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MTEL General Curriculum Mathematics Practice

 Question 1

Which of the following is an irrational number?

 A $$\large \sqrt[3]{8}$$Hint: This answer is the cube root of 8. Since 2 x 2 x 2 =8, this is equal to 2, which is rational because 2 = 2/1. B $$\large \sqrt{8}$$Hint: It is not trivial to prove that this is irrational, but you can get this answer by eliminating the other choices. C $$\large \dfrac{1}{8}$$Hint: 1/8 is the RATIO of two integers, so it is rational. D $$\large -8$$Hint: Negative integers are also rational, -8 = -8/1, a ratio of integers.
Question 1 Explanation:
Topic: Identifying rational and irrational numbers (Objective 0016).
 Question 2

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 2 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 3

4

Hint:
The card blocks more than half of the circles, so this number is too small.

5

Hint:
The card blocks more than half of the circles, so this number is too small.

8

Hint:
The card blocks more than half of the circles, so this number is too small.

12

Hint:
2/5 of the circles or 8 circles are showing. Thus 4 circles represent 1/5 of the circles, and $$4 \times 5=20$$ circles represent 5/5 or all the circles. Thus 12 circles are hidden.
Question 3 Explanation:
Topic: Models of Fractions (Objective 0017)
 Question 4

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 4 Explanation:
Topic: Ordering Fractions (Objective 0017)
 Question 5

Which of the following is a correct equation for the graph of the line depicted above?

 A $$\large y=-\dfrac{1}{2}x+2$$Hint: The slope is -1/2 and the y-intercept is 2. You can also try just plugging in points. For example, this is the only choice that gives y=1 when x=2. B $$\large 4x=2y$$Hint: This line goes through (0,0); the graph above does not. C $$\large y=x+2$$Hint: The line pictured has negative slope. D $$\large y=-x+2$$Hint: Try plugging x=4 into this equation and see if that point is on the graph above.
Question 5 Explanation:
Topic: Find a linear equation that represents a graph (Objective 0022).
 Question 6

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 6 Explanation:
Understand the definition of function and various representations of functions (e.g., input/output machines, tables, graphs, mapping diagrams, formulas). (Objective 0021).
 Question 7

Store B

Hint:
This saves 15% and C saves 25%.

Store D

Hint:
This is about 20% off, which is less of a discount than C.
Question 7 Explanation:
Topic: Understand the meanings and models of integers, fractions, decimals,percents, and mixed numbers and apply them to the solution of word problems (Objective 0017).
 Question 8

$$\large A-B+C\div D\times E$$?

 A $$\large A-B-\dfrac{C}{DE}$$Hint: In the order of operations, multiplication and division have the same priority, so do them left to right; same with addition and subtraction. B $$\large A-B+\dfrac{CE}{D}$$Hint: In practice, you're better off using parentheses than writing an expression like the one in the question. The PEMDAS acronym that many people memorize is misleading. Multiplication and division have equal priority and are done left to right. They have higher priority than addition and subtraction. Addition and subtraction also have equal priority and are done left to right. C $$\large \dfrac{AE-BE+CE}{D}$$Hint: Use order of operations, don't just compute left to right. D $$\large A-B+\dfrac{C}{DE}$$Hint: In the order of operations, multiplication and division have the same priority, so do them left to right
Question 8 Explanation:
Topic: Justify algebraic manipulations by application of the properties of order of operations (Objective 0020).
 Question 9

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

Which of the following is equal to one million three hundred thousand?

 A $$\large1.3\times {{10}^{6}}$$ B $$\large1.3\times {{10}^{9}}$$ Hint: That's one billion three hundred million. C $$\large1.03\times {{10}^{6}}$$ Hint: That's one million thirty thousand. D $$\large1.03\times {{10}^{9}}$$Hint: That's one billion thirty million
Question 10 Explanation:
Topic: Scientific Notation (Objective 0016)
There are 10 questions to complete.

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