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## MTEL General Curriculum Mathematics Practice

 Question 1

#### Which equation can be used to solve for the number of minutes, m (with m>400) that a person would have to spend on the phone each month in order for the bills for plan A and plan B to be equal?

 A $$\large 3.10m=400+0.2m$$Hint: These are the numbers in the problem, but this equation doesn't make sense. If you don't know how to make an equation, try plugging in an easy number like m=500 minutes to see if each side equals what it should. B $$\large 3+0.1m=29.99+.20m$$Hint: Doesn't account for the 400 free minutes. C $$\large 3+0.1m=400+29.99+.20(m-400)$$Hint: Why would you add 400 minutes and $29.99? If you don't know how to make an equation, try plugging in an easy number like m=500 minutes to see if each side equals what it should. D $$\large 3+0.1m=29.99+.20(m-400)$$Hint: The left side is$3 plus $0.10 times the number of minutes. The right is$29.99 plus \$0.20 times the number of minutes over 400.
Question 1 Explanation:
Identify variables and derive algebraic expressions that represent real-world situations (Objective 0020).
 Question 2

#### An equiangular triangle that is not equilateral.

Hint:
The AAA property of triangles states that all triangles with corresponding angles congruent are similar. Thus all triangles with three equal angles are similar, and are equilateral.

#### An equiangular quadrilateral that is not equilateral.

Hint:
A rectangle is equiangular (all angles the same measure), but if it's not a square, it's not equilateral (all sides the same length).

#### An equilateral quadrilateral that is not equiangular.

Hint:
This rhombus has equal sides, but it doesn't have equal angles:

#### An equiangular hexagon that is not equilateral.

Hint:
This hexagon has equal angles, but it doesn't have equal sides:
Question 2 Explanation:
Topic: Classify and analyze polygons using attributes of sides and angles (Objective 0024).
 Question 3

#### The chairs in a large room can be arranged in rows of 18, 25, or 60 with no chairs left over. If C is the smallest possible number of chairs in the room, which of the following inequalities does C satisfy?

 A $$\large C\le 300$$Hint: Find the LCM. B $$\large 300 < C \le 500$$Hint: Find the LCM. C $$\large 500 < C \le 700$$Hint: Find the LCM. D $$\large C>700$$Hint: The LCM is 900, which is the smallest number of chairs.
Question 3 Explanation:
Topic: Apply LCM in "real-world" situations (according to standardized tests....) (Objective 0018).
 Question 4

#### 21 cm

Hint:
How many miles would correspond to 24 cm on the map? Try adjusting from there.

#### 22 cm

Hint:
How many miles would correspond to 24 cm on the map? Try adjusting from there.

#### 23 cm

Hint:
One way to solve this without a calculator is to note that 4 groups of 6 cm is 2808 miles, which is 100 miles too much. Then 100 miles would be about 1/7 th of 6 cm, or about 1 cm less than 24 cm.

#### 24 cm

Hint:
4 groups of 6 cm is over 2800 miles on the map, which is too much.
Question 4 Explanation:
Topic: Apply proportional thinking to estimate quantities in real world situations (Objective 0019).
 Question 5

#### What is the perimeter of the window glass?

 A $$\large 3x+\dfrac{\pi x}{2}$$Hint: By definition, $$\pi$$ is the ratio of the circumference of a circle to its diameter; thus the circumference is $$\pi d$$. Since we have a semi-circle, its perimeter is $$\dfrac{1}{2} \pi x$$. Only 3 sides of the square contribute to the perimeter. B $$\large 3x+2\pi x$$Hint: Make sure you know how to find the circumference of a circle. C $$\large 3x+\pi x$$Hint: Remember it's a semi-circle, not a circle. D $$\large 4x+2\pi x$$Hint: Only 3 sides of the square contribute to the perimeter.
Question 5 Explanation:
Topic: Derive and use formulas for calculating the lengths, perimeters, areas, volumes, and surface areas of geometric shapes and figures (Objective 0023).
 Question 6

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

#### Which of the following is the equation of a linear function?

 A $$\large y={{x}^{2}}+2x+7$$Hint: This is a quadratic function. B $$\large y={{2}^{x}}$$Hint: This is an exponential function. C $$\large y=\dfrac{15}{x}$$Hint: This is an inverse function. D $$\large y=x+(x+4)$$Hint: This is a linear function, y=2x+4, it's graph is a straight line with slope 2 and y-intercept 4.
Question 7 Explanation:
Topic: Distinguish between linear and nonlinear functions (Objective 0022).
 Question 8

#### 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 8 Explanation:
Topic: Using Number Lines (Objective 0017)
 Question 9

#### In which table below is y a function of x?

 A Hint: If x=3, y can have two different values, so it's not a function. B Hint: If x=3, y can have two different values, so it's not a function. C Hint: If x=1, y can have different values, so it's not a function. D Hint: Each value of x always corresponds to the same value of y.
Question 9 Explanation:
Topic: Understand the definition of function and various representations of functions (e.g., input/output machines, tables, graphs, mapping diagrams, formulas) (Objective 0021).
 Question 10

#### What is the greatest common factor of 540 and 216?

 A $$\large{{2}^{2}}\cdot {{3}^{3}}$$Hint: One way to solve this is to factor both numbers: $$540=2^2 \cdot 3^3 \cdot 5$$ and $$216=2^3 \cdot 3^3$$. Then take the smaller power for each prime that is a factor of both numbers. B $$\large2\cdot 3$$Hint: This is a common factor of both numbers, but it's not the greatest common factor. C $$\large{{2}^{3}}\cdot {{3}^{3}}$$Hint: $$2^3 = 8$$ is not a factor of 540. D $$\large{{2}^{2}}\cdot {{3}^{2}}$$Hint: This is a common factor of both numbers, but it's not the greatest common factor.
Question 10 Explanation:
Topic: Find the greatest common factor of a set of numbers (Objective 0018).
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