### All ACT Math Resources

## Example Questions

### Example Question #81 : Variables

A hockey team has 12 forwards, 6 defensemen, and 2 goalies. When they place 3 forwards, 2 defensemen, and 1 goalie on the ice, how many of each type are on the bench, (not on the ice)? F=Forward, D = Defensemen, G= Goalie

**Possible Answers:**

15 F, 8 D, 3 G

6 F, 2 D, 1 G

36 F, 12 D, 2 G

4 F, 3 D, 2 G

9 F, 4 D, 1 G

**Correct answer:**

9 F, 4 D, 1 G

We can represent this as a subtraction of trinomials.

(12F + 6D + 2G) – (3F + 2D + 1G) = 9F + 4D + 1G.

### Example Question #2 : How To Subtract Trinomials

You go to the grocery store and pick up apples, peaches, and oranges. Today you had some friends over who ate apples, peaches, and oranges. Which of the following represents how many of each you now have left if = apples, = peaches, and = oranges?

**Possible Answers:**

**Correct answer:**

1. Represent the situation with two sets of trinomials:

Before your friends ate the fruit:

The fruit your friends ate:

2. Subtract the first trinomial from the second trinomial:

### Example Question #11 : Trinomials

Choose the answer which best simplifies the following expression:

**Possible Answers:**

**Correct answer:**

To solve this expression, merely remove the parentheses (bearing in mind that because the second trinomial is being subtracted, it will be negative) and combine like terms:

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

Choose the answer which best simplifies the following expression:

**Possible Answers:**

**Correct answer:**

To simplify, remove parentheses and combine like terms:

### Example Question #5 : How To Subtract Trinomials

Choose the answer which best simplifies the following expression:

**Possible Answers:**

**Correct answer:**

To simplify, remove parentheses and combine like terms:

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