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## MTEL General Curriculum Mathematics Practice

Question 1 |

#### 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 2 |

#### Which of the following is equal to one million three hundred thousand?

\(\large1.3\times {{10}^{6}}\)
| |

\(\large1.3\times {{10}^{9}}\)
Hint: That's one billion three hundred million. | |

\(\large1.03\times {{10}^{6}}\)
Hint: That's one million thirty thousand. | |

\(\large1.03\times {{10}^{9}}\) Hint: That's one billion thirty million |

Question 3 |

#### In each expression below N represents a negative integer. Which expression could have a negative value?

\( \large {{N}^{2}}\) Hint: Squaring always gives a non-negative value. | |

\( \large 6-N\) Hint: A story problem for this expression is, if it was 6 degrees out at noon and N degrees out at sunrise, by how many degrees did the temperature rise by noon? Since N is negative, the answer to this question has to be positive, and more than 6. | |

\( \large -N\) Hint: If N is negative, then -N is positive | |

\( \large 6+N\) Hint: For example, if \(N=-10\), then \(6+N = -4\) |

Question 4 |

#### 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 5 |

#### Which of the following is an irrational number?

\( \large \sqrt[3]{8}\) Hint: This answer is the cube root of 8. Since 2 x 2 x 2 =8, this is equal to 2, which is rational because 2 = 2/1. | |

\( \large \sqrt{8}\) Hint: It is not trivial to prove that this is irrational, but you can get this answer by eliminating the other choices. | |

\( \large \dfrac{1}{8}\) Hint: 1/8 is the RATIO of two integers, so it is rational. | |

\( \large -8\) Hint: Negative integers are also rational, -8 = -8/1, a ratio of integers. |

Question 6 |

#### Here are some statements:

#### I) 5 is an integer II)\( -5 \) is an integer III) \(0\) is an integer

#### Which of the statements are true?

## I only | |

## I and II only | |

## I and III only | |

## I, II, and IIIHint: The integers are ...-3, -2, -1, 0, 1, 2, 3, .... |

Question 7 |

#### 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 8 |

#### 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 9 |

#### In January 2011, the national debt was about 14 trillion dollars and the US population was about 300 million people. Someone reading these figures estimated that the national debt was about $5,000 per person. Which of these statements best describes the reasonableness of this estimate?

## It is too low by a factor of 10Hint: 14 trillion \( \approx 15 \times {{10}^{12}} \) and 300 million \( \approx 3 \times {{10}^{8}}\), so the true answer is about \( 5 \times {{10}^{4}} \) or $50,000. | |

## It is too low by a factor of 100 | |

## It is too high by a factor of 10 | |

## It is too high by a factor of 100 |

Question 10 |

#### 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 11 |

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

#### \( \large \dfrac{\left( 7,154 \right)\times \left( 896 \right)}{216}\)

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

## 2,000Hint: The answer is bigger than 7,000. | |

## 20,000Hint: Estimate 896/216 first. | |

## 3,000Hint: The answer is bigger than 7,000. | |

## 30,000Hint: \( \dfrac{896}{216} \approx 4\) and \(7154 \times 4\) is over 28,000, so this answer is closest. |

Question 12 |

#### 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. |

Question 13 |

#### 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. |

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