PSAT Math : Exponents

Study concepts, example questions & explanations for PSAT Math

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Example Questions

Example Question #61 : Exponents

Simplify: 

Possible Answers:

This expression cannot be simplified any further

Correct answer:

Explanation:

When you are multiplying and the bases are the same, you add the exponents together. Because both bases are  you add  as your new exponent. You then keep the same base, , to the 7th power. 

Example Question #61 : Exponential Operations

Solve for :

 

Possible Answers:

Correct answer:

Explanation:

 

Now the left side equals  and the right side equals 8.  Hence:

Therefore  must be equal to 11.

Example Question #1 : How To Find The Square Of A Sum

Simplify the radical.

\sqrt{3283}

Possible Answers:

7\sqrt{67}

67\sqrt{49}

7\sqrt{63}

57.3

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 #61 : Exponents

Expand:

Possible Answers:

Correct answer:

Explanation:

Use the perfect square trinomial pattern, setting :

Example Question #61 : Exponents

If  is expanded, what is the coefficient of  ?

Possible Answers:

There is no  term in the expansion of .

Correct answer:

Explanation:

The coefficient of  is therefore 11.

Example Question #1 : How To Find The Square Of A Sum

If  is expanded, what is the coefficient of  ?

Possible Answers:

There is no  term in the expansion of .

Correct answer:

Explanation:

The coefficient of  is therefore 10.

Example Question #1 : How To Find The Square Of A Sum

Expand:

Possible Answers:

Correct answer:

Explanation:

Use the perfect square trinomial pattern, setting :

Example Question #1 : Squaring / Square Roots / Radicals

x2 = 36

Quantity A: x

Quantity B: 6

Possible Answers:

Quantity B is greater

Quantity A is greater

The relationship cannot be determined from the information given

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 #62 : Exponents

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:

4√14

12√5

14√2

8√14

48√77

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 #1 : New Sat Math No Calculator

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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