20 Random Questions

Hints will display for most wrong answers; explanations for most right answers. You can attempt a question multiple times; it will only be scored correct if you get it right the first time.

I used the official objectives and sample test to construct these questions, but cannot promise that they accurately reflect what’s on the real test. Some of the sample questions were more convoluted than I could bear to write. See terms of use. See the MTEL Practice Test main page to view questions on a particular topic or to download paper practice tests.

MTEL General Curriculum Mathematics Practice

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Question 1

Use the problem below to answer the question that follows:

T shirts are on sale for 20% off. Tasha paid $8.73 for a shirt. What is the regular price of the shirt? There is no tax on clothing purchases under $175.

Let p represent the regular price of these t-shirt. Which of the following equations is correct?

A	$ \large 0.8p=\$8.73$ Hint: 80% of the regular price = $8.73.
B	$ \large \$8.73+0.2*\$8.73=p$ Hint: The 20% off was off of the ORIGINAL price, not off the $8.73 (a lot of people make this mistake). Plus this is the same equation as in choice c.
C	$ \large 1.2*\$8.73=p$ Hint: The 20% off was off of the ORIGINAL price, not off the $8.73 (a lot of people make this mistake). Plus this is the same equation as in choice b.
D	$ \large p-0.2*\$8.73=p$ Hint: Subtract p from both sides of this equation, and you have -.2 x 8.73 =0.

Question 1 Explanation:

Topics: Use algebra to solve word problems involving percents and identify variables, and derive algebraic expressions that represent real-world situations (Objective 0020).

Question 2

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

A	30 Hint: The floor is 120 sq feet, and the tiles are smaller than 1 sq foot. Also, remember that 1 sq foot is 12 $\times$ 12=144 sq inches.
B	120 Hint: The floor is 120 sq feet, and the tiles are smaller than 1 sq foot.
C	300 Hint: Recheck your calculations.
D	360 Hint: One way to do this is to note that 6 inches = 1/2 foot and 8 inches = 2/3 foot, so the area of each tile is 1/2 $\times$ 2/3=1/3 sq foot, or each square foot of floor requires 3 tiles. The area of the floor is 120 square feet. Note that the tiles would fit evenly oriented in either direction, parallel to the walls.

Question 2 Explanation:

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

Question 3

The letters A, and B represent digits (possibly equal) in the ten digit number x=1,438,152,A3B. For which values of A and B is x divisible by 12, but not by 9?

A	$ \large A = 0, B = 4$ Hint: Digits add to 31, so not divisible by 3, so not divisible by 12.
B	$ \large A = 7, B = 2$ Hint: Digits add to 36, so divisible by 9.
C	$ \large A = 0, B = 6$ Hint: Digits add to 33, divisible by 3, not 9. Last digits are 36, so divisible by 4, and hence by 12.
D	$ \large A = 4, B = 8$ Hint: Digits add to 39, divisible by 3, not 9. Last digits are 38, so not divisible by 4, so not divisible by 12.

Question 3 Explanation:

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

Question 4

Use the expression below to answer the question that follows.

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

Which of the following is equivalent to the expression above?

A	2 Hint: $10^3 \times 10^4=10^7$, and note that if you're guessing when the answers are so closely related, you're generally better off guessing one of the middle numbers.
B	20 Hint: $ \dfrac{\left( 4\times {{10}^{3}} \right)\times \left( 3\times {{10}^{4}} \right)}{6\times {{10}^{6}}}=\dfrac {12 \times {{10}^{7}}}{6\times {{10}^{6}}}=$$2 \times {{10}^{1}}=20 $
C	200 Hint: $10^3 \times 10^4=10^7$
D	2000 Hint: $10^3 \times 10^4=10^7$, and note that if you're guessing when the answers are so closely related, you're generally better off guessing one of the middle numbers.

Question 4 Explanation:

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

Question 5

The Americans 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?

A	A Hint: Rise is more than 30 inches.
B	B Hint: Run is almost 24 feet, so rise can be almost 2 feet.
C	C Hint: Run is 12 feet, so rise can be at most 1 foot.
D	D Hint: Slope is 1:10 -- too steep.

