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## MTEL General Curriculum Mathematics Practice

 Question 1

#### P divides 30

Hint:
2, 3, and 5 are the prime factors of 240, and all divide 30.

#### P divides 48

Hint:
P=5 doesn't work.

#### P divides 75

Hint:
P=2 doesn't work.

#### P divides 80

Hint:
P=3 doesn't work.
Question 1 Explanation:
Topic: Find the prime factorization of a number and recognize its uses (Objective 0018).
 Question 2

#### The letters A, B, and C represent digits (possibly equal) in the twelve digit number x=111,111,111,ABC.  For which values of A, B, and C is x divisible by 40?

 A $$\large A = 3, B = 2, C=0$$Hint: Note that it doesn't matter what the first 9 digits are, since 1000 is divisible by 40, so DEF,GHI,JKL,000 is divisible by 40 - we need to check the last 3. B $$\large A = 0, B = 0, C=4$$Hint: Not divisible by 10, since it doesn't end in 0. C $$\large A = 4, B = 2, C=0$$Hint: Divisible by 10 and by 4, but not by 40, as it's not divisible by 8. Look at 40 as the product of powers of primes -- 8 x 5, and check each. To check 8, either check whether 420 is divisible by 8, or take ones place + twice tens place + 4 * hundreds place = 18, which is not divisible by 8. D $$\large A =1, B=0, C=0$$Hint: Divisible by 10 and by 4, but not by 40, as it's not divisible by 8. Look at 40 as the product of powers of primes -- 8 x 5, and check each. To check 8, either check whether 100 is divisible by 8, or take ones place + twice tens place + 4 * hundreds place = 4, which is not divisible by 8.
Question 2 Explanation:
Topic: Understand divisibility rules and why they work (Objective 018).
 Question 3

#### 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)?

 A $$\large 343.2\times 60\times 10$$Hint: In kilometers, not meters. B $$\large 343.2\times 60\times 10\times \dfrac{1}{1000}$$Hint: Units are meters/sec $$\times$$ seconds/minute $$\times$$ minutes $$\times$$ kilometers/meter, and the answer is in kilometers. C $$\large 343.2\times \dfrac{1}{60}\times 10$$Hint: Include units and make sure answer is in kilometers. D $$\large 343.2\times \dfrac{1}{60}\times 10\times \dfrac{1}{1000}$$Hint: Include units and make sure answer is in kilometers.
Question 3 Explanation:
Topic: Use unit conversions and dimensional analysis to solve measurement problems (Objective 0023).
 Question 4

#### 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 4 Explanation:
Topic: Match three-dimensional figures and their two-dimensional representations (e.g., nets, projections, perspective drawings) (Objective 0024).
 Question 5

#### Use the samples of a student€™s work below to answer the question that follows:

$$\large \dfrac{2}{3}\times \dfrac{3}{4}=\dfrac{4\times 2}{3\times 3}=\dfrac{8}{9}$$

$$\large \dfrac{2}{5}\times \dfrac{7}{7}=\dfrac{7\times 2}{5\times 7}=\dfrac{2}{5}$$

$$\large \dfrac{7}{6}\times \dfrac{3}{4}=\dfrac{4\times 7}{6\times 3}=\dfrac{28}{18}=\dfrac{14}{9}$$

#### It is not valid. It never produces the correct answer.

Hint:
In the middle example,the answer is correct.

#### It is not valid. It produces the correct answer in a few special cases, but it‘s still not a valid algorithm.

Hint:
Note that this algorithm gives a/b divided by c/d, not a/b x c/d, but some students confuse multiplication and cross-multiplication. If a=0 or if c/d =1, division and multiplication give the same answer.

#### It is valid if the rational numbers in the multiplication problem are in lowest terms.

Hint:
Lowest terms is irrelevant.

#### It is valid for all rational numbers.

Hint:
Can't be correct as the first and last examples have the wrong answers.
Question 5 Explanation:
Topic: Analyze Non-Standard Computational Algorithms (Objective 0019).
 Question 6

#### 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 6 Explanation:
Topic: Ordering decimals and integers (Objective 0017).
 Question 7

#### 1.5°

Hint:
Celsius and Fahrenheit don't increase at the same rate.

#### 1.8°

Hint:
That's how much the Fahrenheit temp increases when the Celsius temp goes up by 1 degree.

#### 2.7°

Hint:
Each degree increase in Celsius corresponds to a $$\dfrac{9}{5}=1.8$$ degree increase in Fahrenheit. Thus the increase is 1.8+0.9=2.7.

#### Not enough information.

Hint:
A linear equation has constant slope, which means that every increase of the same amount in one variable, gives a constant increase in the other variable. It doesn't matter what temperature the patient started out at.
Question 7 Explanation:
Topic: Interpret the meaning of the slope and the intercepts of a linear equation that models a real-world situation (Objective 0022).
 Question 8
 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. $$\large\dfrac{14}{35}$$

#### I, III, V, VI

Hint:
I and V are not at all how fractions and decimals work.

#### III, VI

Hint:
These are right, but there are more.

#### II, III, VI

Hint:
These are right, but there are more.

#### II, III, IV, VI

Question 8 Explanation:
Topic: Converting between fractions, decimals, and percents (Objective 0017)
 Question 9

#### Five million

Hint:
Pay attention to the exponents. Adding 3 and 2 doesn't work because they have different place values.

#### Fifty thousand

Hint:
Pay attention to the exponents. Adding 3 and 2 doesn't work because they have different place values.

Hint:

#### Thirty thousand

Hint:
$$3\times {{10}^{4}} = 30,000;$$ the other term is much smaller and doesn't change the estimate.
Question 9 Explanation:
Topics: Place value, scientific notation, estimation (Objective 0016)
 Question 10

#### 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 10 isosceles triangles.

Question 10 Explanation:
Topic:Classify and analyze three-dimensional figures using attributes of faces, edges, and vertices (Objective 0024).
There are 10 questions to complete.

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