### All ISEE Upper Level Math Resources

## Example Questions

### Example Question #11 : How To Find The Least Common Multiple

What is the least common multiple of and ?

**Possible Answers:**

**Correct answer:**

Find all of the multiples of both numbers:

Find the first number that both sets have in common.

### Example Question #12 : How To Find The Least Common Multiple

Find the LCM of and

**Possible Answers:**

**Correct answer:**

LCM is the least common multiple of the pair. There are a couple of terms at play here, so first find the LCM of 12 and 48. Since 12 goes into 48, 48 is the LCM. Then, look at xy and x. XY is the LCM between those two. So, multiply those together to get as your answer.

### Example Question #13 : How To Find The Least Common Multiple

What is the least common multiple of and ?

**Possible Answers:**

**Correct answer:**

A multiple of x is a number that results when x is multiplied by another whole number.

The least common multiple of two numbers is the smallest number that is a multiple of both the numbers.

24 is a multiple of 8 because 8 times 3 is 24.

24 is also a multiple of 12 because 12 times 2 is 24.

There are no numbers that are smaller than 24 which are also multiples of 8 and 12. Therefore, 24 is the least common multiple.

### Example Question #1 : Exponents

Simplify:

**Possible Answers:**

**Correct answer:**

In order to add or subtract exponential terms, both the base and the exponent must be the same. So we can write:

### Example Question #2 : Exponents

Evaluate:

**Possible Answers:**

**Correct answer:**

In order to add or subtract exponential terms, both the base and the exponent must be the same. So we can write:

Now they must be multiplied out before they can be added:

### Example Question #3 : Exponents

Subtract and simplify:

**Possible Answers:**

**Correct answer:**

Consider a vertical subtraction process:

Rewrite as the addition of the opposite of the second expression, as follows:

### Example Question #4 : Exponents

Define an operation as follows:

For all real numbers ,

.

Evaluate: .

**Possible Answers:**

**Correct answer:**

, so

### Example Question #5 : Exponents

Subtract and simplify:

**Possible Answers:**

The correct answer is not among the other responses.

**Correct answer:**

Consider a vertical subtraction process:

Rewrite as the addition of the opposite of the second expression, as follows:

### Example Question #1 : How To Subtract Exponents

Define an operation as follows:

For all real numbers ,

.

Evaluate: .

**Possible Answers:**

**Correct answer:**

### Example Question #7 : Exponents

Define an operation as follows:

For all real numbers ,

.

Evaluate:

**Possible Answers:**

**Correct answer:**

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