Question 5 Explanation:

Topic: Interpret meaning of slope in a real world situation (Objective 0022).

Question 6

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

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

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

Question 6 Explanation:

Topics: Understand various representations of functions, and translate among different representations of functional relationships (Objective 0021).

Question 7

In January 2011, the national debt was about 14 trillion dollars and the US population was about 300 million people. Someone reading these figures estimated that the national debt was about $5,000 per person. Which of these statements best describes the reasonableness of this estimate?

A	It is too low by a factor of 10 Hint: 14 trillion $ \approx 15 \times {{10}^{12}} $ and 300 million $ \approx 3 \times {{10}^{8}}$, so the true answer is about $ 5 \times {{10}^{4}} $ or $50,000.
B	It is too low by a factor of 100
C	It is too high by a factor of 10
D	It is too high by a factor of 100

Question 7 Explanation:

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

Question 8

Use the expression below to answer the question that follows.

$\large \dfrac{\left( 155 \right)\times \left( 6,124 \right)}{977}$

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

A	100 Hint: 6124/977 is approximately 6.
B	200 Hint: 6124/977 is approximately 6.
C	1,000 Hint: 6124/977 is approximately 6. 155 is approximately 150, and $ 6 \times 150 = 3 \times 300 = 900$, so this answer is closest.
D	2,000 Hint: 6124/977 is approximately 6.

Question 8 Explanation:

Topics: Estimation, simplifying fractions (Objective 0016).

Question 9

If x is an integer, which of the following must also be an integer?

A	$ \large \dfrac{x}{2}$ Hint: If x is odd, then $ \dfrac{x}{2} $ is not an integer, e.g. 3/2 = 1.5.
B	$ \large \dfrac{2}{x}$ Hint: Only an integer if x = -2, -1, 1, or 2.
C	$ \large-x$ Hint: -1 times any integer is still an integer.
D	$\large\sqrt{x}$ Hint: Usually not an integer, e.g. $ \sqrt{2} \approx 1.414 $.

Question 9 Explanation:

Topic: Integers (Objective 0016)

Question 10

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

Which of the following could be the solid shown above?

A	A sphere Hint: All views would be circles.
B	A cylinder
C	A cone Hint: Two views would be triangles, not rectangles.
D	A pyramid Hint: How would one view be a circle?

Question 10 Explanation:

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

Question 11

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

A	$ \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.
B	$ \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.
C	$ \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.
D	$ \large 40{}^\circ $ Hint: Make sure you're calculating the correct angle.

Question 11 Explanation:

Topic: Classify and analyze polygons using attributes of sides and angles, including real-world applications. (Objective 0024).

Question 12

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}$?

A	I, III, V, VI Hint: I and V are not at all how fractions and decimals work.
B	III, VI Hint: These are right, but there are more.
C	II, III, VI Hint: These are right, but there are more.
D	II, III, IV, VI

Question 12 Explanation:

Topic: Converting between fractions, decimals, and percents (Objective 0017)

Question 13

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

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

Question 13 Explanation:

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

Question 14

Below is a portion of a number line:

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

A	$ \large 0.645$ Hint: That point is marked on the line, to the right.
B	$ \large 0.6421$ Hint: That point is to the left of point B.
C	$ \large 0.6422$ Hint: That point is to the left of point B.
D	$ \large 0.6425$

Question 14 Explanation:

Topic: Using Number Lines (Objective 0017)

Question 15

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

A	$ \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.
B	$ \large -0.04,\quad -0.044,\quad 0.044,\quad 0.04$ Hint: 0.04=0.040, which is less than 0.044.
C	$ \large -0.04,\quad -0.044,\quad 0.04,\quad 0.044$ Hint: -0.04=-0.040, which is greater than $-0.044$.
D	$ \large -0.044,\quad -0.04,\quad 0.044,\quad 0.04$ Hint: 0.04=0.040, which is less than 0.044.

Question 15 Explanation:

Topic: Ordering decimals and integers (Objective 0017).

