5 Random Questions

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MTEL General Curriculum Mathematics Practice

Question 1

Some children explored the diagonals in 2 x 2 squares on pages of a calendar (where all four squares have numbers in them).  They conjectured that the sum of the diagonals is always equal; in the example below, 8+16=9+15.

 

Which of the equations below could best be used to explain why the children’s conjecture is correct?

A
\( \large 8x+16x=9x+15x\)
Hint:
What would x represent in this case? Make sure you can describe in words what x represents.
B
\( \large x+(x+2)=(x+1)+(x+1)\)
Hint:
What would x represent in this case? Make sure you can describe in words what x represents.
C
\( \large x+(x+8)=(x+1)+(x+7)\)
Hint:
x is the number in the top left square, x+8 is one below and to the right, x+1 is to the right of x, and x+7 is below x.
D
\( \large x+8+16=x+9+15\)
Hint:
What would x represent in this case? Make sure you can describe in words what x represents.
Question 1 Explanation: 
Topic: Recognize and apply the concepts of variable, equality, and equation to express relationships algebraically (Objective 0020).
Question 2

A family went on a long car trip.  Below is a graph of how far they had driven at each hour.

Which of the following is closest to their average speed driving on the trip?

 
A
\( \large d=20t\)
Hint:
Try plugging t=7 into the equation, and see how it matches the graph.
B
\( \large d=30t\)
Hint:
Try plugging t=7 into the equation, and see how it matches the graph.
C
\( \large d=40t\)
D
\( \large d=50t\)
Hint:
Try plugging t=7 into the equation, and see how it matches the graph.
Question 2 Explanation: 
Topic: Select the linear equation that best models a real-world situation (Objective 0022).
Question 3

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 3 Explanation: 
Topic: Using Number Lines (Objective 0017)
Question 4

Use the table below to answer the question that follows:

Gordon wants to buy three pounds of nuts.  Each of the stores above ordinarily sells the nuts for $4.99 a pound, but is offering a discount this week.  At which store can he buy the nuts for the least amount of money?

A

Store A

Hint:
This would save about $2.50. You can quickly see that D saves more.
B

Store B

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

Store C

D

Store D

Hint:
This is about 20% off, which is less of a discount than C.
Question 4 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 5

The chairs in a large room can be arranged in rows of 18, 25, or 60 with no chairs left over. If C is the smallest possible number of chairs in the room, which of the following inequalities does C satisfy?

A
\( \large C\le 300\)
Hint:
Find the LCM.
B
\( \large 300 < C \le 500 \)
Hint:
Find the LCM.
C
\( \large 500 < C \le 700 \)
Hint:
Find the LCM.
D
\( \large C>700\)
Hint:
The LCM is 900, which is the smallest number of chairs.
Question 5 Explanation: 
Topic: Apply LCM in "real-world" situations (according to standardized tests....) (Objective 0018).
There are 5 questions to complete.

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