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MTEL General Curriculum Mathematics Practice

Question 1

The window glass below has the shape of a semi-circle on top of a square, where the side of the square has length x.  It was cut from one piece of glass.

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

Use the graph below to answer the question that follows:

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

Which of the following points is closest to \( \dfrac{34}{135} \times \dfrac{53}{86}\)?

A

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

B

Hint:
Estimate with simpler fractions.
C

C

Hint:
Estimate with simpler fractions.
D

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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