Mathematics - FTCE

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:

.

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.

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

.

First convert 1 mile per minute into miles per hour by multiplying by 60, then simply convert 60 miles per hour to km per hour by 1.6 to get 96.6, rounded up to 97.

Fluid ounces are the only provided measure of volume. Volume is measured in liquid displaced by an object. Kilometers are a measure of distance, and pounds are a measure of weight, which is related to, but not the same as, volume.

Joules are units of measurement used to describe energy (kinetic or potential). While "electricity" may be a tempting option here, "energy" is more correct; while electrical energy can be measured in Joules, not all energy measured in Joules is electrical in nature.

This is a basic, clear geometric rule that all students must know: for a standard triangle the sum of the sides is equal to the perimeter. No other answer was acceptable.

The area of the square is equal to the length of a side multiplied by itself. Thus, the length of a side is equal to the square root of 196. Since , 196 is the square of 14, and 14 is the square root of 196; it follows that the square has four sides of measure 14 feet. The perimeter of a square is four times the length of a side, so the perimeter of this square is feet.

To solve for in the equation

,

subtract 3 from both sides to reverse the addition of 3:

The height of a triangle is , and the length of its base is . The area of a triangle with base and height is

,

so, substituting these values,

,

the correct response.

The sequence of numbers is formed by starting with 5, and, for each consecutive term, adding a quantity that increases by 1 each time. The sequence is

,

the missing entry.

In the order of operations, any operation within parentheses is always performed first. First, add 12 and 25:

Multiplication takes precedence over subtraction. Multiply 13 by 8 next:

Now subtract:

Add the decimals vertically by aligning the decimal points, and adding the digits without regard to the decimal point:

Round to the nearest hundredth (second place after the decimal point) by examining the next digit to the right. This digit is an 8, so round the hundredths digit up to 7. This makes the correct choice 0.67.

The likelihood of rolling any given number on a 6-sided dice is 16.6%, to get the likelihood of that even happening twice in a row, simply multiply 16.6% by itself, to get 2.7%, rounded up to 3%

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:

.

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.

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

.

First convert 1 mile per minute into miles per hour by multiplying by 60, then simply convert 60 miles per hour to km per hour by 1.6 to get 96.6, rounded up to 97.

Fluid ounces are the only provided measure of volume. Volume is measured in liquid displaced by an object. Kilometers are a measure of distance, and pounds are a measure of weight, which is related to, but not the same as, volume.

Joules are units of measurement used to describe energy (kinetic or potential). While "electricity" may be a tempting option here, "energy" is more correct; while electrical energy can be measured in Joules, not all energy measured in Joules is electrical in nature.

This is a basic, clear geometric rule that all students must know: for a standard triangle the sum of the sides is equal to the perimeter. No other answer was acceptable.