# New SAT Math - No Calculator : New SAT Math - No Calculator

## Example Questions

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### Example Question #31 : How To Find The Solution For A System Of Equations

Solve the following system of equations:

What is the sum of  and ?

Explanation:

This problem can be solved by using substitution.  Write the first equation  in terms of  and substitute it into the second equation.

So  and thus  and solving for  and then .

So the sum of  and  is 7.

### Example Question #1 : How To Factor A Common Factor Out Of Squares

Explanation:

Look for perfect cubes within each term. This will allow us to factor out of the radical.

Simplify.

### Example Question #1 : New Sat Math No Calculator

Simplify:

None of the other responses gives a correct answer.

Explanation:

### Example Question #1 : How To Find The Solution To A Quadratic Equation

What is the sum of all the values of  that satisfy:

Explanation:

With quadratic equations, always begin by getting it into standard form:

Therefore, take our equation:

And rewrite it as:

You could use the quadratic formula to solve this problem.  However, it is possible to factor this if you are careful.  Factored, the equation can be rewritten as:

Now, either one of the groups on the left could be  and the whole equation would be .  Therefore, you set up each as a separate equation and solve for :

OR

The sum of these values is:

### Example Question #2 : New Sat Math No Calculator

Solve the system of equations.

Explanation:

For this system, it will be easiest to solve by substitution. The  variable is already isolated in the second equation. We can replace  in the first equation with , since these two values are equal.

Now we can solve for .

Now that we know the value of , we can solve for  by using our original second equation.

The final answer will be the ordered pair .

### Example Question #3 : New Sat Math No Calculator

Find the product:

Explanation:

Find the product:

Step 1: Use the distributive property.

Step 2: Combine like terms.

### Example Question #4 : New Sat Math No Calculator

Explanation:

The complex conjugate of a complex number  is . Therefore, the complex conjugate of  is ; add them by adding real parts and adding imaginary parts, as follows:

,

the correct response.

### Example Question #5 : New Sat Math No Calculator

The width of a rectangle is .  The length of the rectangle is .  What must be the area?

Explanation:

The area of a rectangle is:

Substitute the variables into the formula.

### Example Question #1 : How To Find The Area Of A Rectangle

George wants to paint the walls in his room blue.  The ceilings are 10 ft tall and a carpet 12 ft by 15 ft covers the floor.  One gallon of paint covers 400 and costs $40. One quart of paint covers 100 and costs$15.  How much money will he spend on the blue paint?

Explanation:

The area of the walls is given by

One gallon of paint covers 400 and the remaining 140 would be covered by two quarts.

So one gallon and two quarts of paint would cost

### Example Question #1 : Exponents And The Distributive Property

Find the product in terms of :

Explanation:

This question can be solved using the FOIL method. So the first terms are multiplied together:

This gives:

The x-squared is due to the x times x.

The outer terms are then multipled together and added to the value above.

The inner two terms are multipled together to give the next term of the expression.

Finally the last terms are multiplied together.

All of the above terms are added together to give:

Combining like terms gives

.

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