All SAT Math Resources
Example Questions
Example Question #4 : How To Use Foil
Expand the following expression:
Expand the following expression:
Let's begin by recalling the meaning of FOIL: First, Outer, Inner, Last.
This means that in a situation such as we are given here, we need to multiply all the terms in a particular way. FOIL makes it easy to remember to multiply each pair of terms.
Let's begin:
First:
Outer:
Inner:
Last:
Now, put it together in standard form to get:
Example Question #1 : How To Find A Ratio Of Exponents
If and are positive integers and , then what is the value of ?
43 = 64
Alternatively written, this is 4(4)(4) = 64 or 43 = 641.
Thus, m = 3 and n = 1.
m/n = 3/1 = 3.
Example Question #2351 : Sat Mathematics
Write the following logarithm in expanded form:
Example Question #2352 : Sat Mathematics
If and are both rational numbers and , what is ?
This question is asking you for the ratio of m to n. To figure it out, the easiest way is to figure out when 4 to an exponent equals 8 to an exponent. The easiest way to do that is to list the first few results of 4 to an exponent and 8 to an exponent and check to see if any match up, before resorting to more drastic means of finding a formula.
And, would you look at that. . Therefore, .
Example Question #2353 : Sat Mathematics
Simplify:
If you don't already have the pattern memorized, use FOIL. It's best to write out the parentheses twice (as below) to avoid mistakes:
Example Question #2354 : Sat Mathematics
Simplify the radical.
We can break the square root down into 2 roots of 67 and 49. 49 is a perfect square and reduces to 7.
Example Question #3 : Squaring / Square Roots / Radicals
Simplify:
If you don't already have the pattern memorized, use FOIL. It's best to write out the parentheses twice (as below) to avoid mistakes:
Example Question #1 : Squaring / Square Roots / Radicals
x2 = 36
Quantity A: x
Quantity B: 6
Quantity A is greater
The relationship cannot be determined from the information given
Quantity B is greater
The two quantities are equal
The relationship cannot be determined from the information given
x2 = 36 -> it is important to remember that this leads to two answers.
x = 6 or x = -6.
If x = 6: A = B.
If x = -6: A < B.
Thus the relationship cannot be determined from the information given.
Example Question #2 : Squaring / Square Roots / Radicals
According to Heron's Formula, the area of a triangle with side lengths of a, b, and c is given by the following:
where s is one-half of the triangle's perimeter.
What is the area of a triangle with side lengths of 6, 10, and 12 units?
14√2
8√14
48√77
12√5
4√14
8√14
We can use Heron's formula to find the area of the triangle. We can let a = 6, b = 10, and c = 12.
In order to find s, we need to find one half of the perimeter. The perimeter is the sum of the lengths of the sides of the triangle.
Perimeter = a + b + c = 6 + 10 + 12 = 28
In order to find s, we must multiply the perimeter by one-half, which would give us (1/2)(28), or 14.
Now that we have a, b, c, and s, we can calculate the area using Heron's formula.
Example Question #2357 : Sat Mathematics
Simplify the radical expression.
Look for perfect cubes within each term. This will allow us to factor out of the radical.
Simplify.
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