### All SAT II Math I Resources

## Example Questions

### Example Question #121 : Single Variable Algebra

Factor completely:

**Possible Answers:**

**Correct answer:**

The grouping technique works here:

The first factor is the difference of squares and can be factored further accordingly:

### Example Question #12 : Simplifying Expressions

Factor completely:

**Possible Answers:**

The polynomial is prime.

**Correct answer:**

The polynomial is prime.

Since the first term is a perfect cube, the factoring pattern we are looking to take advantage of is the difference of cubes pattern. However, 243 is *not* a perfect cube of an integer , so the factoring pattern cannot be applied. No other pattern fits, so the polynomial is a prime.

### Example Question #121 : Single Variable Algebra

Exponentiate:

**Possible Answers:**

**Correct answer:**

Vertical multiplication is perhaps the easiest way to multiply trinomials.

### Example Question #123 : Single Variable Algebra

Exponentiate:

**Possible Answers:**

**Correct answer:**

The difference of two terms can be cubed using the pattern

Where :

### Example Question #281 : Sat Subject Test In Math I

How many of the following are prime factors of ?

I)

II)

III)

IV)

**Possible Answers:**

Four

Two

None

Three

One

**Correct answer:**

Three

Factor all the way to its prime factorization.

can be factored as the difference of two perfect square terms as follows:

is a factor, and, as the sum of squares, it is a prime. is also a factor, but it is not a *prime* factor - it can be factored as the difference of two perfect square terms. We continue:

Therefore, of the given four choices, only is not a factor, so the correct response is three.

### Example Question #1 : How To Find The Solution Of A Rational Equation With A Binomial Denominator

Simplify the expression.

**Possible Answers:**

**Correct answer:**

First, factor the numerator. We need factors that multiply to and add to .

We can plug the factored terms into the original expression.

Note that appears in both the numerator and the denominator. This allows us to cancel the terms.

This is our final answer.

### Example Question #11 : Simplifying Expressions

Simplify the following expression:

**Possible Answers:**

**Correct answer:**

When simplifying an equation,you must find a common factor for all values in the equation, including both sides.

and, can all be divided by so divide them all at once

.

This leaves you with

.

### Example Question #122 : Single Variable Algebra

Simplify the expression

**Possible Answers:**

Already in simplest form

**Correct answer:**

Simplify the numerator by multiplying in the term

Cancel out like terms in the numerator and denominator.

### Example Question #123 : Single Variable Algebra

Simplify:

**Possible Answers:**

**Correct answer:**

Rewrite the denominator of the second fraction using a power.

Using the subtraction rule of exponents, we can simplify this as one term.

The expression becomes:

Apply the addition rule of exponents.

The answer is:

### Example Question #124 : Single Variable Algebra

**Possible Answers:**

**Correct answer:**

Factor an in the numerator to get:

We can now cancel out from the numerator and denominator leaving the answer.

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