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MTEL General Curriculum Mathematics Practice
Question 1 
In January 2011, the national debt was about 14 trillion dollars and the US population was about 300 million people. Someone reading these figures estimated that the national debt was about $5,000 per person. Which of these statements best describes the reasonableness of this estimate?
It is too low by a factor of 10Hint: 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.  
It is too low by a factor of 100  
It is too high by a factor of 10  
It is too high by a factor of 100 
Question 2 
Each individual cube that makes up the rectangular solid depicted below has 6 inch sides. What is the surface area of the solid in square feet?
\( \large 11\text{ f}{{\text{t}}^{2}}\) Hint: Check your units and make sure you're using feet and inches consistently.  
\( \large 16.5\text{ f}{{\text{t}}^{2}}\) Hint: Each square has surface area \(\dfrac{1}{2} \times \dfrac {1}{2}=\dfrac {1}{4}\) sq feet. There are 9 squares on the top and bottom, and 12 on each of 4 sides, for a total of 66 squares. 66 squares \(\times \dfrac {1}{4}\) sq feet/square =16.5 sq feet.  
\( \large 66\text{ f}{{\text{t}}^{2}}\) Hint: The area of each square is not 1.  
\( \large 2376\text{ f}{{\text{t}}^{2}}\) Hint: Read the question more carefully  the answer is supposed to be in sq feet, not sq inches.

Question 3 
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/pageHint: This would mean that each page of the book was 125 cm thick.  
Intercept =0.4 cm, Slope = \(\dfrac{1}{125}\)cm/pageHint: 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.  
Intercept = 125 cm, Slope = 0.4 cmHint: This would mean that with no pages in the book, it would be 125 cm thick.  
Intercept = \(\dfrac{1}{125}\)cm, Slope = 0.4 pages/cmHint: This would mean that each new page of the book made it 0.4 cm thicker. 
Question 4 
Use the graph below to answer the question that follows.
Which of the following is a correct equation for the graph of the line depicted above?
\( \large y=\dfrac{1}{2}x+2\) Hint: The slope is 1/2 and the yintercept is 2. You can also try just plugging in points. For example, this is the only choice that gives y=1 when x=2.  
\( \large 4x=2y\) Hint: This line goes through (0,0); the graph above does not.  
\( \large y=x+2\) Hint: The line pictured has negative slope.  
\( \large y=x+2\) Hint: Try plugging x=4 into this equation and see if that point is on the graph above. 
Question 5 
A class is using baseten block to represent numbers. A large cube represents 1000, a flat represents 100, a rod represents 10, and a little cube represents 1. Which of these is not a correct representation for 2,347?
23 flats, 4 rods, 7 little cubesHint: Be sure you read the question carefully: 2300+40+7=2347  
2 large cubes, 3 flats, 47 rodsHint: 2000+300+470 \( \neq\) 2347  
2 large cubes, 34 rods, 7 little cubesHint: Be sure you read the question carefully: 2000+340+7=2347  
2 large cubes, 3 flats, 4 rods, 7 little cubesHint: Be sure you read the question carefully: 2000+300+40+7=2347 
Question 6 
Some children explored the diagonals in 2 x 2 squares on pages of a calendar (where all four squares have numbers in them). They conjectured that the sum of the diagonals is always equal; in the example below, 8+16=9+15.
Which of the equations below could best be used to explain why the children€™s conjecture is correct?
\( \large 8x+16x=9x+15x\) Hint: What would x represent in this case? Make sure you can describe in words what x represents.  
\( \large x+(x+2)=(x+1)+(x+1)\) Hint: What would x represent in this case? Make sure you can describe in words what x represents.  
\( \large x+(x+8)=(x+1)+(x+7)\) Hint: x is the number in the top left square, x+8 is one below and to the right, x+1 is to the right of x, and x+7 is below x.  
\( \large x+8+16=x+9+15\) Hint: What would x represent in this case? Make sure you can describe in words what x represents. 
Question 7 
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 8 
How many lines of reflective symmetry and how many centers of rotational symmetry does the parallelogram depicted below have?
4 lines of reflective symmetry, 1 center of rotational symmetry.Hint: Try cutting out a shape like this one from paper, and fold where you think the lines of reflective symmetry are (or put a mirror there). Do things line up as you thought they would?  
2 lines of reflective symmetry, 1 center of rotational symmetry.Hint: Try cutting out a shape like this one from paper, and fold where you think the lines of reflective symmetry are (or put a mirror there). Do things line up as you thought they would?  
0 lines of reflective symmetry, 1 center of rotational symmetry.Hint: The intersection of the diagonals is a center of rotational symmetry. There are no lines of reflective symmetry, although many people get confused about this fact (best to play with hands on examples to get a feel). Just fyi, the letter S also has rotational, but not reflective symmetry, and it's one that kids often write backwards.  
