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## MTEL General Curriculum Mathematics Practice

 Question 1

#### 212

Hint:
Can the number of toothpicks be even?

#### 213

Hint:
One way to see this is that every new "house" adds 4 toothpicks to the leftmost vertical toothpick -- so the total number is 1 plus 4 times the number of "houses." There are many other ways to look at the problem too.

#### 217

Hint:
Try your strategy with a smaller number of "houses" so you can count and find your mistake.

#### 265

Hint:
Remember that the "houses" overlap some walls.
Question 1 Explanation:
Topic: Recognize and extend patterns using a variety of representations (e.g., verbal, numeric, pictorial, algebraic). (Objective 0021).
 Question 2

#### Which of the following is a correct equation for the graph of the line depicted above?

 A $$\large y=-\dfrac{1}{2}x+2$$Hint: The slope is -1/2 and the y-intercept is 2. You can also try just plugging in points. For example, this is the only choice that gives y=1 when x=2. B $$\large 4x=2y$$Hint: This line goes through (0,0); the graph above does not. C $$\large y=x+2$$Hint: The line pictured has negative slope. D $$\large y=-x+2$$Hint: Try plugging x=4 into this equation and see if that point is on the graph above.
Question 2 Explanation:
Topic: Find a linear equation that represents a graph (Objective 0022).
 Question 3

#### Five million

Hint:
Pay attention to the exponents. Adding 3 and 2 doesn't work because they have different place values.

#### Fifty thousand

Hint:
Pay attention to the exponents. Adding 3 and 2 doesn't work because they have different place values.

Hint:

#### Thirty thousand

Hint:
$$3\times {{10}^{4}} = 30,000;$$ the other term is much smaller and doesn't change the estimate.
Question 3 Explanation:
Topics: Place value, scientific notation, estimation (Objective 0016)
 Question 4

#### How many factors does 80 have?

 A $$\large8$$Hint: Don't forget 1 and 80. B $$\large9$$Hint: Only perfect squares have an odd number of factors -- otherwise factors come in pairs. C $$\large10$$Hint: 1,2,4,5,8,10,16,20,40,80 D $$\large12$$Hint: Did you count a number twice? Include a number that isn't a factor?
Question 4 Explanation:
Topic: Understand and apply principles of number theory (Objective 0018).
 Question 5

#### Which of the following is equivalent to $$\dfrac{3}{4}-\dfrac{1}{8}+\dfrac{2}{8}\times \dfrac{1}{2}?$$

 A $$\large \dfrac{7}{16}$$Hint: Multiplication comes before addition and subtraction in the order of operations. B $$\large \dfrac{1}{2}$$Hint: Addition and subtraction are of equal priority in the order of operations -- do them left to right. C $$\large \dfrac{3}{4}$$Hint: $$\dfrac{3}{4}-\dfrac{1}{8}+\dfrac{2}{8}\times \dfrac{1}{2}$$=$$\dfrac{3}{4}-\dfrac{1}{8}+\dfrac{1}{8}$$=$$\dfrac{3}{4}+-\dfrac{1}{8}+\dfrac{1}{8}$$=$$\dfrac{3}{4}$$ D $$\large \dfrac{3}{16}$$Hint: Multiplication comes before addition and subtraction in the order of operations.
Question 5 Explanation:
Topic: Operations on Fractions, Order of Operations (Objective 0019).
 Question 6

#### Which of the numbers below is not equivalent to 4%?

 A $$\large \dfrac{1}{25}$$Hint: 1/25=4/100, so this is equal to 4% (be sure you read the question correctly). B $$\large \dfrac{4}{100}$$Hint: 4/100=4% (be sure you read the question correctly). C $$\large 0.4$$Hint: 0.4=40% so this is not equal to 4% D $$\large 0.04$$Hint: 0.04=4/100, so this is equal to 4% (be sure you read the question correctly).
Question 6 Explanation:
Converting between fractions, decimals, and percents (Objective 0017).
 Question 7

#### The commutative property is used incorrectly.

Hint:
The commutative property is $$a+b=b+a$$ or $$ab=ba$$.

#### The associative property is used incorrectly.

Hint:
The associative property is $$a+(b+c)=(a+b)+c$$ or $$a \times (b \times c)=(a \times b) \times c$$.

#### The distributive property is used incorrectly.

Hint:
$$(x+3)(x+3)=x(x+3)+3(x+3)$$=$$x^2+3x+3x+9.$$
Question 7 Explanation:
Topic: Justify algebraic manipulations by application of the properties of equality, the order of operations, the number properties, and the order properties (Objective 0020).
 Question 8

#### Store B

Hint:
This saves 15% and C saves 25%.

#### Store D

Hint:
This is about 20% off, which is less of a discount than C.
Question 8 Explanation:
Topic: Understand the meanings and models of integers, fractions, decimals,percents, and mixed numbers and apply them to the solution of word problems (Objective 0017).
 Question 9

#### The polygon depicted below is drawn on dot paper, with the dots spaced 1 unit apart.  What is the perimeter of the polygon?

 A $$\large 18+\sqrt{2} \text{ units}$$Hint: Be careful with the Pythagorean Theorem. B $$\large 18+2\sqrt{2}\text{ units}$$Hint: There are 13 horizontal or vertical 1 unit segments. The longer diagonal is the hypotenuse of a 3-4-5 right triangle, so its length is 5 units. The shorter diagonal is the hypotenuse of a 45-45-90 right triangle with side 2, so its hypotenuse has length $$2 \sqrt{2}$$. C $$\large 18 \text{ units}$$Hint: Use the Pythagorean Theorem to find the lengths of the diagonal segments. D $$\large 20 \text{ units}$$Hint: Use the Pythagorean Theorem to find the lengths of the diagonal segments.
Question 9 Explanation:
Topic: Recognize and apply connections between algebra and geometry (e.g., the use of coordinate systems, the Pythagorean theorem) (Objective 0024).
 Question 10

#### A family on vacation drove the first 200 miles in 4 hours and the second 200 miles in 5 hours.  Which expression below gives their average speed for the entire trip?

 A $$\large \dfrac{200+200}{4+5}$$Hint: Average speed is total distance divided by total time. B $$\large \left( \dfrac{200}{4}+\dfrac{200}{5} \right)\div 2$$Hint: This seems logical, but the problem is that it weights the first 4 hours and the second 5 hours equally, when each hour should get the same weight in computing the average speed. C $$\large \dfrac{200}{4}+\dfrac{200}{5}$$Hint: This would be an average of 90 miles per hour! D $$\large \dfrac{400}{4}+\dfrac{400}{5}$$Hint: This would be an average of 180 miles per hour! Even a family of race car drivers probably doesn't have that average speed on a vacation!
Question 10 Explanation:
Topic: Solve a variety of measurement problems (e.g., time, temperature, rates, average rates of change) in real-world situations (Objective 0023).
There are 10 questions to complete.

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