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## MTEL General Curriculum Mathematics Practice

 Question 1

#### 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?

 A $$\large 11\text{ f}{{\text{t}}^{2}}$$Hint: Check your units and make sure you're using feet and inches consistently. B $$\large 16.5\text{ f}{{\text{t}}^{2}}$$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. C $$\large 66\text{ f}{{\text{t}}^{2}}$$Hint: The area of each square is not 1. D $$\large 2376\text{ f}{{\text{t}}^{2}}$$Hint: Read the question more carefully -- the answer is supposed to be in sq feet, not sq inches.
Question 1 Explanation:
Topics: Use unit conversions to solve measurement problems, and derive and use formulas for calculating surface areas of geometric shapes and figures (Objective 0023).
 Question 2

#### A

Hint:
Rise is more than 30 inches.

#### B

Hint:
Run is almost 24 feet, so rise can be almost 2 feet.

#### C

Hint:
Run is 12 feet, so rise can be at most 1 foot.

#### D

Hint:
Slope is 1:10 -- too steep.
Question 2 Explanation:
Topic: Interpret meaning of slope in a real world situation (Objective 0022).
 Question 3

#### 2

Hint:
$$10^3 \times 10^4=10^7$$, 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.

#### 20

Hint:
$$\dfrac{\left( 4\times {{10}^{3}} \right)\times \left( 3\times {{10}^{4}} \right)}{6\times {{10}^{6}}}=\dfrac {12 \times {{10}^{7}}}{6\times {{10}^{6}}}=$$$$2 \times {{10}^{1}}=20$$

#### 200

Hint:
$$10^3 \times 10^4=10^7$$

#### 2000

Hint:
$$10^3 \times 10^4=10^7$$, 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 3 Explanation:
Topics: Scientific notation, exponents, simplifying fractions (Objective 0016, although overlaps with other objectives too).
 Question 4

#### A solution requires 4 ml of saline for every 7 ml of medicine. How much saline would be required for 50 ml of medicine?

 A $$\large 28 \dfrac{4}{7}$$ mlHint: 49 ml of medicine requires 28 ml of saline. The extra ml of saline requires 4 ml saline/ 7 ml medicine = 4/7 ml saline per 1 ml medicine. B $$\large 28 \dfrac{1}{4}$$ mlHint: 49 ml of medicine requires 28 ml of saline. How much saline does the extra ml require? C $$\large 28 \dfrac{1}{7}$$ mlHint: 49 ml of medicine requires 28 ml of saline. How much saline does the extra ml require? D $$\large 87.5$$ mlHint: 49 ml of medicine requires 28 ml of saline. How much saline does the extra ml require?
Question 4 Explanation:
Topic: Apply proportional thinking to estimate quantities in real world situations (Objective 0019).
 Question 5

#### If two fair coins are flipped, what is the probability that one will come up heads and the other tails?

 A $$\large \dfrac{1}{4}$$Hint: Think of the coins as a penny and a dime, and list all possibilities. B $$\large \dfrac{1}{3}$$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. C $$\large \dfrac{1}{2}$$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. D $$\large \dfrac{3}{4}$$Hint: Think of the coins as a penny and a dime, and list all possibilities.
Question 5 Explanation:
Topic: Calculate the probabilities of simple and compound events and of independent and dependent events (Objective 0026).
There are 5 questions to complete.

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