### All ACT Math Resources

## Example Questions

### Example Question #3 : Arithmetic

If a = –2 and b = –3, then evaluate a^{3} + b^{2}

**Possible Answers:**

17

9

5

8

1

**Correct answer:**

1

When multiplying negative numbers, we get a negative answer if there are an odd number of negative numbers being multiplied. We get a positive answer if there are an even number of negative numbers being multiplied.

a^{3} + b^{2} becomes (–2)^{3} + (–3)^{2} which equals –8 + 9 = 1^{}

### Example Question #3 : Negative Numbers

Evaluate:

–3 * –7

**Possible Answers:**

–21

10

4

–10

21

**Correct answer:**

21

Multiplying a negative number and another negative number makes the product positive.

### Example Question #4 : Negative Numbers

Evaluate.

**Possible Answers:**

**Correct answer:**

Multiplying a negative and a positive number creates a negative product:

### Example Question #5 : Negative Numbers

Solve.

**Possible Answers:**

**Correct answer:**

A negative number multiplied by a positive number will always be negative.

### Example Question #6 : Negative Numbers

Evaluate 3x^{3} + x^{2} if x = *–*2

**Possible Answers:**

*–*20

28

*–*22

14

**Correct answer:**

*–*20

When multiplying a negative number an odd number of times, the answer is negative. When multiplying a negative number an even number of times, the answer is positive. Order of operations also applies: Parentheses, Exponents, Multiplication and Division, Addition and Subtraction, from left to right. A mnemonic to remember the order of operations is “Please excuse my dear Aunt Sally.”

3(*–*2)^{3} + (*–*2)^{2}

= 3(*–*8) + (4)

= *–*24 + 4

= *–*20

### Example Question #1 : Negative Numbers

Simplify the following expression: (–4)(2)(–1)(–3)

**Possible Answers:**

–16

–24

12

24

**Correct answer:**

–24

First, we multiply –4 and 2. A negative and a positive number multiplied together give us a negative number, so (–4)(2) = –8. A negative times a negative is a positive so (–8)(–1) = 8. (8)(–3) = –24.

### Example Question #8 : Negative Numbers

Evaluate the following:

**Possible Answers:**

**Correct answer:**

Two odd numbers multiplied always result in an even number. Simply multiple the two as though they were even. Thus