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 
Use the four figures below to answer the question that follows:
How many of the figures pictured above have at least one line of reflective symmetry?
\( \large 1\)  
\( \large 2\) Hint: The ellipse has 2 lines of reflective symmetry (horizontal and vertical, through the center) and the triangle has 3. The other two figures have rotational symmetry, but not reflective symmetry.  
\( \large 3\)  
\( \large 4\) Hint: All four have rotational symmetry, but not reflective symmetry. 
Question 2 
The histogram below shows the frequency of a class€™s scores on a 4 question quiz.
What was the mean score on the quiz?
\( \large 2.75\) Hint: There were 20 students who took the quiz. Total points earned: \(2 \times 1+6 \times 2+ 7\times 3+5 \times 4=55\), and 55/20 = 2.75.  
\( \large 2\) Hint: How many students are there total? Did you count them all?  
\( \large 3\) Hint: How many students are there total? Did you count them all? Be sure you're finding the mean, not the median or the mode.  
\( \large 2.5\) Hint: How many students are there total? Did you count them all? Don't just take the mean of 1, 2, 3, 4  you have to weight them properly. 
Question 3 
What is the length of side \(\overline{BD}\) in the triangle below, where \(\angle DBA\) is a right angle?
\( \large 1\) Hint: Use the Pythagorean Theorem.  
\( \large \sqrt{5}\) Hint: \(2^2+e^2=3^2\) or \(4+e^2=9;e^2=5; e=\sqrt{5}\).  
\( \large \sqrt{13}\) Hint: e is not the hypotenuse.  
\( \large 5\) Hint: Use the Pythagorean Theorem. 
Question 4 
Each individual cube that makes up the rectangular solid depicted below has 6 inch sides. What is the surface area of the solid in square feet?
\( \large 11\text{ f}{{\text{t}}^{2}}\) Hint: Check your units and make sure you're using feet and inches consistently.  
\( \large 16.5\text{ f}{{\text{t}}^{2}}\) Hint: Each square has surface area \(\dfrac{1}{2} \times \dfrac {1}{2}=\dfrac {1}{4}\) sq feet. There are 9 squares on the top and bottom, and 12 on each of 4 sides, for a total of 66 squares. 66 squares \(\times \dfrac {1}{4}\) sq feet/square =16.5 sq feet.  
\( \large 66\text{ f}{{\text{t}}^{2}}\) Hint: The area of each square is not 1.  
\( \large 2376\text{ f}{{\text{t}}^{2}}\) Hint: Read the question more carefully  the answer is supposed to be in sq feet, not sq inches.

Question 5 
How many lines of reflective symmetry and how many centers of rotational symmetry does the parallelogram depicted below have?
4 lines of reflective symmetry, 1 center of rotational symmetry.Hint: Try cutting out a shape like this one from paper, and fold where you think the lines of reflective symmetry are (or put a mirror there). Do things line up as you thought they would?  
2 lines of reflective symmetry, 1 center of rotational symmetry.Hint: Try cutting out a shape like this one from paper, and fold where you think the lines of reflective symmetry are (or put a mirror there). Do things line up as you thought they would?  
0 lines of reflective symmetry, 1 center of rotational symmetry.Hint: The intersection of the diagonals is a center of rotational symmetry. There are no lines of reflective symmetry, although many people get confused about this fact (best to play with hands on examples to get a feel). Just fyi, the letter S also has rotational, but not reflective symmetry, and it's one that kids often write backwards.  
2 lines of reflective symmetry, 0 centers of rotational symmetry.Hint: Try cutting out a shape like this one from paper. Trace onto another sheet of paper. See if there's a way to rotate the cut out shape (less than a complete turn) so that it fits within the outlines again. 
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 7 
Use the graph below to answer the question that follows:
The graph above represents the equation \( \large 3x+Ay=B\), where A and B are integers. What are the values of A and B?
\( \large A = 2, B= 6\) Hint: Plug in (2,0) to get B=6, then plug in (0,3) to get A=2.  
\( \large A = 2, B = 6\) Hint: Try plugging (0,3) into this equation.  
\( \large A = 1.5, B=3\) Hint: The problem said that A and B were integers and 1.5 is not an integer. Don't try to use slopeintercept form.  
\( \large A = 2, B = 3\) Hint: Try plugging (2,0) into this equation. 
Question 8 
What is the perimeter of a right triangle with legs of lengths x and 2x?
\( \large 6x\) Hint: Use the Pythagorean Theorem.  
\( \large 3x+5{{x}^{2}}\) Hint: Don't forget to take square roots when you use the Pythagorean Theorem.  
\( \large 3x+\sqrt{5}{{x}^{2}}\) Hint: \(\sqrt {5 x^2}\) is not \(\sqrt {5}x^2\).  
\( \large 3x+\sqrt{5}{{x}^{{}}}\) 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 
At a school fundraising event, people can buy a ticket to spin a spinner like the one below. The region that the spinner lands in tells which, if any, prize the person wins.
If 240 people buy tickets to spin the spinner, what is the best estimate of the number of keychains that will be given away?
40Hint: "Keychain" appears on the spinner twice.  
80Hint: The probability of getting a keychain is 1/3, and so about 1/3 of the time the spinner will win.  
100Hint: What is the probability of winning a keychain?  
120Hint: That would be the answer for getting any prize, not a keychain specifically. 
Question 10 
Which of the following inequalities describes all values of x with \(\large \dfrac{x}{2}\le \dfrac{x}{3}\)?
\( \large x < 0\) Hint: If x =0, then x/2 = x/3, so this answer can't be correct.  
\( \large x \le 0\)  
\( \large x > 0\) Hint: If x =0, then x/2 = x/3, so this answer can't be correct.  
\( \large x \ge 0\) Hint: Try plugging in x = 6. 
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.