SAT Math : SAT Mathematics

Study concepts, example questions & explanations for SAT Math

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Example Questions

Example Question #4 : How To Use Foil

Expand the following expression:

Possible Answers:

Correct answer:

Explanation:

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 ?

Possible Answers:

Correct answer:

Explanation:

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:

 

Possible Answers:

Correct answer:

Explanation:

Example Question #2352 : Sat Mathematics

If  and  are both rational numbers and , what is ?

Possible Answers:

Correct answer:

Explanation:

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: 

Possible Answers:

Correct answer:

Explanation:

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.

\sqrt{3283}

Possible Answers:

7\sqrt{63}

7\sqrt{67}

57.3

67\sqrt{49}

56

Correct answer:

7\sqrt{67}

Explanation:

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: 

Possible Answers:

Correct answer:

Explanation:

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

Possible Answers:

Quantity A is greater

The relationship cannot be determined from the information given

Quantity B is greater

The two quantities are equal

Correct answer:

The relationship cannot be determined from the information given

Explanation:

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:

Hero

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?

Possible Answers:

14√2

8√14

48√77

12√5

4√14

Correct answer:

8√14

Explanation:

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. 

Hero

Hero2

 

 

Example Question #2357 : Sat Mathematics

Simplify the radical expression.

Possible Answers:

Correct answer:

Explanation:

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

Simplify.

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