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## MTEL General Curriculum Mathematics Practice

Question 1 |

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

#### Which of the following does not represent the number of gumdrops in a row of h houses?

\( \large 2+3h\) Hint: Think of this as start with 2 gumdrops on the left wall, and then add 3 gumdrops for each house. | |

\( \large 5+3(h-1)\) Hint: Think of this as start with one house, and then add 3 gumdrops for each of the other h-1 houses. | |

\( \large h+(h+1)+(h+1)\) Hint: Look at the gumdrops in 3 rows: h gumdrops for the "rooftops," h+1 for the tops of the vertical walls, and h+1 for the floors. | |

\( \large 5+3h\) Hint: This one is not a correct equation (which makes it the correct answer!). Compare to choice A. One of them has to be wrong, as they differ by 3. |

Question 2 |

## The student used a method that worked for this problem and can be generalized to any subtraction problem.Hint: Note that this algorithm is taught as the "standard" algorithm in much of Europe (it's where the term "borrowing" came from -- you borrow on top and "pay back" on the bottom). | |

## The student used a method that worked for this problem and that will work for any subtraction problem that only requires one regrouping; it will not work if more regrouping is required.Hint: Try some more examples. | |

## The student used a method that worked for this problem and will work for all three-digit subtraction problems, but will not work for larger problems.Hint: Try some more examples. | |

## The student used a method that does not work. The student made two mistakes that cancelled each other out and was lucky to get the right answer for this problem.Hint: Remember, there are many ways to do subtraction; there is no one "right" algorithm. |

Question 3 |

#### Use the expression below to answer the question that follows.

#### \( \large \dfrac{\left( 4\times {{10}^{3}} \right)\times \left( 3\times {{10}^{4}} \right)}{6\times {{10}^{6}}}\)

#### Which of the following is equivalent to the expression above?

## 2Hint: \(10^3 \times 10^4=10^7\), and note that if you're guessing when the answers are so closely related, you're generally better off guessing one of the middle numbers. | |

## 20Hint: \( \dfrac{\left( 4\times {{10}^{3}} \right)\times \left( 3\times {{10}^{4}} \right)}{6\times {{10}^{6}}}=\dfrac {12 \times {{10}^{7}}}{6\times {{10}^{6}}}=\)\(2 \times {{10}^{1}}=20 \) | |

## 200Hint: \(10^3 \times 10^4=10^7\) | |

## 2000Hint: \(10^3 \times 10^4=10^7\), and note that if you're guessing when the answers are so closely related, you're generally better off guessing one of the middle numbers. |

Question 4 |

#### Which of the numbers below is the decimal equivalent of \( \dfrac{3}{8}?\)

## 0.38Hint: If you are just writing the numerator next to the denominator then your technique is way off, but by coincidence your answer is close; try with 2/3 and 0.23 is nowhere near correct. | |

## 0.125Hint: This is 1/8, not 3/8. | |

## 0.375 | |

## 0.83Hint: 3/8 is less than a half, and 0.83 is more than a half, so they can't be equal. |

Question 5 |

#### Which of the following is equal to eleven billion four hundred thousand?

\( \large 11,400,000\) Hint: That's eleven million four hundred thousand. | |

\(\large11,000,400,000\) | |

\( \large11,000,000,400,000\) Hint: That's eleven trillion four hundred thousand (although with British conventions; this answer is correct, but in the US, it isn't). | |

\( \large 11,400,000,000\) Hint: That's eleven billion four hundred million |

Question 6 |

#### A class is using base-ten block to represent numbers. A large cube represents 1000, a flat represents 100, a rod represents 10, and a little cube represents 1. Which of these is not a correct representation for 2,347?

## 23 flats, 4 rods, 7 little cubesHint: Be sure you read the question carefully: 2300+40+7=2347 | |

## 2 large cubes, 3 flats, 47 rodsHint: 2000+300+470 \( \neq\) 2347 | |

## 2 large cubes, 34 rods, 7 little cubesHint: Be sure you read the question carefully: 2000+340+7=2347 | |

## 2 large cubes, 3 flats, 4 rods, 7 little cubesHint: Be sure you read the question carefully: 2000+300+40+7=2347 |

Question 7 |

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

#### T shirts are on sale for 20% off. Tasha paid $8.73 for a shirt. What is the regular price of the shirt? There is no tax on clothing purchases under $175.

#### Let p represent the regular price of these t-shirt. Which of the following equations is correct?

\( \large 0.8p=\$8.73\) Hint: 80% of the regular price = $8.73. | |

\( \large \$8.73+0.2*\$8.73=p\) Hint: The 20% off was off of the ORIGINAL price, not off the $8.73 (a lot of people make this mistake). Plus this is the same equation as in choice c. | |

\( \large 1.2*\$8.73=p\) Hint: The 20% off was off of the ORIGINAL price, not off the $8.73 (a lot of people make this mistake). Plus this is the same equation as in choice b. | |

\( \large p-0.2*\$8.73=p\) Hint: Subtract p from both sides of this equation, and you have -.2 x 8.73 =0. |

Question 8 |

#### If two fair coins are flipped, what is the probability that one will come up heads and the other tails?

\( \large \dfrac{1}{4}\) Hint: Think of the coins as a penny and a dime, and list all possibilities. | |

\( \large \dfrac{1}{3} \) Hint: This is a very common misconception. There are three possible outcomes -- both heads, both tails, and one of each -- but they are not equally likely. Think of the coins as a penny and a dime, and list all possibilities. | |

\( \large \dfrac{1}{2}\) Hint: The possibilities are HH, HT, TH, TT, and all are equally likely. Two of the four have one of each coin, so the probability is 2/4=1/2. | |

\( \large \dfrac{3}{4}\) Hint: Think of the coins as a penny and a dime, and list all possibilities. |

Question 9 |

#### Which of the following is closest to the height of a college student in centimeters?

## 1.6 cmHint: This is more the height of a Lego toy college student -- less than an inch! | |

## 16 cmHint: Less than knee high on most college students. | |

## 160 cmHint: Remember, a meter stick (a little bigger than a yard stick) is 100 cm. Also good to know is that 4 inches is approximately 10 cm. | |

## 1600 cmHint: This college student might be taller than some campus buildings! |

Question 10 |

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

\( \large y={{x}^{2}}+2x+7\) Hint: This is a quadratic function. | |

\( \large y={{2}^{x}}\) Hint: This is an exponential function. | |

\( \large y=\dfrac{15}{x}\) Hint: This is an inverse function. | |

\( \large y=x+(x+4)\) Hint: This is a linear function, y=2x+4, it's graph is a straight line with slope 2 and y-intercept 4. |

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