### All PSAT Math Resources

## Example Questions

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

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

**Possible Answers:**

**Correct answer:**

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 #1 : How To Simplify An Expression

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

**Possible Answers:**

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

**Correct answer:**

The cube of the difference of a number and nineteen

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 #3 : How To Simplify An Expression

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

**Possible Answers:**

The cube of the difference of seventeen and a number

Seventeen decreased by the cube of a number

Three times the difference of a number and seventeen

The cube of the difference of a number and seventeen

Three times the difference of seventeen and a number

**Correct answer:**

Seventeen decreased by the cube of a number

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

### Example Question #4 : How To Simplify An Expression

Which of the following operations could represent the expression ?

**Possible Answers:**

2 times 7 less than the square of x

7 more than the square of 2x

2 times 7 more than the square of x

7 more than 2 times the square of x

7 less than the square of 2x

**Correct answer:**

7 more than 2 times the square of x

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?

**Possible Answers:**

**Correct answer:**

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.