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

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 1 Explanation:

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

Question 2

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?

A	$ \large 8\text{ c}{{\text{m}}^{2}} $ Hint: Don't just count the dots inside, that doesn't give the area. Try adding segments so that the slanted lines become the diagonals of rectangles.
B	$ \large 11\text{ c}{{\text{m}}^{2}}$ Hint: Try adding segments so that the slanted lines become the diagonals of rectangles.
C	$ \large 11.5\text{ c}{{\text{m}}^{2}}$ Hint: An easy way to do this problem is to use Pick's Theorem (of course, it's better if you understand why Pick's theorem works): area = # pegs inside + half # pegs on the border - 1. In this case 8+9/2-1=11.5. A more appropriate strategy for elementary classrooms is to add segments; here's one way. There are 20 1x1 squares enclosed, and the total area of the triangles that need to be subtracted is 8.5
D	$ \large 12.5\text{ c}{{\text{m}}^{2}}$ Hint: Try adding segments so that the slanted lines become the diagonals of rectangles.

Question 2 Explanation:

Topics: Calculate measurements and derive and use formulas for calculating the areas of geometric shapes and figures (Objective 0023).

Question 3

Which of the following points is closest to $ \dfrac{34}{135} \times \dfrac{53}{86}$?

A	A Hint: $\frac{34}{135} \approx \frac{1}{4}$ and $ \frac{53}{86} \approx \frac {2}{3}$. $\frac {1}{4}$ of $\frac {2}{3}$ is small and closest to A.
B	B Hint: Estimate with simpler fractions.
C	C Hint: Estimate with simpler fractions.
D	D Hint: Estimate with simpler fractions.

Question 3 Explanation:

Topic: Understand meaning and models of operations on fractions (Objective 0019).

Question 4

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 4 Explanation:

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

Question 5

The window glass below has the shape of a semi-circle 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?

A	$ \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 semi-circle, its perimeter is $ \dfrac{1}{2} \pi x$. Only 3 sides of the square contribute to the perimeter.
B	$ \large 3x+2\pi x$ Hint: Make sure you know how to find the circumference of a circle.
C	$ \large 3x+\pi x$ Hint: Remember it's a semi-circle, not a circle.
D	$ \large 4x+2\pi x$ Hint: Only 3 sides of the square contribute to the perimeter.

Question 5 Explanation:

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

Question 6

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.

A	$ \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.
B	$ \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.
C	$ \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.
D	$ \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.

Question 6 Explanation:

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

Question 7

Use the table below to answer the question that follows:

Gordon wants to buy three pounds of nuts. Each of the stores above ordinarily sells the nuts for $4.99 a pound, but is offering a discount this week. At which store can he buy the nuts for the least amount of money?

A	Store A Hint: This would save about $2.50. You can quickly see that D saves more.
B	Store B Hint: This saves 15% and C saves 25%.
C	Store C
D	Store D Hint: This is about 20% off, which is less of a discount than C.

Question 7 Explanation:

Topic: Understand the meanings and models of integers, fractions, decimals,percents, and mixed numbers and apply them to the solution of word problems (Objective 0017).

Question 8

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

A	$ \large \dfrac{1}{2},\quad \dfrac{1}{3},\quad \dfrac{1}{4},\quad \dfrac{1}{5}$ Hint: This is ordered from greatest to least.
B	$ \large \dfrac{1}{3},\quad \dfrac{2}{7},\quad \dfrac{3}{8},\quad \dfrac{4}{11}$ Hint: 1/3 = 2/6 is bigger than 2/7.
C	$ \large \dfrac{1}{4},\quad \dfrac{2}{5},\quad \dfrac{2}{3},\quad \dfrac{4}{5}$ Hint: One way to look at this: 1/4 and 2/5 are both less than 1/2, and 2/3 and 4/5 are both greater than 1/2. 1/4 is 25% and 2/5 is 40%, so 2/5 is greater. The distance from 2/3 to 1 is 1/3 and from 4/5 to 1 is 1/5, and 1/5 is less than 1/3, so 4/5 is bigger.
D	$ \large \dfrac{7}{8},\quad \dfrac{6}{7},\quad \dfrac{5}{6},\quad \dfrac{4}{5}$ Hint: This is in order from greatest to least.

Question 8 Explanation:

Topic: Ordering Fractions (Objective 0017)

Question 9

The picture below shows identical circles drawn on a piece of paper. The rectangle represents an index card that is blocking your view of $ \dfrac{3}{5}$ of the circles on the paper. How many circles are covered by the rectangle?

