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 |

#### Which of the numbers below is a fraction equivalent to \( 0.\bar{6}\)?

\( \large \dfrac{4}{6}\) Hint: \( 0.\bar{6}=\dfrac{2}{3}=\dfrac{4}{6}\) | |

\( \large \dfrac{3}{5}\) Hint: This is equal to 0.6, without the repeating decimal. Answer is equivalent to choice c, which is another way to tell that it's wrong. | |

\( \large \dfrac{6}{10}\) Hint: This is equal to 0.6, without the repeating decimal. Answer is equivalent to choice b, which is another way to tell that it's wrong. | |

\( \large \dfrac{1}{6}\) Hint: This is less than a half, and \( 0.\bar{6}\) is greater than a half. |

Question 2 |

#### Use the table below to answer the question that follows:

#### Each number in the table above represents a value W that is determined by the values of x and y. For example, when x=3 and y=1, W=5. What is the value of W when x=9 and y=14? Assume that the patterns in the table continue as shown.

\( \large W=-5\) Hint: When y is even, W is even. | |

\( \large W=4\) Hint: Note that when x increases by 1, W increases by 2, and when y increases by 1, W decreases by 1. At x=y=0, W=0, so at x=9, y=14, W has increased by \(9 \times 2\) and decreased by 14, or W=18-14=4. | |

\( \large W=6\) Hint: Try fixing x or y at 0, and start by finding W for x=0 y=14 or x=9, y=0. | |

\( \large W=32\) Hint: Try fixing x or y at 0, and start by finding W for x=0 y=14 or x=9, y=0. |

Question 3 |

#### Below are front, side, and top views of a three-dimensional solid.

#### Which of the following could be the solid shown above?

## A sphereHint: All views would be circles. | |

## A cylinder | |

## A coneHint: Two views would be triangles, not rectangles. | |

## A pyramidHint: How would one view be a circle? |

Question 4 |

#### The "houses" below are made of toothpicks and gum drops.

#### How many toothpicks are there in a row of 53 houses?

## 212Hint: Can the number of toothpicks be even? | |

## 213Hint: One way to see this is that every new "house" adds 4 toothpicks to the leftmost vertical toothpick -- so the total number is 1 plus 4 times the number of "houses." There are many other ways to look at the problem too. | |

## 217Hint: Try your strategy with a smaller number of "houses" so you can count and find your mistake. | |

## 265Hint: Remember that the "houses" overlap some walls. |

Question 5 |

#### Which of the following values of x satisfies the inequality \( \large \left| {{(x+2)}^{3}} \right|<3?\)

\( \large x=-3\) Hint: \( \left| {{(-3+2)}^{3}} \right|\)=\( \left | {(-1)}^3 \right | \)=\( \left | -1 \right |=1 \) . | |

\( \large x=0\) Hint: \( \left| {{(0+2)}^{3}} \right|\)=\( \left | {2}^3 \right | \)=\( \left | 8 \right | \) =\( 8\) | |

\( \large x=-4\) Hint: \( \left| {{(-4+2)}^{3}} \right|\)=\( \left | {(-2)}^3 \right | \)=\( \left | -8 \right | \) =\( 8\) | |

\( \large x=1\) Hint: \( \left| {{(1+2)}^{3}} \right|\)=\( \left | {3}^3 \right | \)=\( \left | 27 \right | \) = \(27\) |

Question 6 |

#### The window glass below has the shape of a semi-circle on top of a square, where the side of the square has length x. It was cut from one piece of glass.

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

\( \large 3x+\dfrac{\pi x}{2}\) 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. | |

\( \large 3x+2\pi x\) Hint: Make sure you know how to find the circumference of a circle. | |

\( \large 3x+\pi x\) Hint: Remember it's a semi-circle, not a circle. | |

\( \large 4x+2\pi x\) Hint: Only 3 sides of the square contribute to the perimeter. |

Question 7 |

#### The expression \( \large{{8}^{3}}\cdot {{2}^{-10}}\) is equal to which of the following?

\( \large 2\) Hint: Write \(8^3\) as a power of 2. | |

\( \large \dfrac{1}{2}\) Hint: \(8^3 \cdot {2}^{-10}={(2^3)}^3 \cdot {2}^{-10}\) =\(2^9 \cdot {2}^{-10} =2^{-1}\) | |

\( \large 16\) Hint: Write \(8^3\) as a power of 2. | |

\( \large \dfrac{1}{16}\) Hint: Write \(8^3\) as a power of 2. |

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 |

#### Four children randomly line up, single file. What is the probability that they are in height order, with the shortest child in front? All of the children are different heights.

\( \large \dfrac{1}{4}\) Hint: Try a simpler question with 3 children -- call them big, medium, and small -- and list all the ways they could line up. Then see how to extend your logic to the problem with 4 children. | |

\( \large \dfrac{1}{256}
\) Hint: Try a simpler question with 3 children -- call them big, medium, and small -- and list all the ways they could line up. Then see how to extend your logic to the problem with 4 children. | |

\( \large \dfrac{1}{16}\) Hint: Try a simpler question with 3 children -- call them big, medium, and small -- and list all the ways they could line up. Then see how to extend your logic to the problem with 4 children. | |

\( \large \dfrac{1}{24}\) Hint: The number of ways for the children to line up is \(4!=4 \times 3 \times 2 \times 1 =24\) -- there are 4 choices for who is first in line, then 3 for who is second, etc. Only one of these lines has the children in the order specified. |

Question 10 |

#### Here is a mental math strategy for computing 26 x 16:

#### Step 1: 100 x 16 = 1600

#### Step 2: 25 x 16 = 1600 ÷· 4 = 400

#### Step 3: 26 x 16 = 400 + 16 = 416

#### Which property best justifies Step 3 in this strategy?

## Commutative Property.Hint: For addition, the commutative property is \(a+b=b+a\) and for multiplication it's \( a \times b = b \times a\). | |

## Associative Property.Hint: For addition, the associative property is \((a+b)+c=a+(b+c)\) and for multiplication it's \((a \times b) \times c=a \times (b \times c)\) | |

## Identity Property.Hint: 0 is the additive identity, because \( a+0=a\) and 1 is the multiplicative identity because \(a \times 1=a\). The phrase "identity property" is not standard. | |

## Distributive Property.Hint: \( (25+1) \times 16 = 25 \times 16 + 1 \times 16 \). This is an example of the distributive property of multiplication over addition. |

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.