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MTEL General Curriculum Mathematics Practice
Question 1 |
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 2 |
The prime factorization of n can be written as n=pqr, where p, q, and r are distinct prime numbers. How many factors does n have, including 1 and itself?
\( \large3\) Hint: 1, p, q, r, and pqr are already 5, so this isn't enough. You might try plugging in p=2, q=3, and r=5 to help with this problem. | |
\( \large5\) Hint: Don't forget pq, etc. You might try plugging in p=2, q=3, and r=5 to help with this problem. | |
\( \large6\) Hint: You might try plugging in p=2, q=3, and r=5 to help with this problem. | |
\( \large8\) Hint: 1, p, q, r, pq, pr, qr, pqr. |
Question 3 |
In March of 2012, 1 dollar was worth the same as 0.761 Euros, and 1 dollar was also worth the same as 83.03 Japanese Yen. Which of the expressions below gives the number of Yen that are worth 1 Euro?
\( \large {83}.0{3}\cdot 0.{761}\) Hint: This equation gives less than the number of yen per dollar, but 1 Euro is worth more than 1 dollar. | |
\( \large \dfrac{0.{761}}{{83}.0{3}}\) Hint: Number is way too small. | |
\( \large \dfrac{{83}.0{3}}{0.{761}}\) Hint: One strategy here is to use easier numbers, say 1 dollar = .5 Euros and 100 yen, then 1 Euro would be 200 Yen (change the numbers in the equations and see what works). Another is to use dimensional analysis: we want # yen per Euro, or yen/Euro = yen/dollar \(\times\) dollar/Euro = \(83.03 \times \dfrac {1}{0.761}\) | |
\( \large \dfrac{1}{0.{761}}\cdot \dfrac{1}{{83}.0{3}}\) Hint: Number is way too small. |
Question 4 |
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 5 |
The function d(x) gives the result when 12 is divided by x. Which of the following is a graph of d(x)?
 Hint: d(x) is 12 divided by x, not x divided by 12. | |
 Hint: When x=2, what should d(x) be? | |
 Hint: When x=2, what should d(x) be? | |
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