Question 16

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?

A	$ \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.
B	$ \large 2{{y}^{3}}+3\pi {{y}^{3}}$ Hint: y is the diameter of the circle, not the radius.
C	$ \large {{y}^{3}}+5\pi {{y}^{3}}$ Hint: Don't forget to count both cubes.
D	$ \large 2{{y}^{3}}+\dfrac{3\pi {{y}^{3}}}{8}$ Hint: Make sure you know how to find the volume of a cylinder.

Question 16 Explanation:

Topic: Derive and use formulas for calculating the lengths, perimeters, areas, volumes, and surface areas of geometric shapes and figures (Objective 0023).

Question 17

The "houses" below are made of toothpicks and gum drops.

How many toothpicks are there in a row of 53 houses?

A	212 Hint: Can the number of toothpicks be even?
B	213 Hint: 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.
C	217 Hint: Try your strategy with a smaller number of "houses" so you can count and find your mistake.
D	265 Hint: Remember that the "houses" overlap some walls.

Question 17 Explanation:

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

Question 18

A family has four children. What is the probability that two children are girls and two are boys? Assume the the probability of having a boy (or a girl) is 50%.

A	$ \large \dfrac{1}{2}$ Hint: How many different configurations are there from oldest to youngest, e.g. BGGG? How many of them have 2 boys and 2 girls?
B	$ \large \dfrac{1}{4}$ Hint: How many different configurations are there from oldest to youngest, e.g. BGGG? How many of them have 2 boys and 2 girls?
C	$ \large \dfrac{1}{5}$ Hint: Some configurations are more probable than others -- i.e. it's more likely to have two boys and two girls than all boys. Be sure you are weighting properly.
D	$ \large \dfrac{3}{8}$ Hint: There are two possibilities for each child, so there are $2 \times 2 \times 2 \times 2 =16$ different configurations, e.g. from oldest to youngest BBBG, BGGB, GBBB, etc. Of these configurations, there are 6 with two boys and two girls (this is the combination $_{4}C_{2}$ or "4 choose 2"): BBGG, BGBG, BGGB, GGBB, GBGB, and GBBG. Thus the probability is 6/16=3/8.

Question 18 Explanation:

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

Question 19

There are six gumballs in a bag — two red and four green. Six children take turns picking a gumball out of the bag without looking. They do not return any gumballs to the bag. What is the probability that the first two children to pick from the bag pick the red gumballs?

A	$ \large \dfrac{1}{3}$ Hint: This is the probability that the first child picks a red gumball, but not that the first two children pick red gumballs.
B	$ \large \dfrac{1}{8}$ Hint: Are you adding things that you should be multiplying?
C	$ \large \dfrac{1}{9}$ Hint: This would be the probability if the gumballs were returned to the bag.
D	$ \large \dfrac{1}{15}$ Hint: The probability that the first child picks red is 2/6 = 1/3. Then there are 5 gumballs in the bag, one red, so the probability that the second child picks red is 1/5. Thus 1/5 of the time, after the first child picks red, the second does too, so the probability is 1/5 x 1/3 = 1/15.

Question 19 Explanation:

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

Question 20

The "houses" below are made of toothpicks and gum drops.

Which of the following does not represent the number of gumdrops in a row of h houses?

A	$ \large 2+3h$ Hint: Think of this as start with 2 gumdrops on the left wall, and then add 3 gumdrops for each house.
B	$ \large 5+3(h-1)$ Hint: Think of this as start with one house, and then add 3 gumdrops for each of the other h-1 houses.
C	$ \large h+(h+1)+(h+1)$ Hint: Look at the gumdrops in 3 rows: h gumdrops for the "rooftops," h+1 for the tops of the vertical walls, and h+1 for the floors.
D	$ \large 5+3h$ Hint: This one is not a correct equation (which makes it the correct answer!). Compare to choice A. One of them has to be wrong, as they differ by 3.

Question 20 Explanation:

Topic: Translate among different representations (e.g., tables, graphs, algebraic expressions, verbal descriptions) of functional relationships (Objective 0021).

