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MTEL General Curriculum Mathematics Practice
Question 1 
A sales companies pays its representatives $2 for each item sold, plus 40% of the price of the item. The rest of the money that the representatives collect goes to the company. All transactions are in cash, and all items cost $4 or more. If the price of an item in dollars is p, which expression represents the amount of money the company collects when the item is sold?
\( \large \dfrac{3}{5}p2\) Hint: The company gets 3/5=60% of the price, minus the $2 per item.  
\( \large \dfrac{3}{5}\left( p2 \right)\) Hint: This is sensible, but not what the problem states.  
\( \large \dfrac{2}{5}p+2\) Hint: The company pays the extra $2; it doesn't collect it.  
\( \large \dfrac{2}{5}p2\) Hint: This has the company getting 2/5 = 40% of the price of each item, but that's what the representative gets. 
Question 2 
If two fair coins are flipped, what is the probability that one will come up heads and the other tails?
\( \large \dfrac{1}{4}\) Hint: Think of the coins as a penny and a dime, and list all possibilities.  
\( \large \dfrac{1}{3} \) Hint: This is a very common misconception. There are three possible outcomes  both heads, both tails, and one of each  but they are not equally likely. Think of the coins as a penny and a dime, and list all possibilities.  
\( \large \dfrac{1}{2}\) Hint: The possibilities are HH, HT, TH, TT, and all are equally likely. Two of the four have one of each coin, so the probability is 2/4=1/2.  
\( \large \dfrac{3}{4}\) Hint: Think of the coins as a penny and a dime, and list all possibilities. 
Question 3 
Which of the lines depicted below is a graph of \( \large y=2x5\)?
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 4 
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 5 
Each individual cube that makes up the rectangular solid depicted below has 6 inch sides. What is the surface area of the solid in square feet?
\( \large 11\text{ f}{{\text{t}}^{2}}\) Hint: Check your units and make sure you're using feet and inches consistently.  
\( \large 16.5\text{ f}{{\text{t}}^{2}}\) Hint: Each square has surface area \(\dfrac{1}{2} \times \dfrac {1}{2}=\dfrac {1}{4}\) sq feet. There are 9 squares on the top and bottom, and 12 on each of 4 sides, for a total of 66 squares. 66 squares \(\times \dfrac {1}{4}\) sq feet/square =16.5 sq feet.  
\( \large 66\text{ f}{{\text{t}}^{2}}\) Hint: The area of each square is not 1.  
\( \large 2376\text{ f}{{\text{t}}^{2}}\) Hint: Read the question more carefully  the answer is supposed to be in sq feet, not sq inches.

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