All New SAT Math - No Calculator Resources
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 ?
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 #3 : Squaring / Square Roots / Radicals
Simplify the radical expression.
Look for perfect cubes within each term. This will allow us to factor out of the radical.
Example Question #1 : New Sat Math No Calculator
None of the other responses gives a correct answer.
Example Question #2 : Quadratic Equations
What is the sum of all the values of that satisfy:
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 :
The sum of these values is:
Example Question #34 : How To Find The Solution For A System Of Equations
Solve the system of equations.
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 #4 : New Sat Math No Calculator
Find the product:
Find the product:
Step 1: Use the distributive property.
Step 2: Combine like terms.
Example Question #2 : Complex Numbers
Add and its complex conjugate.
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 #11 : How To Find The Area Of A Rectangle
The width of a rectangle is . The length of the rectangle is . What must be the area?
The area of a rectangle is:
Substitute the variables into the formula.
Example Question #4 : 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?
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 #3 : Exponents And The Distributive Property
Find the product in terms of :
This question can be solved using the FOIL method. So the first terms are multiplied together:
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