# PSAT Math : Expressions

## Example Questions

### Example Question #41 : Evaluating And Simplifying Expressions

The function  is given as . If , what is the value of ?

Explanation:

This is a simple substitution problem. Begin by setting the function  equal to :

Solve for :

A common mistake at this point is to believe that you have finished the question. We are given that . We must now substitute  for  and solve for :

Subtract 2 from both sides:

### Example Question #41 : How To Evaluate Algebraic Expressions

Which of the following numbers is eight more than half of itself?

10

4

24

8

16

16

Explanation:

Word problems like this are a common occurrence on the PSAT. Begin by setting the number we are looking for, let's call it , equivalent to the equation we are given in the words.

Move all terms with the variable to one side:

Multiply both sides by 2:

### Example Question #43 : Expressions

Fahrenheit temperature can be converted to its Celsius equivalent using the formula

.

Celsius temperature can be converted to its Fahrenheit equivalent using the formula

.

Mercury boils at . To the nearest degree, convert this to its equivalent Fahrenheit temperature.

None of the other responses is correct.

Explanation:

The formula to use is

.

Substitute 357 for :

To the nearest degree, this is .

### Example Question #44 : Expressions

Increase  by 70%. Which of the following will this be equal to?

Explanation:

A number increased by 70% is equivalent to 100% of the number plus 70% of the number. This is taking 170% of the number, or, equivalently, multiplying it by 1.7.

Therefore,  increased by 70% is 1.7 times this, or

### Example Question #45 : Expressions

Which of the following phrases can be written as the algebraic expression  ?

Three times the difference of a number and nineteen

The cube of the difference of nineteen and a number

Nineteen less than the cube of a number

Three times the difference of nineteen and a number

The cube of the difference of a number and nineteen

The cube of the difference of a number and nineteen

Explanation:

is the cube of , which is the difference of a number and nineteen; therefore,  is "the cube of the difference of a number and nineteen."

### Example Question #46 : Expressions

Which of the following phrases can be written as the algebraic expression ?

The cube of the difference of a number and seventeen

Seventeen decreased by the cube of a number

Three times the difference of seventeen and a number

Three times the difference of a number and seventeen

The cube of the difference of seventeen and a number

Seventeen decreased by the cube of a number

Explanation:

is seventeen decreased by , which is the cube of a number; therefore,  is "seventeen decreased by the cube of a number."

### Example Question #47 : Expressions

Which of the following operations could represent the expression ?

7 less than the square of 2x

7 more than 2 times the square of x

2 times 7 more than the square of x

2 times 7 less than the square of x

7 more than the square of 2x

7 more than 2 times the square of x

Explanation:

Begin by putting the equation given into your own words. It might sound something similar to:

2 times x squared plus 7

Now, go through each answer choice and see if any of them are similar to this. We immediately see that the answer "7 more than 2 times the square of x" is similar to what we came up with. Let's do a quick run through of the other choices to be sure of our choice:

"2 times 7 more than the square of x" is equal to , which is equivalent to

"2 times 7 less than the square of x" is equal to , which is equivalent to .

"7 more than the square of 2x" is equal to , which is equivalent to .

"7 less than the square of 2x" is equal to , which is equivalent to .

The only answer that works is "7 more than 2 times the square of x". This is the correct answer.

### Example Question #1 : How To Simplify An Expression

What does  equal?

Explanation:

When solving a complex expression, remember the acronym PEMDAS (Parentheses, Exponents, Multiplication, Division, Addition, Subtraction). Reading left to right, begin by doing all operations within the innermost Parentheses first:

Continue simplifying using the acronym PEMDAS:

The expression is equal to -63.

### Example Question #1 : Rational Expressions

Simplify.

Explanation:

Same denominator means you add straight across the numerators, keeping the denominator the same.

Simplify.