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## MTEL General Curriculum Mathematics Practice

 Question 1

#### What is the perimeter of the window glass?

 A $$\large 3x+\dfrac{\pi x}{2}$$Hint: By definition, $$\pi$$ is the ratio of the circumference of a circle to its diameter; thus the circumference is $$\pi d$$. Since we have a semi-circle, its perimeter is $$\dfrac{1}{2} \pi x$$. Only 3 sides of the square contribute to the perimeter. B $$\large 3x+2\pi x$$Hint: Make sure you know how to find the circumference of a circle. C $$\large 3x+\pi x$$Hint: Remember it's a semi-circle, not a circle. D $$\large 4x+2\pi x$$Hint: Only 3 sides of the square contribute to the perimeter.
Question 1 Explanation:
Topic: Derive and use formulas for calculating the lengths, perimeters, areas, volumes, and surface areas of geometric shapes and figures (Objective 0023).
 Question 2

#### The least common multiple of 60 and N is 1260. Which of the following could be the prime factorization of N?

 A $$\large2\cdot 5\cdot 7$$Hint: 1260 is divisible by 9 and 60 is not, so N must be divisible by 9 for 1260 to be the LCM. B $$\large{{2}^{3}}\cdot {{3}^{2}}\cdot 5 \cdot 7$$Hint: 1260 is not divisible by 8, so it isn't a multiple of this N. C $$\large3 \cdot 5 \cdot 7$$Hint: 1260 is divisible by 9 and 60 is not, so N must be divisible by 9 for 1260 to be the LCM. D $$\large{{3}^{2}}\cdot 5\cdot 7$$Hint: $$1260=2^2 \cdot 3^2 \cdot 5 \cdot 7$$ and $$60=2^2 \cdot 3 \cdot 5$$. In order for 1260 to be the LCM, N has to be a multiple of $$3^2$$ and of 7 (because 60 is not a multiple of either of these). N also cannot introduce a factor that would require the LCM to be larger (as in choice b).
Question 2 Explanation:
Topic: Least Common Multiple (Objective 0018)
 Question 3

#### 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 3 Explanation:
Topic: Recognize and apply connections between algebra and geometry (e.g., the use of coordinate systems, the Pythagorean theorem) (Objective 0024).
 Question 4

#### The graph above represents the equation $$\large 3x+Ay=B$$, where A and B are integers.  What are the values of A and B?

 A $$\large A = -2, B= 6$$Hint: Plug in (2,0) to get B=6, then plug in (0,-3) to get A=-2. B $$\large A = 2, B = 6$$Hint: Try plugging (0,-3) into this equation. C $$\large A = -1.5, B=-3$$Hint: The problem said that A and B were integers and -1.5 is not an integer. Don't try to use slope-intercept form. D $$\large A = 2, B = -3$$Hint: Try plugging (2,0) into this equation.
Question 4 Explanation:
Topic: Find a linear equation that represents a graph (Objective 0022).
 Question 5

#### A

Hint:
$$\frac{34}{135} \approx \frac{1}{4}$$ and $$\frac{53}{86} \approx \frac {2}{3}$$. $$\frac {1}{4}$$ of $$\frac {2}{3}$$ is small and closest to A.

#### B

Hint:
Estimate with simpler fractions.

#### C

Hint:
Estimate with simpler fractions.

#### D

Hint:
Estimate with simpler fractions.
Question 5 Explanation:
Topic: Understand meaning and models of operations on fractions (Objective 0019).
There are 5 questions to complete.

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