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 |

#### Cell phone plan A charges $3 per month plus $0.10 per minute. Cell phone plan B charges $29.99 per month, with no fee for the first 400 minutes and then $0.20 for each additional minute.

#### Which equation can be used to solve for the number of minutes, m (with m>400) that a person would have to spend on the phone each month in order for the bills for plan A and plan B to be equal?

\( \large 3.10m=400+0.2m\) Hint: These are the numbers in the problem, but this equation doesn't make sense. If you don't know how to make an equation, try plugging in an easy number like m=500 minutes to see if each side equals what it should. | |

\( \large 3+0.1m=29.99+.20m\) Hint: Doesn't account for the 400 free minutes. | |

\( \large 3+0.1m=400+29.99+.20(m-400)\) Hint: Why would you add 400 minutes and $29.99? If you don't know how to make an equation, try plugging in an easy number like m=500 minutes to see if each side equals what it should. | |

\( \large 3+0.1m=29.99+.20(m-400)\) Hint: The left side is $3 plus $0.10 times the number of minutes. The right is $29.99 plus $0.20 times the number of minutes over 400. |

Question 2 |

#### Below is a pictorial representation of \(2\dfrac{1}{2}\div \dfrac{2}{3}\):

#### Which of the following is the best description of how to find the quotient from the picture?

## The quotient is \(3\dfrac{3}{4}\). There are 3 whole blocks each representing \(\dfrac{2}{3}\) and a partial block composed of 3 small rectangles. The 3 small rectangles represent \(\dfrac{3}{4}\) of \(\dfrac{2}{3}\). | |

## The quotient is \(3\dfrac{1}{2}\). There are 3 whole blocks each representing \(\dfrac{2}{3}\) and a partial block composed of 3 small rectangles. The 3 small rectangles represent \(\dfrac{3}{6}\) of a whole, or \(\dfrac{1}{2}\).Hint: We are counting how many 2/3's are in 2 1/2: the unit becomes 2/3, not 1. | |

## The quotient is \(\dfrac{4}{15}\). There are four whole blocks separated into a total of 15 small rectangles.Hint: This explanation doesn't make much sense. Probably you are doing "invert and multiply," but inverting the wrong thing. | |

## This picture cannot be used to find the quotient because it does not show how to separate \(2\dfrac{1}{2}\) into equal sized groups.Hint: Study the measurement/quotative model of division. It's often very useful with fractions. |

Question 3 |

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

\( \large \dfrac{7}{16}\) Hint: Multiplication comes before addition and subtraction in the order of operations. | |

\( \large \dfrac{1}{2}\) Hint: Addition and subtraction are of equal priority in the order of operations -- do them left to right. | |

\( \large \dfrac{3}{4}\) Hint: \( \dfrac{3}{4}-\dfrac{1}{8}+\dfrac{2}{8}\times \dfrac{1}{2}\)=\( \dfrac{3}{4}-\dfrac{1}{8}+\dfrac{1}{8}\)=\( \dfrac{3}{4}+-\dfrac{1}{8}+\dfrac{1}{8}\)=\( \dfrac{3}{4}\) | |

\( \large \dfrac{3}{16}\) Hint: Multiplication comes before addition and subtraction in the order of operations. |

Question 4 |

#### 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?

## $2Hint: A possible fee, but not the largest possible fee. Check the other choices to see which are factors of all three numbers. | |

## $7Hint: A possible fee, but not the largest possible fee. Check the other choices to see which are factors of all three numbers. | |

## $14Hint: This is the greatest common factor of 70, 126, and 266. | |

## $70Hint: Not a factor of 126 or 266, so couldn't be correct. |

Question 5 |

#### 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?

\( \large A = 3, B = 2, C=0\) 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. | |

\( \large A = 0, B = 0, C=4\) Hint: Not divisible by 10, since it doesn't end in 0. | |

\( \large A = 4, B = 2, C=0\) 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. | |

\( \large A =1, B=0, C=0\) 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 |

#### 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 7 |

#### 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 8 |

#### 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 9 |

#### 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 10 |

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

\( \large 20{}^\circ \) Hint: Angles ACD and ADC are congruent since they are base angles of an isosceles triangle. Since the angles of a triangle sum to 180, they sum to 80, and they are 40 deg each. Thus angle ADE is 140 deg, since it makes a straight line with angle ADC. Angles DAE and DEA are base angles of an isosceles triangle and thus congruent-- they sum to 40 deg, so are 20 deg each. | |

\( \large 25{}^\circ \) Hint: If two sides of a triangle are congruent, then it's isosceles, and the base angles of an isosceles triangle are equal. | |

