SAT II Math I : Single-Variable Algebra

Example Questions

Example Question #63 : Solving Equations

Solve for .

Explanation:

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 .

Explanation:

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.

Subtract  on both sides.

We should still check the answers.

With simplifications,  .  is good.

With simplifications,  .  is good.

Example Question #65 : Solving Equations

Solve for .

Explanation:

Divide  on both sides.

Example Question #66 : Solving Equations

Solve for .

Explanation:

Divide  on both sides.

Example Question #67 : Solving Equations

Solve for .

Explanation:

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 .

Explanation:

Multiply  on both sides.

Square both sides to get rid of the radical.

Example Question #69 : Solving Equations

Solve for .

Explanation:

Distribute the  to each term in the parentheses.

Subtract  on both sides.

Divide  on both sides.

Example Question #70 : Solving Equations

Solve for .

Explanation:

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.

Example Question #71 : Solving Equations

Solve the following equation for when :

Explanation:

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?

Explanation:

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: