### All ISEE Upper Level Math Resources

## Example Questions

### Example Question #1 : How To Multiply Variables

Machine A can produce 4 buttons in 2 days. Machine B can produce 20 buttons in 4 days. How many buttons can Machine A and B, working together, produce in 40 days?

**Possible Answers:**

**Correct answer:**

First determine how many buttons each machine can produce in a day.

Machine A:

Machine B:

Machine A and B can produce 7 buttons per day when they are working together.

### Example Question #1 : How To Multiply Variables

Brian has 3 siblings. When his family orders pizza, each of the 4 children is given of the pizza. Brian does not feel well so he only finishes of his pizza. If the original pizza consisted of 12 slices of pizza, how many slices did Brian eat?

**Possible Answers:**

**Correct answer:**

Brian eats .

So Brian eats

### Example Question #3 : How To Multiply Variables

Solve for :

**Possible Answers:**

**Correct answer:**

### Example Question #2 : How To Multiply Variables

Simplify:

**Possible Answers:**

**Correct answer:**

This can be solved using the pattern for the square of a sum:

### Example Question #1 : How To Multiply Variables

Simplify:

**Possible Answers:**

**Correct answer:**

This can be solved using the pattern for the square of a difference:

### Example Question #3 : How To Multiply Variables

Simplify:

**Possible Answers:**

**Correct answer:**

This can be solved using the pattern for the square of a sum:

### Example Question #7 : How To Multiply Variables

Multiply:

**Possible Answers:**

**Correct answer:**

### Example Question #1 : How To Multiply Variables

Multiply:

**Possible Answers:**

**Correct answer:**

Use the FOIL method:

### Example Question #9 : How To Multiply Variables

Define

What is ?

**Possible Answers:**

**Correct answer:**

Substitute for :

### Example Question #1 : How To Multiply Variables

Simplify:

**Possible Answers:**

**Correct answer:**

First, recognize that raising the fraction to a negative power is the same as raising the inverted fraction to a positive power.

Apply the exponent within the parentheses and simplify. Remember that fractional exponents can be written as roots.

Simplify by taking the roots and canceling common factors.