### All ACT Math Resources

## Example Questions

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

When x = 4 and y = 3, by how much does the value of 2x^{2 }– 2y exceed the value of 2x^{2 }– 2y^{2}

**Possible Answers:**

55

28

14

26

12

**Correct answer:**

12

This problem requires proper order of operations. A useful way of remembering the correct order of operations is PEMDAS. PEMDAS stands for parentheses, exponents, multiplication, division, addition, and subtraction. Thus any operations inside parenthese are the first to be performed, then any operations with exponents, then multiplication, then division, then addition and finally subtraction. The three operations dealt with in this problem are multiplication, exponents and subtraction. From PEMDAS we know that exponential operations are performed first, then we can perform the multiplication operations, and lastly we will perform the subtraction operations. So the correct way to approach this problem would be to solve each expression seperately and then find the difference. The first expression is 2x^{2 }– 2y, we first perform the exponential operation, (4)^{2 }= 16, then we can perform the multiplication operations 2(16) – 2(3), and finally the subtraction operations 32 – 6 leaving us with value of 26. For the other expression we proceed in the same fashion. Exponents first: 4^{2 }= 16, 3^{2 }= 9, then multiplication 2(16) – 2(9) → 32 – 18, and finally subtraction yielding a value of 14. The difference between the first expression and the second is thus 26 – 14 = 12.

### Example Question #2 : Arithmetic

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

**Possible Answers:**

21,746

66.7

2016

2004

2400

**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 : Order Of Operations

Evaluate:

–1 + 2 * –3

**Possible Answers:**

3

7

–3

5

–7

**Correct answer:**

–7

First you perform multiplication 2 * –3 = –6

Then you add –1 which gives you -7.

### Example Question #1 : Order Of Operations

Evaluate:

^{2}

**Possible Answers:**

–1

1

0

–21

21

**Correct answer:**

–1

Evaluate the exponent, then distribute, then add.

### Example Question #1 : Order Of Operations

Evaluate the expression:

(2 + 2)^{2 }– 1

**Possible Answers:**

15

7

4

1

16

**Correct answer:**

15

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

### Example Question #2 : Order Of Operations

Evaluate:

(–1) + (2)^{2} * (–3)

**Possible Answers:**

9

–9

–13

–3

13

**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 #7 : Arithmetic

Solve the following equation:

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

**Possible Answers:**

1014.5

4500

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 #2 : Order Of Operations

Solve the following equation:

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

**Possible Answers:**

98.6

140

86

126

90.6

**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 #1 : How To Find Order Of Operations

Solve: 4 + 2 * 4 = ?

**Possible Answers:**

14

12

10

32

24

**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:**

**–**25

16

86

36

64

**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.

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