### All SAT II Math II Resources

## Example Questions

### Example Question #11 : Single Variable Algebra

Solve the equation:

**Possible Answers:**

**Correct answer:**

Add two on both sides.

Divide by three on both sides.

The answer is:

### Example Question #11 : Solving Equations

Solve:

**Possible Answers:**

**Correct answer:**

To isolate the x-variable, multiply both sides by the coefficient of the x-variable.

The answer is:

### Example Question #11 : Solving Equations

Give the solution set of the following rational equation:

**Possible Answers:**

No solution

**Correct answer:**

No solution

Multiply both sides of the equation by to eliminate the fraction:

Subtract from both sides:

The only possible solution is , However, if this is substituted in the original equation, the expression at left is undefined, as seen here:

An expression with a denominator of 0 has an undefined value, so this statement is false. The equation has no solution.

### Example Question #21 : Single Variable Algebra

Give the set of all real solutions of the following equation:

**Possible Answers:**

None of these

**Correct answer:**

can be seen to fit the perfect square trinomial pattern:

The equation can therefore be rewritten as

Multiply both sides of the equation by the least common denominator of the expressions, which is :

This can be solved using the method. We are looking for two integers whose sum is and whose product is . Through some trial and error, the integers are found to be and , so the above equation can be rewritten, and solved using grouping, as

By the Zero Product Principle, one of these factors is equal to zero:

Either:

Or:

Both solutions can be confirmed by substitution; the solution set is .

### Example Question #11 : Solving Equations

Solve:

**Possible Answers:**

**Correct answer:**

To solve for x, multiply by negative one-third on both sides.

The answer is:

### Example Question #12 : Solving Equations

Solve the equation:

**Possible Answers:**

**Correct answer:**

Add nine on both sides.

Divide by negative six on both sides.

The answer is: