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## MTEL General Curriculum Mathematics Practice

Question 1 |

#### 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 2 |

#### Which of the graphs below represent functions?

**I.**

**II.**

**III.**

**IV.**

## I and IV only.Hint: There are vertical lines that go through 2 points in IV . | |

## I and III only.Hint: Even though III is not continuous, it's still a function (assuming that vertical lines between the "steps" do not go through 2 points). | |

## II and III only.Hint: Learn about the vertical line test. | |

## I, II, and IV only.Hint: There are vertical lines that go through 2 points in II. |

Question 3 |

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

#### \(\large \dfrac{\left( 155 \right)\times \left( 6,124 \right)}{977}\)

#### Which of the following is the best estimate of the expression above?

## 100Hint: 6124/977 is approximately 6. | |

## 200Hint: 6124/977 is approximately 6. | |

## 1,000Hint: 6124/977 is approximately 6. 155 is approximately 150, and \( 6 \times 150 = 3 \times 300 = 900\), so this answer is closest. | |

## 2,000Hint: 6124/977 is approximately 6. |

Question 4 |

#### The expression \( \large {{7}^{-4}}\cdot {{8}^{-6}}\) is equal to which of the following?

\( \large \dfrac{8}{{{\left( 56 \right)}^{4}}}\) Hint: The bases are whole numbers, and the exponents are negative. How can the numerator be 8? | |

\( \large \dfrac{64}{{{\left( 56 \right)}^{4}}}\) Hint: The bases are whole numbers, and the exponents are negative. How can the numerator be 64? | |

\( \large \dfrac{1}{8\cdot {{\left( 56 \right)}^{4}}}\) Hint: \(8^{-6}=8^{-4} \times 8^{-2}\) | |

\( \large \dfrac{1}{64\cdot {{\left( 56 \right)}^{4}}}\) |

Question 5 |

#### The first histogram shows the average life expectancies for women in different countries in Africa in 1998; the second histogram gives similar data for Europe:

#### How much bigger is the range of the data for Africa than the range of the data for Europe?

## 0 yearsHint: Range is the maximum life expectancy minus the minimum life expectancy. | |

## 12 yearsHint: Are you subtracting frequencies? Range is about values of the data, not frequency. | |

## 18 yearsHint: It's a little hard to read the graph, but it doesn't matter if you're consistent. It looks like the range for Africa is 80-38= 42 years and for Europe is 88-64 = 24; 42-24=18. | |

## 42 yearsHint: Read the question more carefully. |

Question 6 |

#### Which of the lists below is in order from least to greatest value?

\( \large \dfrac{1}{2},\quad \dfrac{1}{3},\quad \dfrac{1}{4},\quad \dfrac{1}{5}\) Hint: This is ordered from greatest to least. | |

\( \large \dfrac{1}{3},\quad \dfrac{2}{7},\quad \dfrac{3}{8},\quad \dfrac{4}{11}\) Hint: 1/3 = 2/6 is bigger than 2/7. | |

\( \large \dfrac{1}{4},\quad \dfrac{2}{5},\quad \dfrac{2}{3},\quad \dfrac{4}{5}\) Hint: One way to look at this: 1/4 and 2/5 are both less than 1/2, and 2/3 and 4/5 are both greater than 1/2. 1/4 is 25% and 2/5 is 40%, so 2/5 is greater. The distance from 2/3 to 1 is 1/3 and from 4/5 to 1 is 1/5, and 1/5 is less than 1/3, so 4/5 is bigger. | |

\( \large \dfrac{7}{8},\quad \dfrac{6}{7},\quad \dfrac{5}{6},\quad \dfrac{4}{5}\) Hint: This is in order from greatest to least. |

Question 7 |

#### A biology class requires a lab fee, which is a whole number of dollars, and the same amount for all students. On Monday the instructor collected $70 in fees, on Tuesday she collected $126, and on Wednesday she collected $266. What is the largest possible amount the fee could be?

## $2Hint: A possible fee, but not the largest possible fee. Check the other choices to see which are factors of all three numbers. | |

## $7Hint: A possible fee, but not the largest possible fee. Check the other choices to see which are factors of all three numbers. | |

## $14Hint: This is the greatest common factor of 70, 126, and 266. | |

## $70Hint: Not a factor of 126 or 266, so couldn't be correct. |

Question 8 |

#### 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 9 |

#### 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 10 |

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

#### \( \large 3\times {{10}^{4}}+2.2\times {{10}^{2}}\)

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

## Five millionHint: Pay attention to the exponents. Adding 3 and 2 doesn't work because they have different place values. | |

## Fifty thousandHint: Pay attention to the exponents. Adding 3 and 2 doesn't work because they have different place values. | |

## Three millionHint: Don't add the exponents. | |

## Thirty thousandHint: \( 3\times {{10}^{4}} = 30,000;\) the other term is much smaller and doesn't change the estimate. |

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