\( \large 30{}^\circ \) Hint: If two sides of a triangle are congruent, then it's isosceles, and the base angles of an isosceles triangle are equal. | |

\( \large 40{}^\circ \) Hint: Make sure you're calculating the correct angle. |

Question 11 |

#### 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?

\( \large \$2.60+\$0.40d\) Hint: It's 40 cents for 1/7 of a mile, not per mile. | |

\( \large \$2.60+\$0.40\dfrac{d}{7}\) Hint: According to this equation, going 7 miles would cost $3; does that make sense? | |

\( \large \$2.20+\$2.80d\) 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. | |

\( \large \$2.60+\$2.80d\) Hint: Don't count the first 1/7 of a mile twice. |

Question 12 |

#### 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 13 |

#### 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 14 |

#### 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 15 |

#### Which of the graphs below represent functions?

**I.**

**II.**

**III.**

**IV.**

## I and IV only.Hint: There are vertical lines that go through 2 points in IV . | |

## 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). | |

## II and III only.Hint: Learn about the vertical line test. | |

## I, II, and IV only.Hint: There are vertical lines that go through 2 points in II. |

Question 16 |

#### 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 17 |

#### A family on vacation drove the first 200 miles in 4 hours and the second 200 miles in 5 hours. Which expression below gives their average speed for the entire trip?

\( \large \dfrac{200+200}{4+5}\) Hint: Average speed is total distance divided by total time. | |

\( \large \left( \dfrac{200}{4}+\dfrac{200}{5} \right)\div 2\) Hint: This seems logical, but the problem is that it weights the first 4 hours and the second 5 hours equally, when each hour should get the same weight in computing the average speed. | |

\( \large \dfrac{200}{4}+\dfrac{200}{5} \) Hint: This would be an average of 90 miles per hour! | |

\( \large \dfrac{400}{4}+\dfrac{400}{5} \) Hint: This would be an average of 180 miles per hour! Even a family of race car drivers probably doesn't have that average speed on a vacation! |

Question 18 |

#### 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?

## 30Hint: 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. | |

## 120Hint: The floor is 120 sq feet, and the tiles are smaller than 1 sq foot. | |

## 300Hint: Recheck your calculations. | |

## 360Hint: 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 19 |

#### 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 20 |

#### 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.

\( \large \dfrac{1}{7}\) 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. | |

\( \large \dfrac{1}{14}\) Hint: What would be the sample space here? Ie, how would you list 14 things that you pick one from? | |

\( \large \dfrac{1}{42}\) 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. | |

\( \large \dfrac{1}{49}\) Hint: This is the probability that they are both born on a particular day, e.g. Sunday. |

Question 21 |

#### 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 22 |

#### 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 23 |

#### 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?

## I only | |

## I and II only | |

## I and III only | |

## I, II, and IIIHint: The integers are ...-3, -2, -1, 0, 1, 2, 3, .... |

Question 24 |

#### 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%.

\( \large \dfrac{1}{2}\) Hint: How many different configurations are there from oldest to youngest, e.g. BGGG? How many of them have 2 boys and 2 girls? | |

\( \large \dfrac{1}{4}\) Hint: How many different configurations are there from oldest to youngest, e.g. BGGG? How many of them have 2 boys and 2 girls? | |

\( \large \dfrac{1}{5}\) 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. | |

\( \large \dfrac{3}{8}\) 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 25 |

#### In which table below is y a function of x?

Hint: If x=3, y can have two different values, so it's not a function. | |

Hint: If x=3, y can have two different values, so it's not a function. | |

Hint: If x=1, y can have different values, so it's not a function. | |

Hint: Each value of x always corresponds to the same value of y. |

Question 26 |

#### 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?

\( \large \dfrac{3}{100}=\dfrac{d}{753}\) Hint: Units on both side are inches/mile, and both numerators and denominators correspond -- this one is correct. | |

\( \large \dfrac{3}{100}=\dfrac{753}{d}\) 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. | |

\( \large \dfrac{3}{d}=\dfrac{100}{753}\) 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. | |

\( \large 100d=3\cdot 753\) Hint: This is equivalent to part A. |

Question 27 |

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

\( \large 6x\) Hint: Use the Pythagorean Theorem. | |

\( \large 3x+5{{x}^{2}}\) Hint: Don't forget to take square roots when you use the Pythagorean Theorem. | |

\( \large 3x+\sqrt{5}{{x}^{2}}\) Hint: \(\sqrt {5 x^2}\) is not \(\sqrt {5}x^2\). | |