$q22 fraction dots covered$

A	4 Hint: The card blocks more than half of the circles, so this number is too small.
B	5 Hint: The card blocks more than half of the circles, so this number is too small.
C	8 Hint: The card blocks more than half of the circles, so this number is too small.
D	12 Hint: 2/5 of the circles or 8 circles are showing. Thus 4 circles represent 1/5 of the circles, and $4 \times 5=20$ circles represent 5/5 or all the circles. Thus 12 circles are hidden.

Question 9 Explanation:

Topic: Models of Fractions (Objective 0017)

Question 10

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?

A	40 Hint: "Keychain" appears on the spinner twice.
B	80 Hint: The probability of getting a keychain is 1/3, and so about 1/3 of the time the spinner will win.
C	100 Hint: What is the probability of winning a keychain?
D	120 Hint: That would be the answer for getting any prize, not a keychain specifically.

Question 10 Explanation:

Topic: I would call this topic expected value, which is not listed on the objectives. This question is very similar to one on the sample test. It's not a good question in that it's oversimplified (a more difficult and interesting question would be something like, "The school bought 100 keychains for prizes, what is the probability that they will run out before 240 people play?"). In any case, I believe the objective this is meant for is, "Recognize the difference between experimentally and theoretically determined probabilities in real-world situations. (Objective 0026)." This is not something easily assessed with multiple choice .

Question 11

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?

A	$ \large 11\text{ f}{{\text{t}}^{2}}$ Hint: Check your units and make sure you're using feet and inches consistently.
B	$ \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.
C	$ \large 66\text{ f}{{\text{t}}^{2}}$ Hint: The area of each square is not 1.
D	$ \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 11 Explanation:

Topics: Use unit conversions to solve measurement problems, and derive and use formulas for calculating surface areas of geometric shapes and figures (Objective 0023).

Question 12

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

A	$ \large {{N}^{2}}$ Hint: Squaring always gives a non-negative value.
B	$ \large 6-N$ Hint: A story problem for this expression is, if it was 6 degrees out at noon and N degrees out at sunrise, by how many degrees did the temperature rise by noon? Since N is negative, the answer to this question has to be positive, and more than 6.
C	$ \large -N$ Hint: If N is negative, then -N is positive
D	$ \large 6+N$ Hint: For example, if $N=-10$, then $6+N = -4$

Question 12 Explanation:

If you are stuck on a question like this, try a few examples to eliminate some choices and to help you understand what the question means. Topic: Characteristics of integers (Objective 0016).

Question 13

What set of transformations will transform the leftmost image into the rightmost image?

A	A 90 degree clockwise rotation about (2,1) followed by a translation of two units to the right. Hint: Part of the figure would move below the x-axis with these transformations.
B	A translation 3 units up, followed by a reflection about the line y=x. Hint: See what happens to the point (5,1) under this set of transformations.
C	A 90 degree clockwise rotation about (5,1), followed by a translation of 2 units up.
D	A 90 degree clockwise rotation about (2,1) followed by a translation of 2 units to the right. Hint: See what happens to the point (3,3) under this set of transformations.

Question 13 Explanation:

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

Question 14

Here is a method that a student used for subtraction:

Which of the following is correct?

A	The student used a method that worked for this problem and can be generalized to any subtraction problem. Hint: Note that this algorithm is taught as the "standard" algorithm in much of Europe (it's where the term "borrowing" came from -- you borrow on top and "pay back" on the bottom).
B	The student used a method that worked for this problem and that will work for any subtraction problem that only requires one regrouping; it will not work if more regrouping is required. Hint: Try some more examples.
C	The student used a method that worked for this problem and will work for all three-digit subtraction problems, but will not work for larger problems. Hint: Try some more examples.
D	The student used a method that does not work. The student made two mistakes that cancelled each other out and was lucky to get the right answer for this problem. Hint: Remember, there are many ways to do subtraction; there is no one "right" algorithm.

Question 14 Explanation:

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

Question 15

Which of the numbers below is the decimal equivalent of $ \dfrac{3}{8}?$

A	0.38 Hint: If you are just writing the numerator next to the denominator then your technique is way off, but by coincidence your answer is close; try with 2/3 and 0.23 is nowhere near correct.
B	0.125 Hint: This is 1/8, not 3/8.
C	0.375
D	0.83 Hint: 3/8 is less than a half, and 0.83 is more than a half, so they can't be equal.

