FTCE : Knowledge of algebraic thinking and the coordinate plane

Study concepts, example questions & explanations for FTCE

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Example Questions

Example Question #1 : Knowledge Of Algebraic Thinking And The Coordinate Plane

and .

If , then evaluate .

Possible Answers:

Correct answer:

Explanation:

If , then can be determined from the equation

first by substituting 18 for :

then by dividing both sides by 18 to isolate the :

Now, in the other equation, substitute 4 for :

Divide both sides by 4 to isolate the :

,

the correct choice.

Example Question #2 : Knowledge Of Algebraic Thinking And The Coordinate Plane

Which of the following equations does not describe a line through the point ?

Possible Answers:

Correct answer:

Explanation:

If the line of an equation passes through , then, if and , the equation should be true. Therefore, we can identify the correct choice by substituting 2 and 6 for and , respectively, in each equation.

True

True

True

True

False

The correct choice is

.

Example Question #3 : Knowledge Of Algebraic Thinking And The Coordinate Plane

What value of makes this a true statement?

Possible Answers:

Correct answer:

Explanation:

Isolate the on the left side of the equation by performing the same steps on both sides. These steps should be the opposite of the operations performed on , as follows:

Multiplication precedes subtraction in the order of operations, so reverse the subtraction of 12 by adding 12 to both sides:

Now reverse multiplication by 2 by dividing by 2:

.

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