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FTCE : Knowledge of algebraic thinking and the coordinate plane

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Example Questions

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

ab = 56 $\displaystyle ab = 56$ and ac = 72 $\displaystyle ac = 72$.

If c = 18 $\displaystyle c = 18$, then evaluate $\displaystyle b$.

Possible Answers:

b= 14 $\displaystyle b= 14$

b= 12 $\displaystyle b= 12$

b= 24 $\displaystyle b= 24$

b= 22 $\displaystyle b= 22$

b= 16 $\displaystyle b= 16$

Correct answer:

b= 14 $\displaystyle b= 14$

Explanation:

If c= 18 $\displaystyle c= 18$, then $\displaystyle a$ can be determined from the equation

ac = 72 $\displaystyle ac = 72$

first by substituting 18 for $\displaystyle c$:

$a \cdot 18 = 72$ $\displaystyle a \cdot 18 = 72$

then by dividing both sides by 18 to isolate the $\displaystyle a$:

$a \cdot 18 \div 18= 72 \div 18$ $\displaystyle a \cdot 18 \div 18= 72 \div 18$

a = 4 $\displaystyle a = 4$

Now, in the other equation, substitute 4 for $\displaystyle a$:

4b = 56 $\displaystyle 4b = 56$

Divide both sides by 4 to isolate the $\displaystyle b$:

$4b \div 4= 56 \div 4$ $\displaystyle 4b \div 4= 56 \div 4$

b= 14 $\displaystyle b= 14$,

the correct choice.

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

Which of the following equations does not describe a line through the point (2, 6) $\displaystyle (2, 6)$ ?

Possible Answers:

$\displaystyle 3x + 2y = 18$

$\displaystyle -5x + 4y = 16$

$\displaystyle 2x + 3y = 22$

$\displaystyle -3x + 5y = 24$

$\displaystyle 5x - y=4$

Correct answer:

$\displaystyle -5x + 4y = 16$

Explanation:

If the line of an equation passes through (2, 6) $\displaystyle (2, 6)$, then, if x= 2 $\displaystyle x= 2$ and y = 6 $\displaystyle y = 6$, the equation should be true. Therefore, we can identify the correct choice by substituting 2 and 6 for $\displaystyle x$ and $\displaystyle y$, respectively, in each equation.

$\displaystyle 2x + 3y = 22$

$\displaystyle 2 (2) + 3(6) = 22$

$\displaystyle 4+18 = 22$

True

$\displaystyle 5x - y=4$

$\displaystyle 5 (2) - 6=4$

$\displaystyle 10-6 = 4$

True

$\displaystyle -3x + 5y = 24$

$\displaystyle -3(2) + 5(6) = 24$

$\displaystyle -6+30 = 24$

True

$\displaystyle 3x + 2y = 18$

$\displaystyle 3(2) + 2(6) = 18$

$\displaystyle 6+ 12 = 18$

True

$\displaystyle -5x + 4y = 16$

$\displaystyle -5 (2) + 4(6) = 16$

$\displaystyle -10 + 24 = 16$

14=16 $\displaystyle 14=16$

False

The correct choice is

$\displaystyle -5x + 4y = 16$.

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

$\displaystyle 2y- 12 = 66$

What value of $\displaystyle y$ makes this a true statement?

Possible Answers:

y= 27 $\displaystyle y= 27$

$\textup{None of these}$ $\displaystyle \textup{None of these}$

y = 156 $\displaystyle y = 156$

y= 39 $\displaystyle y= 39$

y = 108 $\displaystyle y = 108$

Correct answer:

y= 39 $\displaystyle y= 39$

Explanation:

Isolate the $\displaystyle y$ 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 $\displaystyle y$, as follows:

$\displaystyle 2y- 12 = 66$

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

$\displaystyle 2y - 12 + 12= 66+12$

2y = 78 $\displaystyle 2y = 78$

Now reverse multiplication by 2 by dividing by 2:

$2y \div2 = 78 \div 2$ $\displaystyle 2y \div2 = 78 \div 2$

y = 39 $\displaystyle y = 39$.

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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

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

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

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