Question 15 Explanation:

Topic: Converting between fractions and decimals (Objective 0017)

Question 16

How many lines of reflective symmetry and how many centers of rotational symmetry does the parallelogram depicted below have?

A	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?
B	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?
C	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.
D	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 16 Explanation:

Topic: Analyze geometric transformations (e.g., translations, rotations, reflections, dilations); relate them to concepts of symmetry (Objective 0024).

Question 17

Which of the following is equivalent to

$ \large A-B+C\div D\times E$?

A	$ \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.
B	$ \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.
C	$ \large \dfrac{AE-BE+CE}{D}$ Hint: Use order of operations, don't just compute left to right.
D	$ \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 17 Explanation:

Topic: Justify algebraic manipulations by application of the properties of order of operations (Objective 0020).

Question 18

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.

A	$ \large W=-5$ Hint: When y is even, W is even.
B	$ \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.
C	$ \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.
D	$ \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 18 Explanation:

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

Question 19

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?

A	$ \large A = -2, B= 6$ Hint: Plug in (2,0) to get B=6, then plug in (0,-3) to get A=-2.
B	$ \large A = 2, B = 6$ Hint: Try plugging (0,-3) into this equation.
C	$ \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.
D	$ \large A = 2, B = -3$ Hint: Try plugging (2,0) into this equation.

Question 19 Explanation:

Topic: Find a linear equation that represents a graph (Objective 0022).

Question 20

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

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

Question 20 Explanation:

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

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A	\( \large 8\text{ c}{{\text{m}}^{2}} \) Hint: Don't just count the dots inside, that doesn't give the area. Try adding segments so that the slanted lines become the diagonals of rectangles.
B	\( \large 11\text{ c}{{\text{m}}^{2}}\) Hint: Try adding segments so that the slanted lines become the diagonals of rectangles.
C	\( \large 11.5\text{ c}{{\text{m}}^{2}}\) Hint: An easy way to do this problem is to use Pick's Theorem (of course, it's better if you understand why Pick's theorem works): area = # pegs inside + half # pegs on the border - 1. In this case 8+9/2-1=11.5. A more appropriate strategy for elementary classrooms is to add segments; here's one way. There are 20 1x1 squares enclosed, and the total area of the triangles that need to be subtracted is 8.5
D	\( \large 12.5\text{ c}{{\text{m}}^{2}}\) Hint: Try adding segments so that the slanted lines become the diagonals of rectangles.

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	\( \large 3x+\dfrac{\pi x}{2}\) 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 semi-circle, its perimeter is \( \dfrac{1}{2} \pi x\). Only 3 sides of the square contribute to the perimeter.
B	\( \large 3x+2\pi x\) Hint: Make sure you know how to find the circumference of a circle.
C	\( \large 3x+\pi x\) Hint: Remember it's a semi-circle, not a circle.
D	\( \large 4x+2\pi x\) Hint: Only 3 sides of the square contribute to the perimeter.

A	\( \large \dfrac{1}{4}\) 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.
B	\( \large \dfrac{1}{256} \) 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.
C	\( \large \dfrac{1}{16}\) 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.
D	\( \large \dfrac{1}{24}\) 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.

A	\( \large \dfrac{1}{2},\quad \dfrac{1}{3},\quad \dfrac{1}{4},\quad \dfrac{1}{5}\) Hint: This is ordered from greatest to least.
B	\( \large \dfrac{1}{3},\quad \dfrac{2}{7},\quad \dfrac{3}{8},\quad \dfrac{4}{11}\) Hint: 1/3 = 2/6 is bigger than 2/7.
C	\( \large \dfrac{1}{4},\quad \dfrac{2}{5},\quad \dfrac{2}{3},\quad \dfrac{4}{5}\) Hint: One way to look at this: 1/4 and 2/5 are both less than 1/2, and 2/3 and 4/5 are both greater than 1/2. 1/4 is 25% and 2/5 is 40%, so 2/5 is greater. The distance from 2/3 to 1 is 1/3 and from 4/5 to 1 is 1/5, and 1/5 is less than 1/3, so 4/5 is bigger.
D	\( \large \dfrac{7}{8},\quad \dfrac{6}{7},\quad \dfrac{5}{6},\quad \dfrac{4}{5}\) Hint: This is in order from greatest to least.

