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## MTEL General Curriculum Mathematics Practice

Question 1 |

#### Taxicab fares in Boston (Spring 2012) are $2.60 for the first \(\dfrac{1}{7}\) of a mile or less and $0.40 for each \(\dfrac{1}{7}\) of a mile after that.

#### Let d represent the distance a passenger travels in miles (with \(d>\dfrac{1}{7}\)). Which of the following expressions represents the total fare?

\( \large \$2.60+\$0.40d\) Hint: It's 40 cents for 1/7 of a mile, not per mile. | |

\( \large \$2.60+\$0.40\dfrac{d}{7}\) Hint: According to this equation, going 7 miles would cost $3; does that make sense? | |

\( \large \$2.20+\$2.80d\) Hint: You can think of the fare as $2.20 to enter the cab, and then $0.40 for each 1/7 of a mile, including the first 1/7 of a mile (or $2.80 per mile).
Alternatively, you pay $2.60 for the first 1/7 of a mile, and then $2.80 per mile for d-1/7 miles. The total is 2.60+2.80(d-1/7) = 2.60+ 2.80d -.40 = 2.20+2.80d. | |

\( \large \$2.60+\$2.80d\) Hint: Don't count the first 1/7 of a mile twice. |

Question 2 |

#### A solution requires 4 ml of saline for every 7 ml of medicine. How much saline would be required for 50 ml of medicine?

\( \large 28 \dfrac{4}{7}\) ml Hint: 49 ml of medicine requires 28 ml of saline. The extra ml of saline requires 4 ml saline/ 7 ml medicine = 4/7 ml saline per 1 ml medicine. | |

\( \large 28 \dfrac{1}{4}\) ml Hint: 49 ml of medicine requires 28 ml of saline. How much saline does the extra ml require? | |

\( \large 28 \dfrac{1}{7}\) ml Hint: 49 ml of medicine requires 28 ml of saline. How much saline does the extra ml require? | |

\( \large 87.5\) ml Hint: 49 ml of medicine requires 28 ml of saline. How much saline does the extra ml require? |

Question 3 |

## AHint: \(\frac{34}{135} \approx \frac{1}{4}\) and \( \frac{53}{86} \approx \frac {2}{3}\). \(\frac {1}{4}\) of \(\frac {2}{3}\) is small and closest to A. | |

## BHint: Estimate with simpler fractions. | |

## CHint: Estimate with simpler fractions. | |

## DHint: Estimate with simpler fractions. |

Question 4 |

#### 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 5 |

#### 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. | |

\( \large521\) |

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