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

In which table below is y a function of x?

A	Hint: If x=3, y can have two different values, so it's not a function.
B	Hint: If x=3, y can have two different values, so it's not a function.
C	Hint: If x=1, y can have different values, so it's not a function.
D	Hint: Each value of x always corresponds to the same value of y.

Question 1 Explanation:

Topic: Understand the definition of function and various representations of functions (e.g., input/output machines, tables, graphs, mapping diagrams, formulas) (Objective 0021).

Question 2

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 2 Explanation:

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

Question 3

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 3 Explanation:

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

Question 4

Use the graph below to answer the question that follows:

The graph above best matches which of the following scenarios:

A	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.
B	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.
C	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.
D	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 4 Explanation:

Topic: Use qualitative graphs to represent functional relationships in the real world (Objective 0021).

Question 5

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

A	$ \large 350\times \left( \dfrac{10}{4} \right)$ Hint: The final result should be smaller than 350, and this answer is bigger.
B	$ \large 350\times \left( \dfrac{4}{10} \right)$ Hint: Dimensional analysis can help here: $350 \text{cm} \times \dfrac{4 \text{in}}{10 \text{cm}}$. The cm's cancel and the answer is in inches.
C	$ \large (10-4) \times 350 $ Hint: This answer doesn't make much sense. Try with a simpler example (e.g. 20 cm not 350 cm) to make sure that your logic makes sense.
D	$ \large (350-10) \times 4$ Hint: This answer doesn't make much sense. Try with a simpler example (e.g. 20 cm not 350 cm) to make sure that your logic makes sense.

Question 5 Explanation:

Topic: Applying fractions to word problems (Objective 0017) This problem is similar to one on the official sample test for that objective, but it might fit better into unit conversion and dimensional analysis (Objective 0023: Measurement)

Question 6

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

A	$ \large y={{x}^{2}}+2x+7$ Hint: This is a quadratic function.
B	$ \large y={{2}^{x}}$ Hint: This is an exponential function.
C	$ \large y=\dfrac{15}{x}$ Hint: This is an inverse function.
D	$ \large y=x+(x+4)$ Hint: This is a linear function, y=2x+4, it's graph is a straight line with slope 2 and y-intercept 4.

Question 6 Explanation:

Topic: Distinguish between linear and nonlinear functions (Objective 0022).

Question 7

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

A	$ \large \dfrac{7}{16}$ Hint: Multiplication comes before addition and subtraction in the order of operations.
B	$ \large \dfrac{1}{2}$ Hint: Addition and subtraction are of equal priority in the order of operations -- do them left to right.
C	$ \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}$
D	$ \large \dfrac{3}{16}$ Hint: Multiplication comes before addition and subtraction in the order of operations.

Question 7 Explanation:

Topic: Operations on Fractions, Order of Operations (Objective 0019).

Question 8

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 8 Explanation:

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

Question 9

Which of the lists below contains only irrational numbers?

A	$ \large\pi , \quad \sqrt{6},\quad \sqrt{\dfrac{1}{2}}$
B	$ \large\pi , \quad \sqrt{9}, \quad \pi +1$ Hint: $ \sqrt{9}=3$
C	$ \large\dfrac{1}{3},\quad \dfrac{5}{4},\quad \dfrac{2}{9}$ Hint: These are all rational.
D	$ \large-3,\quad 14,\quad 0$ Hint: These are all rational.

Question 9 Explanation:

Topic: Identifying rational and irrational numbers (Objective 0016).

Question 10

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?

A	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.
B	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.
C	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.
D	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 10 Explanation:

Topic: Analyze and interpret various graphic and nongraphic data representations (e.g., frequency distributions, percentiles) (Objective 0025).

Question 11

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?

A	7.5 meters Hint: 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.
B	22.5 meters Hint: Draw a picture.
C	30 meters Hint: Draw a picture.
D	45 meters Hint: Draw a picture.

Question 11 Explanation:

Topic: Apply geometric transformations (e.g., translations, rotations, reflections, dilations); relate them to similarity, ; and use these concepts to solve problems (Objective 0024) . Fits in other places too.

Question 12

Use the samples of a student's work below to answer the question that follows:

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

$ \large \dfrac{2}{3} \div \dfrac{3}{4} \longrightarrow \dfrac{8}{12} \div \dfrac{9}{12} \longrightarrow 8 \div 9 = \dfrac {8}{9}$ $ \large \dfrac{2}{5} \div \dfrac{7}{20} \longrightarrow \dfrac{8}{20} \div \dfrac{7}{20} \longrightarrow 8 \div 7 = \dfrac {8}{7}$ $ \large \dfrac{7}{6} \div \dfrac{3}{4} \longrightarrow \dfrac{14}{12} \div \dfrac{9}{12} \longrightarrow 14 \div 9 = \dfrac {14}{9}$

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

A	It is not valid. Common denominators are for adding and subtracting fractions, not for dividing them. Hint: Don't be so rigid! Usually there's more than one way to do something in math.
B	It got the right answer in these three cases, but it isn‘t valid for all rational numbers. Hint: Did you try some other examples? What makes you say it's not valid?
C	It is valid if the rational numbers in the division problem are in lowest terms and the divisor is not zero. Hint: Lowest terms doesn't affect this problem at all.
D	It is valid for all rational numbers, as long as the divisor is not zero. Hint: When we have common denominators, the problem is in the form a/b divided by c/b, and the answer is a/c, as the student's algorithm predicts.

Question 12 Explanation:

Topic: Analyze Non-Standard Computational Algorithms (Objective 0019).

Question 13

Below is a pictorial representation of $2\dfrac{1}{2}\div \dfrac{2}{3}$:

$Q45 frac div model$

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

A	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 $\dfrac{2}{3}$.
B	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.
C	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.
D	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 13 Explanation:

Topic: Recognize and analyze pictorial representations of number operations. (Objective 0019).

Question 14

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?

A	314 Hint: Try your procedure on a smaller number that you can count to see where you made a mistake.
B	317 Hint: Are there ever an odd number of white squares?
C	320 Hint: 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).
D	322 Hint: Try your procedure on a smaller number that you can count to see where you made a mistake.

Question 14 Explanation:

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

Question 15

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

A	$ \large 6x$ Hint: Use the Pythagorean Theorem.
B	$ \large 3x+5{{x}^{2}}$ Hint: Don't forget to take square roots when you use the Pythagorean Theorem.
C	$ \large 3x+\sqrt{5}{{x}^{2}}$ Hint: $\sqrt {5 x^2}$ is not $\sqrt {5}x^2$.
D	$ \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 15 Explanation:

Topic: Recognize and apply connections between algebra and geometry (e.g., the use of coordinate systems, the Pythagorean theorem) (Objective 0024).

Question 16

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

A	$ \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.
B	$ \large 28 \dfrac{1}{4}$ ml Hint: 49 ml of medicine requires 28 ml of saline. How much saline does the extra ml require?
C	$ \large 28 \dfrac{1}{7}$ ml Hint: 49 ml of medicine requires 28 ml of saline. How much saline does the extra ml require?
D	$ \large 87.5$ ml Hint: 49 ml of medicine requires 28 ml of saline. How much saline does the extra ml require?

Question 16 Explanation:

Topic: Apply proportional thinking to estimate quantities in real world situations (Objective 0019).

Question 17

P is a prime number that divides 240. Which of the following must be true?

A	P divides 30 Hint: 2, 3, and 5 are the prime factors of 240, and all divide 30.
B	P divides 48 Hint: P=5 doesn't work.
C	P divides 75 Hint: P=2 doesn't work.
D	P divides 80 Hint: P=3 doesn't work.

Question 17 Explanation:

Topic: Find the prime factorization of a number and recognize its uses (Objective 0018).

Question 18

The least common multiple of 60 and N is 1260. Which of the following could be the prime factorization of N?

A	$ \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.
B	$ \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.
C	$ \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.
D	$ \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 18 Explanation:

Topic: Least Common Multiple (Objective 0018)

Question 19

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?

A	$ \large N2+205-100\div 10=N$ Hint: Use parentheses or else order of operations is off.
B	$ \large \left( \left( 2N+20 \right)5-100 \right)\div 10=N$
C	$ \large \left( N+N+20 \right)*5-100\div 10=N$ Hint: With this answer you would subtract 10, instead of subtracting 100 and then dividing by 10.
D	$ \large \left( \left( \left( N\div 10 \right)-100 \right)5+20 \right)2=N$ Hint: This answer is quite backwards.

Question 19 Explanation:

Topic: Recognize and apply the concepts of variable, function, equality, and equation to express relationships algebraically (Objective 0020).

Question 20

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 20 Explanation:

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

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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	\( \large 350\times \left( \dfrac{10}{4} \right)\) Hint: The final result should be smaller than 350, and this answer is bigger.
B	\( \large 350\times \left( \dfrac{4}{10} \right)\) Hint: Dimensional analysis can help here: \(350 \text{cm} \times \dfrac{4 \text{in}}{10 \text{cm}}\). The cm's cancel and the answer is in inches.
C	\( \large (10-4) \times 350 \) Hint: This answer doesn't make much sense. Try with a simpler example (e.g. 20 cm not 350 cm) to make sure that your logic makes sense.
D	\( \large (350-10) \times 4\) Hint: This answer doesn't make much sense. Try with a simpler example (e.g. 20 cm not 350 cm) to make sure that your logic makes sense.

