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## MTEL General Curriculum Mathematics Practice

Question 1 |

#### 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 2 |

#### 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 3 |

#### If x is an integer, which of the following must also be an integer?

\( \large \dfrac{x}{2}\) Hint: If x is odd, then \( \dfrac{x}{2} \) is not an integer, e.g. 3/2 = 1.5. | |

\( \large \dfrac{2}{x}\) Hint: Only an integer if x = -2, -1, 1, or 2. | |

\( \large-x\) Hint: -1 times any integer is still an integer. | |

\(\large\sqrt{x}\) Hint: Usually not an integer, e.g. \( \sqrt{2} \approx 1.414 \). |

Question 4 |

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

#### The graph above best matches which of the following scenarios:

## George left home at 10:00 and drove to work on a crooked path. He was stopped in traffic at 10:30 and 10:45. He drove 30 miles total.Hint: Just because he ended up 30 miles from home doesn't mean he drove 30 miles total. | |

## George drove to work. On the way to work there is a little hill and a big hill. He slowed down for them. He made it to work at 11:15.Hint: The graph is not a picture of the roads. | |

## George left home at 10:15. He drove 10 miles, then realized he‘d forgotten something at home. He turned back and got what he‘d forgotten. Then he drove in a straight line, at many different speeds, until he got to work around 11:15.Hint: A straight line on a distance versus time graph means constant speed. | |

## George left home at 10:15. He drove 10 miles, then realized he‘d forgotten something at home. He turned back and got what he‘d forgotten. Then he drove at a constant speed until he got to work around 11:15. |

Question 5 |

#### The table below gives the result of a survey at a college, asking students whether they were residents or commuters:

#### Based on the above data, what is the probability that a randomly chosen commuter student is a junior or a senior?

\( \large \dfrac{34}{43}\) | |

\( \large \dfrac{34}{71}\) Hint: This is the probability that a randomly chosen junior or senior is a commuter student. | |

\( \large \dfrac{34}{147}\) Hint: This is the probability that a randomly chosen student is a junior or senior who is a commuter. | |

\( \large \dfrac{71}{147}\) Hint: This is the probability that a randomly chosen student is a junior or a senior. |

Question 6 |

#### P is a prime number that divides 240. Which of the following must be true?

## P divides 30Hint: 2, 3, and 5 are the prime factors of 240, and all divide 30. | |

## P divides 48Hint: P=5 doesn't work. | |

## P divides 75Hint: P=2 doesn't work. | |

## P divides 80Hint: P=3 doesn't work. |

Question 7 |

#### The least common multiple of 60 and N is 1260. Which of the following could be the prime factorization of N?

\( \large2\cdot 5\cdot 7\) Hint: 1260 is divisible by 9 and 60 is not, so N must be divisible by 9 for 1260 to be the LCM. | |

\( \large{{2}^{3}}\cdot {{3}^{2}}\cdot 5 \cdot 7\) Hint: 1260 is not divisible by 8, so it isn't a multiple of this N. | |

\( \large3 \cdot 5 \cdot 7\) Hint: 1260 is divisible by 9 and 60 is not, so N must be divisible by 9 for 1260 to be the LCM. | |

\( \large{{3}^{2}}\cdot 5\cdot 7\) Hint: \(1260=2^2 \cdot 3^2 \cdot 5 \cdot 7\) and \(60=2^2 \cdot 3 \cdot 5\). In order for 1260 to be the LCM, N has to be a multiple of \(3^2\) and of 7 (because 60 is not a multiple of either of these). N also cannot introduce a factor that would require the LCM to be larger (as in choice b). |

Question 8 |

#### 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 9 |

#### Which of the lists below contains only irrational numbers?

\( \large\pi , \quad \sqrt{6},\quad \sqrt{\dfrac{1}{2}}\) | |

\( \large\pi , \quad \sqrt{9}, \quad \pi +1\) Hint: \( \sqrt{9}=3\) | |

\( \large\dfrac{1}{3},\quad \dfrac{5}{4},\quad \dfrac{2}{9}\) Hint: These are all rational. | |

\( \large-3,\quad 14,\quad 0\) Hint: These are all rational. |

Question 10 |

#### A map has a scale of 3 inches = 100 miles. Cities A and B are 753 miles apart. Let d be the distance between the two cities on the map. Which of the following is not correct?

\( \large \dfrac{3}{100}=\dfrac{d}{753}\) Hint: Units on both side are inches/mile, and both numerators and denominators correspond -- this one is correct. | |

\( \large \dfrac{3}{100}=\dfrac{753}{d}\) Hint: Unit on the left is inches per mile, and on the right is miles per inch. The proportion is set up incorrectly (which is what we wanted). Another strategy is to notice that one of A or B has to be the answer because they cannot both be correct proportions. Then check that cross multiplying on A gives part D, so B is the one that is different from the other 3. | |

\( \large \dfrac{3}{d}=\dfrac{100}{753}\) Hint: Unitless on each side, as inches cancel on the left and miles on the right. Numerators correspond to the map, and denominators to the real life distances -- this one is correct. | |

\( \large 100d=3\cdot 753\) Hint: This is equivalent to part A. |

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