### All ACT Math Resources

## Example Questions

### Example Question #1 : Arithmetic

5 * (482 – 82) + 100 / (3 + 2)^{2 }= ?

**Possible Answers:**

2016

21,746

2400

2004

66.7

**Correct answer:**

2004

Order of operations: "PEMDAS” or "Please Excuse My Dear Aunt Sally"

"Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction".

5 * (482 – 82) + 100 / (3 + 2)^{2 }= ?

5 * (400) + 100 / (5)^{ 2 }=

2000 + 100 / 25 =

2000 + 4 = 2004

### Example Question #1 : How To Find Order Of Operations

Evaluate:

–1 + 2 * –3

**Possible Answers:**

5

7

–3

3

–7

**Correct answer:**

–7

First you perform multiplication 2 * –3 = –6

Then you add –1 which gives you -7.

### Example Question #3 : Arithmetic

Evaluate:

^{2}

**Possible Answers:**

1

21

0

–1

–21

**Correct answer:**

–1

Evaluate the exponent, then distribute, then add.

### Example Question #2 : How To Find Order Of Operations

Evaluate the expression:

(2 + 2)^{2 }– 1

**Possible Answers:**

7

16

4

15

1

**Correct answer:**

15

First you perform the operation in the parentheses and then you multiply the exponent; after that, subtract one.

### Example Question #5 : Arithmetic

Evaluate:

(–1) + (2)^{2} * (–3)

**Possible Answers:**

9

–3

13

–13

–9

**Correct answer:**

–13

First you evaluate the exponent. Then you multiply it by (–3) which gives you –12. Add –1 makes it –13.

### Example Question #1 : How To Find Order Of Operations

Solve the following equation:

(9 + 1) * (4^{2} + 2) * (7^{2} + 1) / 2 = ?

**Possible Answers:**

4500

1014.5

39

9000

1500

**Correct answer:**

4500

Order of operations: "PEMDAS” or "Please Excuse My Dear Aunt Sally"

"Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction".

(9 + 1) * (4^{2} + 2) * (7^{2} + 1) / 2 =

(10) * (16 + 2) * (49 + 1) / 2 =

(10) * (18) * (50) / 2 =

9000/2 = 4500

### Example Question #7 : Arithmetic

Solve the following equation:

(4 * 12) / (5 + 6 + 1) + 72 + (2 * 1 + 2)^{3} = ?

**Possible Answers:**

140

90.6

126

86

98.6

**Correct answer:**

140

Order of operations: "PEMDAS” or "Please Excuse My Dear Aunt Sally"

"Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction".

(4 * 12) / (5 + 6 + 1) + 72 + (2 * 1 + 2)^{3} =

(48)/(12) + 72 + (2 + 2)^{3} =

(48)/(12) + 72 + (4)^{ 3} =

(48)/(12) + 72 + 64 =

4 + 72 + 64 = 140

### Example Question #8 : Arithmetic

Solve: 4 + 2 * 4 = ?

**Possible Answers:**

32

12

24

10

14

**Correct answer:**

12

To solve you must use the order of operations PEMDAS.

Multiplication comes first 4 * 2 = 8. Then add 4 + 8 = 12.

### Example Question #1 : Arithmetic

The operation ¤ is defined as “cube the number that is to the right of the ¤ and subtract the result from the number that is to the left of ¤.” What is the value of 100 ¤ (5 ¤ 1)?

**Possible Answers:**

16

**–**25

64

86

36

**Correct answer:**

36

Starting inside the parentheses, cube the number to the right of the symbol, which is 1, and then subtract that from the number to the left of the symbol, 5, to get 4. Then we perform the same operation by cubing 4 to get 64, and then subtracting that from 100 to get 36.

### Example Question #1 : Order Of Operations

The expression is equivalent to:

**Possible Answers:**

**Correct answer:**

In order to find the equivalent expression, distribute to get .

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