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If you found a mistake or have comments on a particular question, please contact me (please copy and paste at least part of the question into the form, as the numbers change depending on how quizzes are displayed). General comments can be left here.

A	\( \large 0.8p=\$8.73\) Hint: 80% of the regular price = $8.73.
B	\( \large \$8.73+0.2*\$8.73=p\) Hint: The 20% off was off of the ORIGINAL price, not off the $8.73 (a lot of people make this mistake). Plus this is the same equation as in choice c.
C	\( \large 1.2*\$8.73=p\) Hint: The 20% off was off of the ORIGINAL price, not off the $8.73 (a lot of people make this mistake). Plus this is the same equation as in choice b.
D	\( \large p-0.2*\$8.73=p\) Hint: Subtract p from both sides of this equation, and you have -.2 x 8.73 =0.

A	\( \large A = 0, B = 4\) Hint: Digits add to 31, so not divisible by 3, so not divisible by 12.
B	\( \large A = 7, B = 2\) Hint: Digits add to 36, so divisible by 9.
C	\( \large A = 0, B = 6\) Hint: Digits add to 33, divisible by 3, not 9. Last digits are 36, so divisible by 4, and hence by 12.
D	\( \large A = 4, B = 8\) Hint: Digits add to 39, divisible by 3, not 9. Last digits are 38, so not divisible by 4, so not divisible by 12.

A	2 Hint: \(10^3 \times 10^4=10^7\), and note that if you're guessing when the answers are so closely related, you're generally better off guessing one of the middle numbers.
B	20 Hint: \( \dfrac{\left( 4\times {{10}^{3}} \right)\times \left( 3\times {{10}^{4}} \right)}{6\times {{10}^{6}}}=\dfrac {12 \times {{10}^{7}}}{6\times {{10}^{6}}}=\)\(2 \times {{10}^{1}}=20 \)
C	200 Hint: \(10^3 \times 10^4=10^7\)
D	2000 Hint: \(10^3 \times 10^4=10^7\), and note that if you're guessing when the answers are so closely related, you're generally better off guessing one of the middle numbers.

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

A	\( \large \dfrac{x}{2}\) Hint: If x is odd, then \( \dfrac{x}{2} \) is not an integer, e.g. 3/2 = 1.5.
B	\( \large \dfrac{2}{x}\) Hint: Only an integer if x = -2, -1, 1, or 2.
C	\( \large-x\) Hint: -1 times any integer is still an integer.
D	\(\large\sqrt{x}\) Hint: Usually not an integer, e.g. \( \sqrt{2} \approx 1.414 \).

A	\( \large 20{}^\circ \) 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.
B	\( \large 25{}^\circ \) Hint: If two sides of a triangle are congruent, then it's isosceles, and the base angles of an isosceles triangle are equal.
C	\( \large 30{}^\circ \) Hint: If two sides of a triangle are congruent, then it's isosceles, and the base angles of an isosceles triangle are equal.
D	\( \large 40{}^\circ \) Hint: Make sure you're calculating the correct angle.

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. \(\large\dfrac{14}{35}\)

A	\( \large 0.645\) Hint: That point is marked on the line, to the right.
B	\( \large 0.6421\) Hint: That point is to the left of point B.
C	\( \large 0.6422\) Hint: That point is to the left of point B.
D	\( \large 0.6425\)

A	\( \large -0.044,\quad -0.04,\quad 0.04,\quad 0.044\) 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.
B	\( \large -0.04,\quad -0.044,\quad 0.044,\quad 0.04\) Hint: 0.04=0.040, which is less than 0.044.
C	\( \large -0.04,\quad -0.044,\quad 0.04,\quad 0.044\) Hint: -0.04=-0.040, which is greater than \(-0.044\).
D	\( \large -0.044,\quad -0.04,\quad 0.044,\quad 0.04\) Hint: 0.04=0.040, which is less than 0.044.

