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.  To see ten new questions, reload the page.

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

 Question 1

#### The expression $$\large {{7}^{-4}}\cdot {{8}^{-6}}$$ is equal to which of the following?

 A $$\large \dfrac{8}{{{\left( 56 \right)}^{4}}}$$Hint: The bases are whole numbers, and the exponents are negative. How can the numerator be 8? B $$\large \dfrac{64}{{{\left( 56 \right)}^{4}}}$$Hint: The bases are whole numbers, and the exponents are negative. How can the numerator be 64? C $$\large \dfrac{1}{8\cdot {{\left( 56 \right)}^{4}}}$$Hint: $$8^{-6}=8^{-4} \times 8^{-2}$$ D $$\large \dfrac{1}{64\cdot {{\left( 56 \right)}^{4}}}$$
Question 1 Explanation:
Topics: Laws of exponents (Objective 0019).
 Question 2

#### 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 2 Explanation:
Topics: Place value, scientific notation, estimation (Objective 0016)
 Question 3

#### A family on vacation drove the first 200 miles in 4 hours and the second 200 miles in 5 hours.  Which expression below gives their average speed for the entire trip?

 A $$\large \dfrac{200+200}{4+5}$$Hint: Average speed is total distance divided by total time. B $$\large \left( \dfrac{200}{4}+\dfrac{200}{5} \right)\div 2$$Hint: This seems logical, but the problem is that it weights the first 4 hours and the second 5 hours equally, when each hour should get the same weight in computing the average speed. C $$\large \dfrac{200}{4}+\dfrac{200}{5}$$Hint: This would be an average of 90 miles per hour! D $$\large \dfrac{400}{4}+\dfrac{400}{5}$$Hint: This would be an average of 180 miles per hour! Even a family of race car drivers probably doesn't have that average speed on a vacation!
Question 3 Explanation:
Topic: Solve a variety of measurement problems (e.g., time, temperature, rates, average rates of change) in real-world situations (Objective 0023).
 Question 4

#### The commutative property is used incorrectly.

Hint:
The commutative property is $$a+b=b+a$$ or $$ab=ba$$.

#### The associative property is used incorrectly.

Hint:
The associative property is $$a+(b+c)=(a+b)+c$$ or $$a \times (b \times c)=(a \times b) \times c$$.

#### The distributive property is used incorrectly.

Hint:
$$(x+3)(x+3)=x(x+3)+3(x+3)$$=$$x^2+3x+3x+9.$$
Question 4 Explanation:
Topic: Justify algebraic manipulations by application of the properties of equality, the order of operations, the number properties, and the order properties (Objective 0020).
 Question 5

#### The prime factorization of  n can be written as n=pqr, where p, q, and r are distinct prime numbers.  How many factors does n have, including 1 and itself?

 A $$\large3$$Hint: 1, p, q, r, and pqr are already 5, so this isn't enough. You might try plugging in p=2, q=3, and r=5 to help with this problem. B $$\large5$$Hint: Don't forget pq, etc. You might try plugging in p=2, q=3, and r=5 to help with this problem. C $$\large6$$Hint: You might try plugging in p=2, q=3, and r=5 to help with this problem. D $$\large8$$Hint: 1, p, q, r, pq, pr, qr, pqr.
Question 5 Explanation:
Topic: Recognize uses of prime factorization of a number (Objective 0018).
 Question 6

#### 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.

#### 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.

#### 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.

#### 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 6 Explanation:
Topic: Analyze and interpret various graphic and nongraphic data representations (e.g., frequency distributions, percentiles) (Objective 0025).
 Question 7

#### $$7-4=3$$ and $$8-5=3$$, so the fractions are equal.

Hint:
Not how to compare fractions. By this logic, 1/2 and 3/4 are equal, but 1/2 and 2/4 are not.

#### $$4\times 8=32$$ and $$7\times 5=35$$. Since $$32<35$$ , $$\dfrac{5}{8}<\dfrac{4}{7}$$

Hint:
Starts out as something that works, but the conclusion is wrong. 4/7 = 32/56 and 5/8 = 35/56. The cross multiplication gives the numerators, and 35/56 is bigger.

#### $$4<5$$ and $$7<8$$, so $$\dfrac{4}{7}<\dfrac{5}{8}$$

Hint:
Conclusion is correct, logic is wrong. With this reasoning, 1/2 would be less than 2/100,000.
Question 7 Explanation:
Topics: Comparing fractions, and understanding the meaning of fractions (Objective 0017).
 Question 8

#### Which of the numbers below is a fraction equivalent to $$0.\bar{6}$$?

 A $$\large \dfrac{4}{6}$$Hint: $$0.\bar{6}=\dfrac{2}{3}=\dfrac{4}{6}$$ B $$\large \dfrac{3}{5}$$Hint: This is equal to 0.6, without the repeating decimal. Answer is equivalent to choice c, which is another way to tell that it's wrong. C $$\large \dfrac{6}{10}$$Hint: This is equal to 0.6, without the repeating decimal. Answer is equivalent to choice b, which is another way to tell that it's wrong. D $$\large \dfrac{1}{6}$$Hint: This is less than a half, and $$0.\bar{6}$$ is greater than a half.
Question 8 Explanation:
Topic: Converting between fraction and decimal representations (Objective 0017)
 Question 9

#### What is the probability that two randomly selected people were born on the same day of the week?  Assume that all days are equally probable.

 A $$\large \dfrac{1}{7}$$Hint: It doesn't matter what day the first person was born on. The probability that the second person will match is 1/7 (just designate one person the first and the other the second). Another way to look at it is that if you list the sample space of all possible pairs, e.g. (Wed, Sun), there are 49 such pairs, and 7 of them are repeats of the same day, and 7/49=1/7. B $$\large \dfrac{1}{14}$$Hint: What would be the sample space here? Ie, how would you list 14 things that you pick one from? C $$\large \dfrac{1}{42}$$Hint: If you wrote the seven days of the week on pieces of paper and put the papers in a jar, this would be the probability that the first person picked Sunday and the second picked Monday from the jar -- not the same situation. D $$\large \dfrac{1}{49}$$Hint: This is the probability that they are both born on a particular day, e.g. Sunday.
Question 9 Explanation:
Topic: Calculate the probabilities of simple and compound events and of independent and dependent events (Objective 0026).
 Question 10

#### Tetrahedron

Hint:
All the faces of a tetrahedron are triangles.

#### Triangular Prism

Hint:
A prism has two congruent, parallel bases, connected by parallelograms (since this is a right prism, the parallelograms are rectangles).

#### Triangular Pyramid

Hint:
A pyramid has one base, not two.

#### Trigon

Hint:
A trigon is a triangle (this is not a common term).
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.

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.