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

#### Point B is halfway between two tick marks.  What number is represented by Point B?

 A $$\large 0.645$$Hint: That point is marked on the line, to the right. B $$\large 0.6421$$Hint: That point is to the left of point B. C $$\large 0.6422$$Hint: That point is to the left of point B. D $$\large 0.6425$$
Question 1 Explanation:
Topic: Using Number Lines (Objective 0017)
 Question 2

#### Which of the graphs below represent functions?

I. II. III. IV.

#### I and IV only.

Hint:
There are vertical lines that go through 2 points in IV .

#### I and III only.

Hint:
Even though III is not continuous, it's still a function (assuming that vertical lines between the "steps" do not go through 2 points).

#### II and III only.

Hint:
Learn about the vertical line test.

#### I, II, and IV only.

Hint:
There are vertical lines that go through 2 points in II.
Question 2 Explanation:
Understand the definition of function and various representations of functions (e.g., input/output machines, tables, graphs, mapping diagrams, formulas). (Objective 0021).
 Question 3

#### 100

Hint:
6124/977 is approximately 6.

#### 200

Hint:
6124/977 is approximately 6.

#### 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.

#### 2,000

Hint:
6124/977 is approximately 6.
Question 3 Explanation:
Topics: Estimation, simplifying fractions (Objective 0016).
 Question 4

#### 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 4 Explanation:
Topics: Laws of exponents (Objective 0019).
 Question 5

#### 0 years

Hint:
Range is the maximum life expectancy minus the minimum life expectancy.

#### 12 years

Hint:
Are you subtracting frequencies? Range is about values of the data, not frequency.

#### 18 years

Hint:
It's a little hard to read the graph, but it doesn't matter if you're consistent. It looks like the range for Africa is 80-38= 42 years and for Europe is 88-64 = 24; 42-24=18.

#### 42 years

Hint:
Question 5 Explanation:
Topic: Compare different data sets (Objective 0025).
 Question 6

#### 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 6 Explanation:
Topic: Ordering Fractions (Objective 0017)
 Question 7

#### A biology class requires a lab fee, which is a whole number of dollars, and the same amount for all students. On Monday the instructor collected $70 in fees, on Tuesday she collected$126, and on Wednesday she collected $266. What is the largest possible amount the fee could be? ####$2

Hint:
A possible fee, but not the largest possible fee. Check the other choices to see which are factors of all three numbers.

#### $7 Hint: A possible fee, but not the largest possible fee. Check the other choices to see which are factors of all three numbers. ####$14

Hint:
This is the greatest common factor of 70, 126, and 266.

#### \$70

Hint:
Not a factor of 126 or 266, so couldn't be correct.
Question 7 Explanation:
Topic: Use GCF in real-world context (Objective 0018)
 Question 8

#### Based on the above data, what is the probability that a randomly chosen commuter student is a junior or a senior?

 A $$\large \dfrac{34}{43}$$ B $$\large \dfrac{34}{71}$$Hint: This is the probability that a randomly chosen junior or senior is a commuter student. C $$\large \dfrac{34}{147}$$Hint: This is the probability that a randomly chosen student is a junior or senior who is a commuter. D $$\large \dfrac{71}{147}$$Hint: This is the probability that a randomly chosen student is a junior or a senior.
Question 8 Explanation:
Topic: Recognize and apply the concept of conditional probability (Objective 0026).
 Question 9

#### 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 9 Explanation:
Topic: Recognize and apply connections between algebra and geometry (e.g., the use of coordinate systems, the Pythagorean theorem) (Objective 0024).
 Question 10

#### 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.

#### Three million

Hint:
$$3\times {{10}^{4}} = 30,000;$$ the other term is much smaller and doesn't change the estimate.