A	\( \large 2{{y}^{3}}+\dfrac{3\pi {{y}^{3}}}{4}\) 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.
B	\( \large 2{{y}^{3}}+3\pi {{y}^{3}}\) Hint: y is the diameter of the circle, not the radius.
C	\( \large {{y}^{3}}+5\pi {{y}^{3}}\) Hint: Don't forget to count both cubes.
D	\( \large 2{{y}^{3}}+\dfrac{3\pi {{y}^{3}}}{8}\) Hint: Make sure you know how to find the volume of a cylinder.

A	\( \large \dfrac{1}{2}\) Hint: How many different configurations are there from oldest to youngest, e.g. BGGG? How many of them have 2 boys and 2 girls?
B	\( \large \dfrac{1}{4}\) Hint: How many different configurations are there from oldest to youngest, e.g. BGGG? How many of them have 2 boys and 2 girls?
C	\( \large \dfrac{1}{5}\) Hint: Some configurations are more probable than others -- i.e. it's more likely to have two boys and two girls than all boys. Be sure you are weighting properly.
D	\( \large \dfrac{3}{8}\) Hint: There are two possibilities for each child, so there are \(2 \times 2 \times 2 \times 2 =16\) different configurations, e.g. from oldest to youngest BBBG, BGGB, GBBB, etc. Of these configurations, there are 6 with two boys and two girls (this is the combination \(_{4}C_{2}\) or "4 choose 2"): BBGG, BGBG, BGGB, GGBB, GBGB, and GBBG. Thus the probability is 6/16=3/8.

A	\( \large \dfrac{1}{3}\) Hint: This is the probability that the first child picks a red gumball, but not that the first two children pick red gumballs.
B	\( \large \dfrac{1}{8}\) Hint: Are you adding things that you should be multiplying?
C	\( \large \dfrac{1}{9}\) Hint: This would be the probability if the gumballs were returned to the bag.
D	\( \large \dfrac{1}{15}\) Hint: The probability that the first child picks red is 2/6 = 1/3. Then there are 5 gumballs in the bag, one red, so the probability that the second child picks red is 1/5. Thus 1/5 of the time, after the first child picks red, the second does too, so the probability is 1/5 x 1/3 = 1/15.

A	\( \large 2+3h\) Hint: Think of this as start with 2 gumdrops on the left wall, and then add 3 gumdrops for each house.
B	\( \large 5+3(h-1)\) Hint: Think of this as start with one house, and then add 3 gumdrops for each of the other h-1 houses.
C	\( \large h+(h+1)+(h+1)\) Hint: Look at the gumdrops in 3 rows: h gumdrops for the "rooftops," h+1 for the tops of the vertical walls, and h+1 for the floors.
D	\( \large 5+3h\) Hint: This one is not a correct equation (which makes it the correct answer!). Compare to choice A. One of them has to be wrong, as they differ by 3.

MTEL General Curriculum Mathematics Practice

Use the problem below to answer the question that follows:

T shirts are on sale for 20% off. Tasha paid $8.73 for a shirt. What is the regular price of the shirt? There is no tax on clothing purchases under $175.

Let p represent the regular price of these t-shirt. Which of the following equations is correct?

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

30

120

300

360

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?

Use the expression below to answer the question that follows.

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

Which of the following is equivalent to the expression above?

2

20

200

2000

A

B

C

D

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?

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 10

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

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?

100

200

1,000

2,000

If x is an integer, which of the following must also be an integer?

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

Which of the following could be the solid shown above?

A sphere

A cylinder

A cone

A pyramid

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

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

I, III, V, VI

III, VI

II, III, VI

II, III, IV, VI

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

Below is a portion of a number line:

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

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

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?

The "houses" below are made of toothpicks and gum drops.

How many toothpicks are there in a row of 53 houses?

212

213

217

265

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%.

There are six gumballs in a bag — two red and four green. Six children take turns picking a gumball out of the bag without looking. They do not return any gumballs to the bag. What is the probability that the first two children to pick from the bag pick the red gumballs?

The "houses" below are made of toothpicks and gum drops.

Which of the following does not represent the number of gumdrops in a row of h houses?