### All New SAT Math - No Calculator Resources

## Example Questions

### Example Question #241 : Algebra

Solve the following system of equations:

What is the sum of and ?

**Possible Answers:**

**Correct answer:**

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 : Squaring / Square Roots / Radicals

Simplify the radical expression.

**Possible Answers:**

**Correct answer:**

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:

**Possible Answers:**

None of the other responses gives a correct answer.

**Correct answer:**

### Example Question #1 : Quadratic Equations

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

**Possible Answers:**

**Correct answer:**

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 #1 : New Sat Math No Calculator

Solve the system of equations.

**Possible Answers:**

**Correct answer:**

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 #1 : New Sat Math No Calculator

Find the product:

**Possible Answers:**

**Correct answer:**

Find the product:

Step 1: Use the distributive property.

Step 2: Combine like terms.

### Example Question #1 : Complex Numbers

Add and its complex conjugate.

**Possible Answers:**

**Correct answer:**

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 #2 : New Sat Math No Calculator

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

**Possible Answers:**

**Correct answer:**

The area of a rectangle is:

Substitute the variables into the formula.

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

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?

**Possible Answers:**

**Correct answer:**

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 #4 : New Sat Math No Calculator

Find the product in terms of :

**Possible Answers:**

**Correct answer:**

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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