\( \large 3x+\sqrt{5}{{x}^{{}}}\) 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 28 |

#### Which of the following is equivalent to

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

\( \large A-B-\dfrac{C}{DE}
\) Hint: In the order of operations, multiplication and division have the same priority, so do them left to right; same with addition and subtraction. | |

\( \large A-B+\dfrac{CE}{D}\) 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. | |

\( \large \dfrac{AE-BE+CE}{D}\) Hint: Use order of operations, don't just compute left to right. | |

\( \large A-B+\dfrac{C}{DE}\) Hint: In the order of operations, multiplication and division have the same priority, so do them left to right |

Question 29 |

#### Here is a student€™s work on several multiplication problems:

#### For which of the following problems is this student most likely to get the correct solution, even though he is using an incorrect algorithm?

## 58 x 22Hint: This problem involves regrouping, which the student does not do correctly. | |

## 16 x 24Hint: This problem involves regrouping, which the student does not do correctly. | |

## 31 x 23Hint: There is no regrouping with this problem. | |

## 141 x 32Hint: This problem involves regrouping, which the student does not do correctly. |

Question 30 |

#### 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 31 |

#### 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 32 |

#### 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?

Hint: Try following the point (1,4) to see where it goes after each transformation. | |

Hint: Make sure you're reflecting in the correct axis. | |

Hint: Make sure you're rotating the correct direction. |

Question 33 |

#### How many factors does 80 have?

\( \large8\) Hint: Don't forget 1 and 80. | |

\( \large9\) Hint: Only perfect squares have an odd number of factors -- otherwise factors come in pairs. | |

\( \large10\) Hint: 1,2,4,5,8,10,16,20,40,80 | |

\( \large12\) Hint: Did you count a number twice? Include a number that isn't a factor? |

Question 34 |

#### 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 35 |

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

## TetrahedronHint: All the faces of a tetrahedron are triangles. | |

## Triangular PrismHint: A prism has two congruent, parallel bases, connected by parallelograms (since this is a right prism, the parallelograms are rectangles). | |

## Triangular PyramidHint: A pyramid has one base, not two. | |

## TrigonHint: A trigon is a triangle (this is not a common term). |

Question 36 |

#### 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 37 |

#### 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?

## 100Hint: 6124/977 is approximately 6. | |

## 200Hint: 6124/977 is approximately 6. | |

## 1,000Hint: 6124/977 is approximately 6. 155 is approximately 150, and \( 6 \times 150 = 3 \times 300 = 900\), so this answer is closest. | |

## 2,000Hint: 6124/977 is approximately 6. |

Question 38 |

## AHint: \(\frac{34}{135} \approx \frac{1}{4}\) and \( \frac{53}{86} \approx \frac {2}{3}\). \(\frac {1}{4}\) of \(\frac {2}{3}\) is small and closest to A. | |

## BHint: Estimate with simpler fractions. | |

## CHint: Estimate with simpler fractions. | |

## DHint: Estimate with simpler fractions. |

Question 39 |

#### 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 40 |

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

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

\( \large -0.04,\quad -0.044,\quad 0.044,\quad 0.04\) Hint: 0.04=0.040, which is less than 0.044. | |

\( \large -0.04,\quad -0.044,\quad 0.04,\quad 0.044\) Hint: -0.04=-0.040, which is greater than \(-0.044\). | |

\( \large -0.044,\quad -0.04,\quad 0.044,\quad 0.04\) Hint: 0.04=0.040, which is less than 0.044. |

Question 41 |

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

## 0.38Hint: 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. | |

## 0.125Hint: This is 1/8, not 3/8. | |

## 0.375 | |

## 0.83Hint: 3/8 is less than a half, and 0.83 is more than a half, so they can't be equal. |

Question 42 |

#### What is the greatest common factor of 540 and 216?

\( \large{{2}^{2}}\cdot {{3}^{3}}\) 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 take the smaller power for each prime that is a factor of both numbers. | |

\( \large2\cdot 3\) Hint: This is a common factor of both numbers, but it's not the greatest common factor. | |

\( \large{{2}^{3}}\cdot {{3}^{3}}\) Hint: \(2^3 = 8\) is not a factor of 540. | |

\( \large{{2}^{2}}\cdot {{3}^{2}}\) Hint: This is a common factor of both numbers, but it's not the greatest common factor. |

Question 43 |

#### 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 44 |

#### 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 45 |

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

#### Which of the following could be the solid shown above?

## A sphereHint: All views would be circles. | |

## A cylinder | |

## A coneHint: Two views would be triangles, not rectangles. | |

## A pyramidHint: How would one view be a circle? |

List |

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