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MTEL General Curriculum Mathematics Practice

Question 1

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 1 Explanation: 
Topics: Estimation, Scientific Notation in the real world (Objective 0016).
Question 2

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 2 Explanation: 
Topic: Least Common Multiple (Objective 0018)
Question 3

The following story situations model \( 12\div 3\):

I)  Jack has 12 cookies, which he wants to share equally between himself and two friends.  How many cookies does each person get?

II) Trent has 12 cookies, which he wants to put into bags of 3 cookies each.  How many bags can he make?

III) Cicely has $12.  Cookies cost $3 each.  How many cookies can she buy?

Which of these questions illustrate the same model of division, either partitive (partioning) or measurement (quotative)?

A

I and II

B

I and III

C

II and III

Hint:
Problem I is partitive (or partitioning or sharing) -- we put 12 objects into 3 groups. Problems II and III are quotative (or measurement) -- we put 12 objects in groups of 3.
D

All three problems model the same meaning of division

Question 3 Explanation: 
Topic: Understand models of operations on numbers (Objective 0019).
Question 4

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 4 Explanation: 
Topics: Estimation, simplifying fractions (Objective 0016).
Question 5

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 5 Explanation: 
Topic: Converting between fraction and decimal representations (Objective 0017)
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