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 |

#### Below is a portion of a number line:

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

\( \large 0.645\) Hint: That point is marked on the line, to the right. | |

\( \large 0.6421\) Hint: That point is to the left of point B. | |

\( \large 0.6422\) Hint: That point is to the left of point B. | |

\( \large 0.6425\) |

Question 2 |

#### 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 slope-intercept form. | |

\( \large A = 2, B = -3\) Hint: Try plugging (2,0) into this equation. |

Question 3 |

#### Exactly one of the numbers below is a prime number. Which one is it?

\( \large511 \) Hint: Divisible by 7. | |

\( \large517\) Hint: Divisible by 11. | |

\( \large519\) Hint: Divisible by 3. | |

\( \large521\) |

Question 4 |

#### The pattern below consists of a row of black squares surrounded by white squares.

#### How many white squares would surround a row of 157 black squares?

## 314Hint: Try your procedure on a smaller number that you can count to see where you made a mistake. | |

## 317Hint: Are there ever an odd number of white squares? | |

## 320Hint: One way to see this is that there are 6 tiles on the left and right ends, and the rest of the white tiles are twice the number of black tiles (there are many other ways to look at it too). | |

## 322Hint: Try your procedure on a smaller number that you can count to see where you made a mistake. |

Question 5 |

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

\( \large{{2}^{2}}\cdot {{3}^{3}}\) 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. | |

\( \large2\cdot 3\) Hint: This is a common factor of both numbers, but it's not the greatest common factor. | |

\( \large{{2}^{3}}\cdot {{3}^{3}}\) Hint: \(2^3 = 8\) is not a factor of 540. | |

\( \large{{2}^{2}}\cdot {{3}^{2}}\) Hint: This is a common factor of both numbers, but it's not the greatest common factor. |

Question 6 |

#### Which of the numbers below is not equivalent to 4%?

\( \large \dfrac{1}{25}\) Hint: 1/25=4/100, so this is equal to 4% (be sure you read the question correctly). | |

\( \large \dfrac{4}{100}\) Hint: 4/100=4% (be sure you read the question correctly). | |

\( \large 0.4\) Hint: 0.4=40% so this is not equal to 4% | |

\( \large 0.04\) Hint: 0.04=4/100, so this is equal to 4% (be sure you read the question correctly). |

Question 7 |

#### The column below consists of two cubes and a cylinder. The cylinder has diameter y, which is also the length of the sides of each cube. The total height of the column is 5y. Which of the formulas below gives the volume of the column?

\( \large 2{{y}^{3}}+\dfrac{3\pi {{y}^{3}}}{4}\) Hint: The cubes each have volume \(y^3\). The cylinder has radius \(\dfrac{y}{2}\) and height \(3y\). The volume of a cylinder is \(\pi r^2 h=\pi ({\dfrac{y}{2}})^2(3y)=\dfrac{3\pi {{y}^{3}}}{4}\). Note that the volume of a cylinder is analogous to that of a prism -- area of the base times height. | |

\( \large 2{{y}^{3}}+3\pi {{y}^{3}}\) Hint: y is the diameter of the circle, not the radius. | |

\( \large {{y}^{3}}+5\pi {{y}^{3}}\) Hint: Don't forget to count both cubes. | |

\( \large 2{{y}^{3}}+\dfrac{3\pi {{y}^{3}}}{8}\) Hint: Make sure you know how to find the volume of a cylinder. |

Question 8 |

#### The function d(x) gives the result when 12 is divided by x. Which of the following is a graph of d(x)?

Hint: d(x) is 12 divided by x, not x divided by 12. | |

Hint: When x=2, what should d(x) be? | |

Hint: When x=2, what should d(x) be? | |

Question 9 |

#### 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?

## 100Hint: 6124/977 is approximately 6. | |

## 200Hint: 6124/977 is approximately 6. | |

## 1,000Hint: 6124/977 is approximately 6. 155 is approximately 150, and \( 6 \times 150 = 3 \times 300 = 900\), so this answer is closest. | |

## 2,000Hint: 6124/977 is approximately 6. |

Question 10 |

#### The table below gives data from various years on how many young girls drank milk.

#### Based on the data given above, what was the probability that a randomly chosen girl in 1990 drank milk?

\( \large \dfrac{502}{1222}\) Hint: This is the probability that a randomly chosen girl who drinks milk was in the 1989-1991 food survey. | |

\( \large \dfrac{502}{2149}\) Hint: This is the probability that a randomly chosen girl from the whole survey drank milk and was also surveyed in 1989-1991. | |

\( \large \dfrac{502}{837}\) | |

\( \large \dfrac{1222}{2149}\) Hint: This is the probability that a randomly chosen girl from any year of the survey drank milk. |

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.