### All SAT Math Resources

## Example Questions

### Example Question #1231 : Psat Mathematics

Write in radical notation:

**Possible Answers:**

**Correct answer:**

Properties of Radicals

### Example Question #1232 : Psat Mathematics

Express in radical form :

**Possible Answers:**

**Correct answer:**

Properties of Radicals

### Example Question #1233 : Psat Mathematics

Simplify:

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**Correct answer:**

### Example Question #1234 : Psat Mathematics

Simplify:

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**Correct answer:**

Convert the given expression into a single radical e.g. the expression inside the radical is:

and the cube root of this is :

### Example Question #1235 : Psat Mathematics

Solve for .

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**Correct answer:**

Hence must be equal to 2.

### Example Question #1236 : Psat Mathematics

Simplify:

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**Correct answer:**

Now

Hence the correct answer is

### Example Question #1237 : Psat Mathematics

Solve for .

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**Correct answer:**

If we combine into a single logarithmic function we get:

Solving for we get .

### Example Question #1238 : Psat Mathematics

If is the complex number such that , evaluate the following expression:

**Possible Answers:**

**Correct answer:**

The powers of i form a sequence that repeats every four terms.

i^{1 }= i

i^{2} = -1

i^{3} = -i

i^{4} = 1

i^{5} = i

Thus:

i^{25} = i

i^{23} = -i

i^{21} = i

i^{19}= -i

Now we can evalulate the expression.

i^{25} - i^{23 }+ i^{21 }- i^{19} + i^{17}..... + i

= i + (-1)(-i) + i + (-1)(i) ..... + i

= i + i + i + i + ..... + i

Each term reduces to +i. Since there are 13 terms in the expression, the final result is 13i.

### Example Question #15 : Algebra

If , then which of the following must also be true?

**Possible Answers:**

**Correct answer:**

We know that the expression must be negative. Therefore one or all of the terms x^{7}, y^{8} and z^{10} must be negative; however, even powers always produce positive numbers, so y^{8} and z^{10} will both be positive. Odd powers can produce both negative and positive numbers, depending on whether the base term is negative or positive. In this case, x^{7} must be negative, so x must be negative. Thus, the answer is x < 0.

### Example Question #17 : Algebra

Simplify the following:

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**Correct answer:**

With problems like this, it is always best to break apart your values into their prime factors. Let's look at the numerator and the denominator separately:

**Numerator**

Continuing the simplification:

Now, these factors have in common a . Factor this out:

**Denominator**

This is much simpler:

Now, return to your fraction:

Cancel out the common factors of :