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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 |

#### 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. |

Question 3 |

#### The equation \( \large F=\frac{9}{5}C+32\) is used to convert a temperature measured in Celsius to the equivalent Farentheit temperature.

#### A patient's temperature increased by 1.5° Celcius. By how many degrees Fahrenheit did her temperature increase?

## 1.5°Hint: Celsius and Fahrenheit don't increase at the same rate. | |

## 1.8°Hint: That's how much the Fahrenheit temp increases when the Celsius temp goes up by 1 degree. | |

## 2.7°Hint: Each degree increase in Celsius corresponds to a \(\dfrac{9}{5}=1.8\) degree increase in Fahrenheit. Thus the increase is 1.8+0.9=2.7. | |

## Not enough information.Hint: A linear equation has constant slope, which means that every increase of the same amount in one variable, gives a constant increase in the other variable. It doesn't matter what temperature the patient started out at. |

Question 4 |

#### Cell phone plan A charges $3 per month plus $0.10 per minute. Cell phone plan B charges $29.99 per month, with no fee for the first 400 minutes and then $0.20 for each additional minute.

#### Which equation can be used to solve for the number of minutes, m (with m>400) that a person would have to spend on the phone each month in order for the bills for plan A and plan B to be equal?

\( \large 3.10m=400+0.2m\) Hint: These are the numbers in the problem, but this equation doesn't make sense. If you don't know how to make an equation, try plugging in an easy number like m=500 minutes to see if each side equals what it should. | |

\( \large 3+0.1m=29.99+.20m\) Hint: Doesn't account for the 400 free minutes. | |

\( \large 3+0.1m=400+29.99+.20(m-400)\) Hint: Why would you add 400 minutes and $29.99? If you don't know how to make an equation, try plugging in an easy number like m=500 minutes to see if each side equals what it should. | |

\( \large 3+0.1m=29.99+.20(m-400)\) Hint: The left side is $3 plus $0.10 times the number of minutes. The right is $29.99 plus $0.20 times the number of minutes over 400. |

Question 5 |

#### How many lines of reflective symmetry and how many centers of rotational symmetry does the parallelogram depicted below have?

## 4 lines of reflective symmetry, 1 center of rotational symmetry.Hint: Try cutting out a shape like this one from paper, and fold where you think the lines of reflective symmetry are (or put a mirror there). Do things line up as you thought they would? | |

## 2 lines of reflective symmetry, 1 center of rotational symmetry.Hint: Try cutting out a shape like this one from paper, and fold where you think the lines of reflective symmetry are (or put a mirror there). Do things line up as you thought they would? | |

## 0 lines of reflective symmetry, 1 center of rotational symmetry.Hint: The intersection of the diagonals is a center of rotational symmetry. There are no lines of reflective symmetry, although many people get confused about this fact (best to play with hands on examples to get a feel). Just fyi, the letter S also has rotational, but not reflective symmetry, and it's one that kids often write backwards. | |

## 2 lines of reflective symmetry, 0 centers of rotational symmetry.Hint: Try cutting out a shape like this one from paper. Trace onto another sheet of paper. See if there's a way to rotate the cut out shape (less than a complete turn) so that it fits within the outlines again. |

Question 6 |

#### The table below gives data from various years on how many young girls drank milk.

#### Based on the data given above, what was the probability that a randomly chosen girl in 1990 drank milk?

\( \large \dfrac{502}{1222}\) Hint: This is the probability that a randomly chosen girl who drinks milk was in the 1989-1991 food survey. | |

\( \large \dfrac{502}{2149}\) Hint: This is the probability that a randomly chosen girl from the whole survey drank milk and was also surveyed in 1989-1991. | |

\( \large \dfrac{502}{837}\) | |

\( \large \dfrac{1222}{2149}\) Hint: This is the probability that a randomly chosen girl from any year of the survey drank milk. |

Question 7 |

#### In the triangle below, \(\overline{AC}\cong \overline{AD}\cong \overline{DE}\) and \(m\angle CAD=100{}^\circ \). What is \(m\angle DAE\)?

\( \large 20{}^\circ \) Hint: Angles ACD and ADC are congruent since they are base angles of an isosceles triangle. Since the angles of a triangle sum to 180, they sum to 80, and they are 40 deg each. Thus angle ADE is 140 deg, since it makes a straight line with angle ADC. Angles DAE and DEA are base angles of an isosceles triangle and thus congruent-- they sum to 40 deg, so are 20 deg each. | |

\( \large 25{}^\circ \) Hint: If two sides of a triangle are congruent, then it's isosceles, and the base angles of an isosceles triangle are equal. | |

\( \large 30{}^\circ \) Hint: If two sides of a triangle are congruent, then it's isosceles, and the base angles of an isosceles triangle are equal. | |

\( \large 40{}^\circ \) Hint: Make sure you're calculating the correct angle. |

Question 8 |

#### In which table below is y a function of x?

Hint: If x=3, y can have two different values, so it's not a function. | |

Hint: If x=3, y can have two different values, so it's not a function. | |

Hint: If x=1, y can have different values, so it's not a function. | |

Hint: Each value of x always corresponds to the same value of y. |

Question 9 |

#### 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. | |

\( \large521\) |

Question 10 |

I. \(\large \dfrac{1}{2}+\dfrac{1}{3}\) | II. \( \large .400000\) | III. \(\large\dfrac{1}{5}+\dfrac{1}{5}\) |

IV. \( \large 40\% \) | V. \( \large 0.25 \) | VI. \(\large\dfrac{14}{35}\) |

#### Which of the lists below includes all of the above expressions that are equivalent to \( \dfrac{2}{5}\)?

## I, III, V, VIHint: I and V are not at all how fractions and decimals work. | |

## III, VIHint: These are right, but there are more. | |

## II, III, VIHint: These are right, but there are more. | |

## II, III, IV, VI |

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