A	A Hint: \(\frac{34}{135} \approx \frac{1}{4}\) and \( \frac{53}{86} \approx \frac {2}{3}\). \(\frac {1}{4}\) of \(\frac {2}{3}\) is small and closest to A.
B	B Hint: Estimate with simpler fractions.
C	C Hint: Estimate with simpler fractions.
D	D Hint: Estimate with simpler fractions.

A	\( \large 11\text{ f}{{\text{t}}^{2}}\) Hint: Check your units and make sure you're using feet and inches consistently.
B	\( \large 16.5\text{ f}{{\text{t}}^{2}}\) 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.
C	\( \large 66\text{ f}{{\text{t}}^{2}}\) Hint: The area of each square is not 1.
D	\( \large 2376\text{ f}{{\text{t}}^{2}}\) Hint: Read the question more carefully -- the answer is supposed to be in sq feet, not sq inches.

A	\( \large {{N}^{2}}\) Hint: Squaring always gives a non-negative value.
B	\( \large 6-N\) Hint: A story problem for this expression is, if it was 6 degrees out at noon and N degrees out at sunrise, by how many degrees did the temperature rise by noon? Since N is negative, the answer to this question has to be positive, and more than 6.
C	\( \large -N\) Hint: If N is negative, then -N is positive
D	\( \large 6+N\) Hint: For example, if \(N=-10\), then \(6+N = -4\)

A	\( \large A-B-\dfrac{C}{DE} \) Hint: In the order of operations, multiplication and division have the same priority, so do them left to right; same with addition and subtraction.
B	\( \large A-B+\dfrac{CE}{D}\) 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.
C	\( \large \dfrac{AE-BE+CE}{D}\) Hint: Use order of operations, don't just compute left to right.
D	\( \large A-B+\dfrac{C}{DE}\) Hint: In the order of operations, multiplication and division have the same priority, so do them left to right

A	\( \large W=-5\) Hint: When y is even, W is even.
B	\( \large W=4\) 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.
C	\( \large W=6\) Hint: Try fixing x or y at 0, and start by finding W for x=0 y=14 or x=9, y=0.
D	\( \large W=32\) Hint: Try fixing x or y at 0, and start by finding W for x=0 y=14 or x=9, y=0.

A	\( \large A = -2, B= 6\) Hint: Plug in (2,0) to get B=6, then plug in (0,-3) to get A=-2.
B	\( \large A = 2, B = 6\) Hint: Try plugging (0,-3) into this equation.
C	\( \large A = -1.5, B=-3\) 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.
D	\( \large A = 2, B = -3\) Hint: Try plugging (2,0) into this equation.

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

MTEL General Curriculum Mathematics Practice

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

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?

Which of the following points is closest to \( \dfrac{34}{135} \times \dfrac{53}{86}\)?

A

B

C

D

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 window glass below has the shape of a semi-circle 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?

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.

Use the table below to answer the question that follows:

Gordon wants to buy three pounds of nuts. Each of the stores above ordinarily sells the nuts for $4.99 a pound, but is offering a discount this week. At which store can he buy the nuts for the least amount of money?

Store A

Store B

Store C

Store D

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

The picture below shows identical circles drawn on a piece of paper. The rectangle represents an index card that is blocking your view of \( \dfrac{3}{5}\) of the circles on the paper. How many circles are covered by the rectangle?

4

5

8

12

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?

40

80

100

120

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?

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

What set of transformations will transform the leftmost image into the rightmost image?

A 90 degree clockwise rotation about (2,1) followed by a translation of two units to the right.

A translation 3 units up, followed by a reflection about the line y=x.

A 90 degree clockwise rotation about (5,1), followed by a translation of 2 units up.

A 90 degree clockwise rotation about (2,1) followed by a translation of 2 units to the right.

Here is a method that a student used for subtraction:

Which of the following is correct?

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

The student used a method that worked for this problem and that will work for any subtraction problem that only requires one regrouping; it will not work if more regrouping is required.

The student used a method that worked for this problem and will work for all three-digit subtraction problems, but will not work for larger problems.

The student used a method that does not work. The student made two mistakes that cancelled each other out and was lucky to get the right answer for this problem.

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

0.38

0.125

0.375

0.83

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.

2 lines of reflective symmetry, 1 center of rotational symmetry.

0 lines of reflective symmetry, 1 center of rotational symmetry.

2 lines of reflective symmetry, 0 centers of rotational symmetry.

Which of the following is equivalent to

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

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.

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?

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