Mathematics - FTCE

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.

denotes the union of and , the set of all elements that are in , , or both. To find this set, first, collect the elements in both sets:

Arranging:

Removing duplicates:

There are 12 elements in this set.

denotes the intersection of and , the set of all elements the two sets have in common. These elements are underlined below:

is a set with three elements.

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%

The mean of a group of scores is equal to their sum divided by the number of scores , or,

Set and , and solve for :

Multiply both sides by 10 to reverse division by 10:

The sum of the scores must be 300. Add the known scores:

Subtract this sum from 300:

,

the missing tenth score.