\pi {{y}^{3}}\) Hint: y is the diameter of the circle, not the radius. | |

\( \large {{y}^{3}}+5\pi {{y}^{3}}\) Hint: Don't forget to count both cubes. | |

\( \large 2{{y}^{3}}+\dfrac{3\pi {{y}^{3}}}{8}\) Hint: Make sure you know how to find the volume of a cylinder. |

Question 26 |

#### 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?

\( \large A(n)=n+4\) 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. | |

\( \large A(n)=n+2\) 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. | |

\( \large A(n)=2n+2\) 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. | |

\( \large A(n)=2\left( n+2 \right)\) 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 27 |

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

\( \large x < 0\) Hint: If x =0, then x/2 = x/3, so this answer can't be correct. | |

\( \large x \le 0\) | |

\( \large x > 0\) Hint: If x =0, then x/2 = x/3, so this answer can't be correct. | |

\( \large x \ge 0\) Hint: Try plugging in x = 6. |

Question 28 |

#### Which of the following nets will not fold into a cube?

Hint: If you have trouble visualizing, cut them out and fold (during the test, you can tear paper to approximate). | |

Hint: If you have trouble visualizing, cut them out and fold (during the test, you can tear paper to approximate). | |

Hint: If you have trouble visualizing, cut them out and fold (during the test, you can tear paper to approximate). |

Question 29 |

#### Use the graph below to answer the question that follows:

#### The graph above represents the equation \( \large 3x+Ay=B\), where A and B are integers. What are the values of A and B?

\( \large A = -2, B= 6\) Hint: Plug in (2,0) to get B=6, then plug in (0,-3) to get A=-2. | |

\( \large A = 2, B = 6\) Hint: Try plugging (0,-3) into this equation. | |

\( \large A = -1.5, B=-3\) Hint: The problem said that A and B were integers and -1.5 is not an integer. Don't try to use slope-intercept form. | |

\( \large A = 2, B = -3\) Hint: Try plugging (2,0) into this equation. |

Question 30 |

#### Aya and Kendra want to estimate the height of a tree. On a sunny day, Aya measures Kendra€™s shadow as 3 meters long, and Kendra measures the tree€™s shadow as 15 meters long. Kendra is 1.5 meters tall. How tall is the tree?

## 7.5 metersHint: Here is a picture, note that the large and small right triangles are similar: One way to do the problem is to note that there is a dilation (scale) factor of 5 on the shadows, so there must be that factor on the heights too. Another way is to note that the shadows are twice as long as the heights. | |

## 22.5 metersHint: Draw a picture. | |

## 30 metersHint: Draw a picture. | |

## 45 metersHint: Draw a picture. |

Question 31 |

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

\( \large 1\) Hint: Use the Pythagorean Theorem. | |

\( \large \sqrt{5}\) Hint: \(2^2+e^2=3^2\) or \(4+e^2=9;e^2=5; e=\sqrt{5}\). | |

\( \large \sqrt{13}\) Hint: e is not the hypotenuse. | |

\( \large 5\) Hint: Use the Pythagorean Theorem. |

Question 32 |

#### There are 15 students for every teacher. Let t represent the number of teachers and let s represent the number of students. Which of the following equations is correct?

\( \large t=s+15\) Hint: When there are 2 teachers, how many students should there be? Do those values satisfy this equation? | |

\( \large s=t+15\) Hint: When there are 2 teachers, how many students should there be? Do those values satisfy this equation? | |

\( \large t=15s\) Hint: This is a really easy mistake to make, which comes from transcribing directly from English, "1 teachers equals 15 students." To see that it's wrong, plug in s=2; do you really need 30 teachers for 2 students? To avoid this mistake, insert the word "number," "Number of teachers equals 15 times number of students" is more clearly problematic. | |

\( \large s=15t\) |

Question 33 |

#### 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?

\( \large \dfrac{502}{1222}\) Hint: This is the probability that a randomly chosen girl who drinks milk was in the 1989-1991 food survey. | |

\( \large \dfrac{502}{2149}\) Hint: This is the probability that a randomly chosen girl from the whole survey drank milk and was also surveyed in 1989-1991. | |

\( \large \dfrac{502}{837}\) | |

\( \large \dfrac{1222}{2149}\) Hint: This is the probability that a randomly chosen girl from any year of the survey drank milk. |

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?

## 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. | |

## 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. | |

## 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. | |

## 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 35 |

#### Given that 10 cm is approximately equal to 4 inches, which of the following expressions models a way to find out approximately how many inches are equivalent to 350 cm?

\( \large 350\times \left( \dfrac{10}{4} \right)\) Hint: The final result should be smaller than 350, and this answer is bigger. | |

\( \large 350\times \left( \dfrac{4}{10} \right)\) Hint: Dimensional analysis can help here: \(350 \text{cm} \times \dfrac{4 \text{in}}{10 \text{cm}}\). The cm's cancel and the answer is in inches. | |

\( \large (10-4) \times 350
\) Hint: This answer doesn't make much sense. Try with a simpler example (e.g. 20 cm not 350 cm) to make sure that your logic makes sense. | |

\( \large (350-10) \times 4\) Hint: This answer doesn't make much sense. Try with a simpler example (e.g. 20 cm not 350 cm) to make sure that your logic makes sense. |

Question 36 |

#### The picture below represents a board with pegs on it, where the closest distance between two pegs is 1 cm. What is the area of the pentagon shown?

