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## MTEL General Curriculum Mathematics Practice

Question 1 |

#### Which of the lines depicted below is a graph of \( \large y=2x-5\)?

## aHint: The slope of line a is negative. | |

## bHint: Wrong slope and wrong intercept. | |

## cHint: The intercept of line c is positive. | |

## dHint: Slope is 2 -- for every increase of 1 in x, y increases by 2. Intercept is -5 -- the point (0,-5) is on the line. |

Question 2 |

#### 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 3 |

#### What is the perimeter of a right triangle with legs of lengths x and 2x?

\( \large 6x\) Hint: Use the Pythagorean Theorem. | |

\( \large 3x+5{{x}^{2}}\) Hint: Don't forget to take square roots when you use the Pythagorean Theorem. | |

\( \large 3x+\sqrt{5}{{x}^{2}}\) Hint: \(\sqrt {5 x^2}\) is not \(\sqrt {5}x^2\). | |

\( \large 3x+\sqrt{5}{{x}^{{}}}\) Hint: To find the hypotenuse, h, use the Pythagorean Theorem: \(x^2+(2x)^2=h^2.\) \(5x^2=h^2,h=\sqrt{5}x\). The perimeter is this plus x plus 2x. |

Question 4 |

#### Which of the following sets of polygons can be assembled to form a pentagonal pyramid?

## 2 pentagons and 5 rectangles.Hint: These can be assembled to form a pentagonal prism, not a pentagonal pyramid. | |

## 1 square and 5 equilateral triangles.Hint: You need a pentagon for a pentagonal pyramid. | |

## 1 pentagon and 5 isosceles triangles. | |

## 1 pentagon and 10 isosceles triangles. |

Question 5 |

#### Here is a number trick:

#### 1) Pick a whole number

#### 2) Double your number.

#### 3) Add 20 to the above result.

#### 4) Multiply the above by 5

#### 5) Subtract 100

#### 6) Divide by 10

#### The result is always the number that you started with! Suppose you start by picking N. Which of the equations below best demonstrates that the result after Step 6 is also N?

\( \large N*2+20*5-100\div 10=N\) Hint: Use parentheses or else order of operations is off. | |

\( \large \left( \left( 2*N+20 \right)*5-100 \right)\div 10=N\) | |

\( \large \left( N+N+20 \right)*5-100\div 10=N\) Hint: With this answer you would subtract 10, instead of subtracting 100 and then dividing by 10. | |

\( \large \left( \left( \left( N\div 10 \right)-100 \right)*5+20 \right)*2=N\) Hint: This answer is quite backwards. |

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