A	\( \large y={{x}^{2}}+2x+7\) Hint: This is a quadratic function.
B	\( \large y={{2}^{x}}\) Hint: This is an exponential function.
C	\( \large y=\dfrac{15}{x}\) Hint: This is an inverse function.
D	\( \large y=x+(x+4)\) Hint: This is a linear function, y=2x+4, it's graph is a straight line with slope 2 and y-intercept 4.

A	\( \large \dfrac{7}{16}\) Hint: Multiplication comes before addition and subtraction in the order of operations.
B	\( \large \dfrac{1}{2}\) Hint: Addition and subtraction are of equal priority in the order of operations -- do them left to right.
C	\( \large \dfrac{3}{4}\) Hint: \( \dfrac{3}{4}-\dfrac{1}{8}+\dfrac{2}{8}\times \dfrac{1}{2}\)=\( \dfrac{3}{4}-\dfrac{1}{8}+\dfrac{1}{8}\)=\( \dfrac{3}{4}+-\dfrac{1}{8}+\dfrac{1}{8}\)=\( \dfrac{3}{4}\)
D	\( \large \dfrac{3}{16}\) Hint: Multiplication comes before addition and subtraction in the order of operations.

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.

A	\( \large\pi , \quad \sqrt{6},\quad \sqrt{\dfrac{1}{2}}\)
B	\( \large\pi , \quad \sqrt{9}, \quad \pi +1\) Hint: \( \sqrt{9}=3\)
C	\( \large\dfrac{1}{3},\quad \dfrac{5}{4},\quad \dfrac{2}{9}\) Hint: These are all rational.
D	\( \large-3,\quad 14,\quad 0\) Hint: These are all rational.

A	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 \(\dfrac{2}{3}\).
B	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.
C	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.
D	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.

A	\( \large 6x\) Hint: Use the Pythagorean Theorem.
B	\( \large 3x+5{{x}^{2}}\) Hint: Don't forget to take square roots when you use the Pythagorean Theorem.
C	\( \large 3x+\sqrt{5}{{x}^{2}}\) Hint: \(\sqrt {5 x^2}\) is not \(\sqrt {5}x^2\).
D	\( \large 3x+\sqrt{5}{{x}^{{}}}\) 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.

A	\( \large 28 \dfrac{4}{7}\) 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.
B	\( \large 28 \dfrac{1}{4}\) ml Hint: 49 ml of medicine requires 28 ml of saline. How much saline does the extra ml require?
C	\( \large 28 \dfrac{1}{7}\) ml Hint: 49 ml of medicine requires 28 ml of saline. How much saline does the extra ml require?
D	\( \large 87.5\) ml Hint: 49 ml of medicine requires 28 ml of saline. How much saline does the extra ml require?

A	\( \large2\cdot 5\cdot 7\) Hint: 1260 is divisible by 9 and 60 is not, so N must be divisible by 9 for 1260 to be the LCM.
B	\( \large{{2}^{3}}\cdot {{3}^{2}}\cdot 5 \cdot 7\) Hint: 1260 is not divisible by 8, so it isn't a multiple of this N.
C	\( \large3 \cdot 5 \cdot 7\) Hint: 1260 is divisible by 9 and 60 is not, so N must be divisible by 9 for 1260 to be the LCM.
D	\( \large{{3}^{2}}\cdot 5\cdot 7\) 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).

A	\( \large N2+205-100\div 10=N\) Hint: Use parentheses or else order of operations is off.
B	\( \large \left( \left( 2N+20 \right)5-100 \right)\div 10=N\)
C	\( \large \left( N+N+20 \right)*5-100\div 10=N\) Hint: With this answer you would subtract 10, instead of subtracting 100 and then dividing by 10.
D	\( \large \left( \left( \left( N\div 10 \right)-100 \right)5+20 \right)2=N\) Hint: This answer is quite backwards.

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.

MTEL General Curriculum Mathematics Practice

In which table below is y a function of x?

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?

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

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.

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.

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.

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.

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

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

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

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 contains only irrational numbers?

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.

At most 25% of 7 year old boys can do 19 or more sit-ups in 60 seconds.

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.

At least 75% of 16 year old boys can only do 51 or fewer sit-ups in 60 seconds.

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 meters

22.5 meters

30 meters

45 meters

Use the samples of a student's work below to answer the question that follows:

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

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

It is not valid. Common denominators are for adding and subtracting fractions, not for dividing them.

It got the right answer in these three cases, but it isn‘t valid for all rational numbers.

It is valid if the rational numbers in the division problem are in lowest terms and the divisor is not zero.

It is valid for all rational numbers, as long as the divisor is not zero.

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 \(\dfrac{1}{2}\).

The quotient is \(\dfrac{4}{15}\). There are four whole blocks separated into a total of 15 small rectangles.

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.