Question 37 |

I. \(\large \dfrac{1}{2}+\dfrac{1}{3}\) | II. \( \large .400000\) | III. \(\large\dfrac{1}{5}+\dfrac{1}{5}\) |

IV. \( \large 40\% \) | V. \( \large 0.25 \) | VI. \(\large\dfrac{14}{35}\) |

#### Which of the lists below includes all of the above expressions that are equivalent to \( \dfrac{2}{5}\)?

## I, III, V, VIHint: I and V are not at all how fractions and decimals work. | |

## III, VIHint: These are right, but there are more. | |

## II, III, VIHint: These are right, but there are more. | |

## II, III, IV, VI |

Question 38 |

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

Hint: d(x) is 12 divided by x, not x divided by 12. | |

Hint: When x=2, what should d(x) be? | |

Hint: When x=2, what should d(x) be? | |

Question 39 |

#### 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?

\( \large0.26\) Hint: Please reread the question. | |

\( \large0.2625\) Hint: This is one-quarter of the distance between 0.26 and 0.27, which is not what the question asked. | |

\( \large0.265\) | |

\( \large0.27\) 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 40 |

#### Use the expression below to answer the question that follows:

#### \( \large \dfrac{\left( 7,154 \right)\times \left( 896 \right)}{216}\)

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

## 2,000Hint: The answer is bigger than 7,000. | |

## 20,000Hint: Estimate 896/216 first. | |

## 3,000Hint: The answer is bigger than 7,000. | |

## 30,000Hint: \( \dfrac{896}{216} \approx 4\) and \(7154 \times 4\) is over 28,000, so this answer is closest. |

Question 41 |

#### The expression \( \large {{7}^{-4}}\cdot {{8}^{-6}}\) is equal to which of the following?

\( \large \dfrac{8}{{{\left( 56 \right)}^{4}}}\) Hint: The bases are whole numbers, and the exponents are negative. How can the numerator be 8? | |

\( \large \dfrac{64}{{{\left( 56 \right)}^{4}}}\) Hint: The bases are whole numbers, and the exponents are negative. How can the numerator be 64? | |

\( \large \dfrac{1}{8\cdot {{\left( 56 \right)}^{4}}}\) Hint: \(8^{-6}=8^{-4} \times 8^{-2}\) | |

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

Question 42 |

#### 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?

\( \large A = 0, B = 4\) Hint: Digits add to 31, so not divisible by 3, so not divisible by 12. | |

\( \large A = 7, B = 2\) Hint: Digits add to 36, so divisible by 9. | |

\( \large A = 0, B = 6\) Hint: Digits add to 33, divisible by 3, not 9. Last digits are 36, so divisible by 4, and hence by 12. | |

\( \large A = 4, B = 8\) 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 43 |

#### The chairs in a large room can be arranged in rows of 18, 25, or 60 with no chairs left over. If C is the smallest possible number of chairs in the room, which of the following inequalities does C satisfy?

\( \large C\le 300\) Hint: Find the LCM. | |

\( \large 300 < C \le 500 \) Hint: Find the LCM. | |

\( \large 500 < C \le 700 \) Hint: Find the LCM. | |

\( \large C>700\) Hint: The LCM is 900, which is the smallest number of chairs. |

Question 44 |

#### 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?

\( \large \dfrac{34}{43}\) | |

\( \large \dfrac{34}{71}\) Hint: This is the probability that a randomly chosen junior or senior is a commuter student. | |

\( \large \dfrac{34}{147}\) Hint: This is the probability that a randomly chosen student is a junior or senior who is a commuter. | |

\( \large \dfrac{71}{147}\) Hint: This is the probability that a randomly chosen student is a junior or a senior. |

Question 45 |

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

\( \large \dfrac{1}{4}\) Hint: Try a simpler question with 3 children -- call them big, medium, and small -- and list all the ways they could line up. Then see how to extend your logic to the problem with 4 children. | |

\( \large \dfrac{1}{256}
\) Hint: Try a simpler question with 3 children -- call them big, medium, and small -- and list all the ways they could line up. Then see how to extend your logic to the problem with 4 children. | |

\( \large \dfrac{1}{16}\) Hint: Try a simpler question with 3 children -- call them big, medium, and small -- and list all the ways they could line up. Then see how to extend your logic to the problem with 4 children. | |

\( \large \dfrac{1}{24}\) Hint: The number of ways for the children to line up is \(4!=4 \times 3 \times 2 \times 1 =24\) -- there are 4 choices for who is first in line, then 3 for who is second, etc. Only one of these lines has the children in the order specified. |

List |

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