2 lines of reflective symmetry, 0 centers of rotational symmetry.Hint: Try cutting out a shape like this one from paper. Trace onto another sheet of paper. See if there's a way to rotate the cut out shape (less than a complete turn) so that it fits within the outlines again. 
Question 9 
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)?
\( \large 343.2\times 60\times 10\) Hint: In kilometers, not meters.  
\( \large 343.2\times 60\times 10\times \dfrac{1}{1000}\) Hint: Units are meters/sec \(\times\) seconds/minute \(\times\) minutes \(\times\) kilometers/meter, and the answer is in kilometers.  
\( \large 343.2\times \dfrac{1}{60}\times 10\) Hint: Include units and make sure answer is in kilometers.  
\( \large 343.2\times \dfrac{1}{60}\times 10\times \dfrac{1}{1000}\) Hint: Include units and make sure answer is in kilometers. 
Question 10 
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 11 
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 12 
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 13 
An aboveground 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 14 
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 15 
The window glass below has the shape of a semicircle on top of a square, where the side of the square has length x. It was cut from one piece of glass.
What is the perimeter of the window glass?
\( \large 3x+\dfrac{\pi x}{2}\) Hint: By definition, \(\pi\) is the ratio of the circumference of a circle to its diameter; thus the circumference is \(\pi d\). Since we have a semicircle, its perimeter is \( \dfrac{1}{2} \pi x\). Only 3 sides of the square contribute to the perimeter.  
\( \large 3x+2\pi x\) Hint: Make sure you know how to find the circumference of a circle.  
\( \large 3x+\pi x\) Hint: Remember it's a semicircle, not a circle.  
\( \large 4x+2\pi x\) Hint: Only 3 sides of the square contribute to the perimeter. 
Question 16 
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 17 
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 18 
Use the solution procedure below to answer the question that follows:
\( \large {\left( x+3 \right)}^{2}=10\)
\( \large \left( x+3 \right)\left( x+3 \right)=10\)
\( \large {x}^{2}+9=10\)
\( \large {x}^{2}+99=109\)
\( \large {x}^{2}=1\)
\( \large x=1\text{ or }x=1\)
Which of the following is incorrect in the procedure shown above?
The commutative property is used incorrectly.Hint: The commutative property is \(a+b=b+a\) or \(ab=ba\).  
The associative property is used incorrectly.Hint: The associative property is \(a+(b+c)=(a+b)+c\) or
\(a \times (b \times c)=(a \times b) \times c\).  
Order of operations is done incorrectly.  
The distributive property is used incorrectly.Hint: \((x+3)(x+3)=x(x+3)+3(x+3)\)=\(x^2+3x+3x+9.\) 
Question 19 
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 20 
Here is a number trick:
1) Pick a whole number
2) Double your number.
3) Add 20 to the above result.
4) Multiply the above by 5
5) Subtract 100
6) Divide by 10
The result is always the number that you started with! Suppose you start by picking N. Which of the equations below best demonstrates that the result after Step 6 is also N?
\( \large N*2+20*5100\div 10=N\) Hint: Use parentheses or else order of operations is off.  
\( \large \left( \left( 2*N+20 \right)*5100 \right)\div 10=N\)  
\( \large \left( N+N+20 \right)*5100\div 10=N\) Hint: With this answer you would subtract 10, instead of subtracting 100 and then dividing by 10.  
\( \large \left( \left( \left( N\div 10 \right)100 \right)*5+20 \right)*2=N\) Hint: This answer is quite backwards. 
Question 21 
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 22 
The least common multiple of 60 and N is 1260. Which of the following could be the prime factorization of N?
\( \large2\cdot 5\cdot 7\) Hint: 1260 is divisible by 9 and 60 is not, so N must be divisible by 9 for 1260 to be the LCM.  
\( \large{{2}^{3}}\cdot {{3}^{2}}\cdot 5 \cdot 7\) Hint: 1260 is not divisible by 8, so it isn't a multiple of this N.  
\( \large3 \cdot 5 \cdot 7\) Hint: 1260 is divisible by 9 and 60 is not, so N must be divisible by 9 for 1260 to be the LCM.  
\( \large{{3}^{2}}\cdot 5\cdot 7\) Hint: \(1260=2^2 \cdot 3^2 \cdot 5 \cdot 7\) and \(60=2^2 \cdot 3 \cdot 5\). In order for 1260 to be the LCM, N has to be a multiple of \(3^2\) and of 7 (because 60 is not a multiple of either of these). N also cannot introduce a factor that would require the LCM to be larger (as in choice b). 
Question 23 
The histogram below shows the frequency of a class€™s scores on a 4 question quiz.
What was the mean score on the quiz?
\( \large 2.75\) Hint: There were 20 students who took the quiz. Total points earned: \(2 \times 1+6 \times 2+ 7\times 3+5 \times 4=55\), and 55/20 = 2.75.  
