### All SAT II Math I Resources

## Example Questions

### Example Question #63 : Solving Equations

Solve for .

**Possible Answers:**

**Correct answer:**

Divide on both sides.

Take the square root on both sides. Remember to account for a negative square root. Two negatives multiplied is a positive number.

### Example Question #71 : Single Variable Algebra

Solve for .

**Possible Answers:**

**Correct answer:**

Cross-multiply.

Foil out the terms and simplify.

Subtract on both sides.

We have a quadratic equation. We need to find two terms that multiply to and aso add to .

Set them individualy equal to zero.

Add to both sides.

Subtract on both sides.

We should still check the answers.

With simplifications, . is good.

With simplifications, . is good.

Answers are .

### Example Question #65 : Solving Equations

Solve for .

**Possible Answers:**

**Correct answer:**

Add on both sides.

Divide on both sides.

### Example Question #66 : Solving Equations

Solve for .

**Possible Answers:**

**Correct answer:**

Add on both sides.

Divide on both sides.

### Example Question #67 : Solving Equations

Solve for .

**Possible Answers:**

**Correct answer:**

Subtract on both sides.

Divide on both sides.

Since it's absolute value, we need to accept both positive and negative answers.

### Example Question #68 : Solving Equations

Solve for .

**Possible Answers:**

**Correct answer:**

Multiply on both sides.

Add on both sides.

Square both sides to get rid of the radical.

### Example Question #69 : Solving Equations

Solve for .

**Possible Answers:**

**Correct answer:**

Distribute the to each term in the parentheses.

Subtract on both sides.

Divide on both sides.

### Example Question #70 : Solving Equations

Solve for .

**Possible Answers:**

**Correct answer:**

Take the square root on both sides. When you do that, you also need to consider both positive and negative values. Remember, two negatives multiplied create a positive number.

Subtract on both sides.

Divide on both sides.

Subtract on both sides.

Answers are .

### Example Question #71 : Solving Equations

Solve the following equation for when :

**Possible Answers:**

**Correct answer:**

The first step will be to plug our given variable into the equation to get

.

Then you do the multiplication first so it is now,

.

Finally, subtract from to get .

### Example Question #80 : Single Variable Algebra

A cubic polynomial with rational coefficients whose lead term is has 2 and as two of its zeroes. Which of the following is this polynomial?

**Possible Answers:**

**Correct answer:**

A cubic polynomial has three zeroes, if a zero of degree is counted times. Since its lead term is , we know that, in factored form,

,

where , , and are its zeroes.

A polynomial with rational coefficients has its imaginary zeroes in conjugate pairs. Since is such a polynomial, then, since is one of its zeroes, so is its complex conjugate, . It has one other known zero, 2.

Therefore, we can set , , in the factored form of , and

To rewrite this, first multiply the first two factors with the help of the difference of squares pattern and the square of a binomial pattern:

Thus,

Distributing:

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