### All ACT Math Resources

## Example Questions

### Example Question #10 : Arithmetic

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

**Possible Answers:**

17

1

8

5

9

**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 #34 : Integers

Evaluate:

–3 * –7

**Possible Answers:**

21

4

–21

–10

10

**Correct answer:**

21

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

### Example Question #35 : Integers

Evaluate.

**Possible Answers:**

**Correct answer:**

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

### Example Question #36 : Integers

Solve.

**Possible Answers:**

**Correct answer:**

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

### Example Question #37 : Integers

Evaluate 3x^{3} + x^{2} if x = *–*2

**Possible Answers:**

14

*–*22

28

*–*20

**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 #38 : Integers

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

**Possible Answers:**

12

24

–24

–16

**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 #39 : Integers

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