\( \large 2\) Hint: How many students are there total? Did you count them all?  
\( \large 3\) Hint: How many students are there total? Did you count them all? Be sure you're finding the mean, not the median or the mode.  
\( \large 2.5\) Hint: How many students are there total? Did you count them all? Don't just take the mean of 1, 2, 3, 4  you have to weight them properly. 
Question 24 
Elena is going to use a calculator to check whether or not 267 is prime. She will pick certain divisors, and then find 267 divided by each, and see if she gets a whole number. If she never gets a whole number, then she€™s found a prime. Which numbers does Elena NEED to check before she can stop checking and be sure she has a prime?
All natural numbers from 2 to 266.Hint: She only needs to check primes  checking the prime factors of any composite is enough to look for divisors. As a test taking strategy, the other three choices involve primes, so worth thinking about.  
All primes from 2 to 266 .Hint: Remember, factors come in pairs (except for square root factors), so she would first find the smaller of the pair and wouldn't need to check the larger.  
All primes from 2 to 133 .Hint: She doesn't need to check this high. Factors come in pairs, and something over 100 is going to be paired with something less than 3, so she will find that earlier.  
All primes from \( \large 2\) to \( \large \sqrt{267}\).Hint: \(\sqrt{267} \times \sqrt{267}=267\). Any other pair of factors will have one factor less than \( \sqrt{267}\) and one greater, so she only needs to check up to \( \sqrt{267}\). 
Question 25 
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 26 
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 27 
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 28 
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 29 
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 30 
The pattern below consists of a row of black squares surrounded by white squares.
How many white squares would surround a row of 157 black squares?
314Hint: Try your procedure on a smaller number that you can count to see where you made a mistake.  
317Hint: Are there ever an odd number of white squares?  
320Hint: One way to see this is that there are 6 tiles on the left and right ends, and the rest of the white tiles are twice the number of black tiles (there are many other ways to look at it too).  
322Hint: Try your procedure on a smaller number that you can count to see where you made a mistake. 
Question 31 
The "houses" below are made of toothpicks and gum drops.
How many toothpicks are there in a row of 53 houses?
212Hint: Can the number of toothpicks be even?  
213Hint: One way to see this is that every new "house" adds 4 toothpicks to the leftmost vertical toothpick  so the total number is 1 plus 4 times the number of "houses." There are many other ways to look at the problem too.  
217Hint: Try your strategy with a smaller number of "houses" so you can count and find your mistake.  
265Hint: Remember that the "houses" overlap some walls. 
Question 32 
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 33 
Which of the lines depicted below is a graph of \( \large y=2x5\)?
aHint: The slope of line a is negative.  
bHint: Wrong slope and wrong intercept.  
cHint: The intercept of line c is positive.  
dHint: Slope is 2  for every increase of 1 in x, y increases by 2. Intercept is 5  the point (0,5) is on the line. 
Question 34 
In March of 2012, 1 dollar was worth the same as 0.761 Euros, and 1 dollar was also worth the same as 83.03 Japanese Yen. Which of the expressions below gives the number of Yen that are worth 1 Euro?
\( \large {83}.0{3}\cdot 0.{761}\) Hint: This equation gives less than the number of yen per dollar, but 1 Euro is worth more than 1 dollar.  
\( \large \dfrac{0.{761}}{{83}.0{3}}\) Hint: Number is way too small.  
\( \large \dfrac{{83}.0{3}}{0.{761}}\) Hint: One strategy here is to use easier numbers, say 1 dollar = .5 Euros and 100 yen, then 1 Euro would be 200 Yen (change the numbers in the equations and see what works). Another is to use dimensional analysis: we want # yen per Euro, or yen/Euro = yen/dollar \(\times\) dollar/Euro = \(83.03 \times \dfrac {1}{0.761}\)  
\( \large \dfrac{1}{0.{761}}\cdot \dfrac{1}{{83}.0{3}}\) Hint: Number is way too small. 
Question 35 
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 36 
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.  
\( \large 3+0.1m=400+29.99+.20(m400)\) 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.  
\( \large 3+0.1m=29.99+.20(m400)\) 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 37 
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 38 
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 39 
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 d1/7 miles. The total is 2.60+2.80(d1/7) = 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 40 
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 41 
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 42 
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 43 
The chart below gives percentiles for the number of situps 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 situps 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 situps 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 situps in 60 seconds and half can do more than 41 situps 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 situps 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 44 
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 45 
Below is a portion of a number line:
Point B is halfway between two tick marks. What number is represented by Point B?
\( \large 0.645\) Hint: That point is marked on the line, to the right.  
\( \large 0.6421\) Hint: That point is to the left of point B.  
\( \large 0.6422\) Hint: That point is to the left of point B.  
\( \large 0.6425\) 
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