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MTEL General Curriculum Mathematics Practice

Question 1

Below is a portion of a number line:

 Point B is halfway between two tick marks.  What number is represented by Point B?

 
A
\( \large 0.645\)
Hint:
That point is marked on the line, to the right.
B
\( \large 0.6421\)
Hint:
That point is to the left of point B.
C
\( \large 0.6422\)
Hint:
That point is to the left of point B.
D
\( \large 0.6425\)
Question 1 Explanation: 
Topic: Using Number Lines (Objective 0017)
Question 2

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 2 Explanation: 
Topic: Find a linear equation that represents a graph (Objective 0022).
Question 3

Exactly one of the numbers below is a prime number.  Which one is it?

A
\( \large511 \)
Hint:
Divisible by 7.
B
\( \large517\)
Hint:
Divisible by 11.
C
\( \large519\)
Hint:
Divisible by 3.
D
\( \large521\)
Question 3 Explanation: 
Topics: Identify prime and composite numbers and demonstrate knowledge of divisibility rules (Objective 0018).
Question 4

The pattern below consists of a row of black squares surrounded by white squares.

 How many white squares would surround a row of 157 black squares?

A

314

Hint:
Try your procedure on a smaller number that you can count to see where you made a mistake.
B

317

Hint:
Are there ever an odd number of white squares?
C

320

Hint:
One way to see this is that there are 6 tiles on the left and right ends, and the rest of the white tiles are twice the number of black tiles (there are many other ways to look at it too).
D

322

Hint:
Try your procedure on a smaller number that you can count to see where you made a mistake.
Question 4 Explanation: 
Topic: Recognize and extend patterns using a variety of representations (e.g., verbal, numeric, pictorial, algebraic) (Objective 0021).
Question 5

What is the greatest common factor of 540 and 216?

A
\( \large{{2}^{2}}\cdot {{3}^{3}}\)
Hint:
One way to solve this is to factor both numbers: \(540=2^2 \cdot 3^3 \cdot 5\) and \(216=2^3 \cdot 3^3\). Then take the smaller power for each prime that is a factor of both numbers.
B
\( \large2\cdot 3\)
Hint:
This is a common factor of both numbers, but it's not the greatest common factor.
C
\( \large{{2}^{3}}\cdot {{3}^{3}}\)
Hint:
\(2^3 = 8\) is not a factor of 540.
D
\( \large{{2}^{2}}\cdot {{3}^{2}}\)
Hint:
This is a common factor of both numbers, but it's not the greatest common factor.
Question 5 Explanation: 
Topic: Find the greatest common factor of a set of numbers (Objective 0018).
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 column below consists of two cubes and a cylinder.  The cylinder has diameter y, which is also the length of the sides of each cube.   The total height of the column is 5y.  Which of the formulas below gives the volume of the column?

 
A
\( \large 2{{y}^{3}}+\dfrac{3\pi {{y}^{3}}}{4}\)
Hint:
The cubes each have volume \(y^3\). The cylinder has radius \(\dfrac{y}{2}\) and height \(3y\). The volume of a cylinder is \(\pi r^2 h=\pi ({\dfrac{y}{2}})^2(3y)=\dfrac{3\pi {{y}^{3}}}{4}\). Note that the volume of a cylinder is analogous to that of a prism -- area of the base times height.
B
\( \large 2{{y}^{3}}+3\pi {{y}^{3}}\)
Hint:
y is the diameter of the circle, not the radius.
C
\( \large {{y}^{3}}+5\pi {{y}^{3}}\)
Hint:
Don't forget to count both cubes.
D
\( \large 2{{y}^{3}}+\dfrac{3\pi {{y}^{3}}}{8}\)
Hint:
Make sure you know how to find the volume of a cylinder.
Question 7 Explanation: 
Topic: Derive and use formulas for calculating the lengths, perimeters, areas, volumes, and surface areas of geometric shapes and figures (Objective 0023).
Question 8

The function d(x) gives the result when 12 is divided by x.  Which of the following is a graph of d(x)?

 
A
Hint:
d(x) is 12 divided by x, not x divided by 12.
B
Hint:
When x=2, what should d(x) be?
C
Hint:
When x=2, what should d(x) be?
D
Question 8 Explanation: 
Topic: Identify and analyze direct and inverse relationships in tables, graphs, algebraic expressions and real-world situations (Objective 0021)
Question 9

Use the expression below to answer the question that follows.

                 \(\large \dfrac{\left( 155 \right)\times \left( 6,124 \right)}{977}\)

Which of the following is the best estimate of the expression above?

A

100

Hint:
6124/977 is approximately 6.
B

200

Hint:
6124/977 is approximately 6.
C

1,000

Hint:
6124/977 is approximately 6. 155 is approximately 150, and \( 6 \times 150 = 3 \times 300 = 900\), so this answer is closest.
D

2,000

Hint:
6124/977 is approximately 6.
Question 9 Explanation: 
Topics: Estimation, simplifying fractions (Objective 0016).
Question 10

The table below gives data from various years on how many young girls drank milk.

Based on the data given above, what was the probability that a randomly chosen girl in 1990 drank milk?

A
\( \large \dfrac{502}{1222}\)
Hint:
This is the probability that a randomly chosen girl who drinks milk was in the 1989-1991 food survey.
B
\( \large \dfrac{502}{2149}\)
Hint:
This is the probability that a randomly chosen girl from the whole survey drank milk and was also surveyed in 1989-1991.
C
\( \large \dfrac{502}{837}\)
D
\( \large \dfrac{1222}{2149}\)
Hint:
This is the probability that a randomly chosen girl from any year of the survey drank milk.
Question 10 Explanation: 
Topic: Recognize and apply the concept of conditional probability (Objective 0026).
There are 10 questions to complete.

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