# New SAT Math - Calculator : New SAT Math - Calculator

## Example Questions

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### Example Question #1 : Introduction To Functions

The graph below is the graph of a piece-wise function in some interval.  Identify, in interval notation, the decreasing interval.

Explanation:

As is clear from the graph, in the interval between  ( included) to , the  is constant at  and then from ( not included) to  ( not included), the  is a decreasing function.

### Example Question #1 : How To Use The Inverse Variation Formula

If  varies inversely as , and  when , find  when .

Explanation:

The formula for inverse variation is as follows:

Use the x and y values from the first part of the sentence to find k.

Then use that k value and the given x value to find y.

### Example Question #1 : New Sat Math Calculator

Refer to the above diagram:

True or false:  may also called .

False

True

False

Explanation:

A line can be named after any two points it passes through. The line  is indicated in green below.

The line does not pass through , so  cannot be part of the name of the line. Specifically,  is not a valid name.

### Example Question #1 : New Sat Math Calculator

Sally sells custom picture frames.  Her monthly fixed costs are $350. It costs$10 to make each frame.  Sally sells her picture frames for \$35 each.

How many picture frames must Sally sell in order to break even?

Explanation:

The break-even point is where the costs equal the revenues.

Let  = # of frames sold

Costs:

Revenues:

Thus,

So 14 picture frames must be sold each month to break-even.

### Example Question #2 : New Sat Math Calculator

Mrs. Smith's 8th grade class has a weekly quiz. The graph below depicts the number of questions students got incorrect on their quiz and their corresponding quiz grade. Examining the graph, what type of correlation if any, exists?

The graph depicts a constant correlation.

The graph depicts a negative correlation.

The graph depicts no correlation.

The graph depicts a positive correlation.

The graph depicts a negative correlation.

Explanation:

Mrs. Smith's 8th grade class had a quiz last week. The graph below depicts the number of questions students got incorrect on their quiz and their corresponding quiz grade. In other words, the graph in this particular question is a dot plot and the question asks to find a correlation if one exists.

Recall that a correlation is a trend seen in the data. Graphically, trends can be either:

I. Positive

II. Negative

III. Constant

IV. No trend

For a trend to be positive the x and y variable both increase. A trend is negative when the y variable (dependent variable) decreases as the x variable (independent variable) increases. A constant trend occurs when the y variable stays the same as the x variable increases. No trend exists when the data appears to be scattered with no association between the x and y variables.

Examining the graph given it is seen that the x variable is the number of questions missed and the y variable is the overall score on the quiz. It is seen that as the number of questions missed increases, the overall score on the quiz decreases. This describes  a negative trend.

In other words, the graph depicts a negative correlation.

### Example Question #241 : New Sat

Convert three yards to inches.

Explanation:

To solve this problem, we need to know the conversions between yards to feet, and feet to inches.  Write their correct conversions.

Convert three yards to feet.

Convert nine feet to inches.

### Example Question #3 : New Sat Math Calculator

Above is a graph which gives the high and low temperatures, in degrees Celsius, over a one week period for Washington City. Temperature given in degrees Celsius can be converted to the Fahrenheit scale using the following formula, where  and  are the temperature expressed in degrees Celsius and degrees Fahrenheit, respectively:

On how many days of the week shown on the graph did the temperature get above ?

Six

Seven

Four

Five

Three

Three

Explanation:

Convert  to the Celsius scale by setting  in the conversion formula and solving for :

The question is therefore asking for the number of days that the temperature topped . Examine the graph below:

The high temperature was greater than  on Tuesday, Friday, and Saturday - three different days.

### Example Question #2 : How To Find Absolute Value

Define an operation  as follows:

For all real numbers ,

Evaluate: .

None of the other responses is correct.

The expression is undefined.

Explanation:

, or, equivalently,

### Example Question #12 : How To Find A Solution Set

Which of the following is a true statement?

Explanation:

Looking at the second statement, isolate x on one side with all other constants and variables on the other side.

Looking at the third statement, isolate z on one side with all other constants and variables on the other side.

Looking at the first statement, isolate y on one side with all other constants and variables on the other side.

From here, use these equivalencies so solve for y.

Substituting twice:

### Example Question #11 : Equations / Inequalities

Solve for .

Explanation:

Find all factors of 24

1, 2, 3,4, 6, 8, 12, 24

Now find two factors that add up to  and multiply to and  are the two factors.

By factoring, you can set the equation to be

If you FOIL it out, it gives you .

Set each part of the equation equal to 0, and solve for .

and

and

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