Evaluating Expressions and Operations

The video tutorial covers common ACT Algebra 1 questions, focusing on evaluating expressions. It explains the concept of evaluation, emphasizing the importance of using parentheses, especially with exponents. The tutorial provides several example problems, including basic evaluation, word problems, and complex expressions with custom operations. It highlights the need to substitute values correctly and apply PEMDAS rules. The video aims to prepare students for typical ACT questions by demonstrating multiple skills, such as solving equations and handling imaginary numbers.

What is the primary reason for using parentheses when substituting values in expressions?

• To simplify the expression

• To make the expression look neat

• To ensure correct order of operations

• To avoid errors with negative numbers and exponents

In the expression X^2 + 2 + Y^2 - 3, what is the result when X = 3 and Y = -3?

• 15

• 17

• 19

• 21

When solving a word problem involving a spring's length, what is the first step?

• Convert units to meters

• Ignore the given variables

• Evaluate the given length in the equation

• Solve for the force directly

How do you solve for F in the equation after substituting the length?

• Subtract 0.03 and multiply by 3/2

• Divide by 3/2

• Multiply by 2/3

• Add 0.03 to both sides

In the expression X = 3 + Y, what is the result of (3 + Y - Y)^2?

• 12

• 15

• 9

• 6

What is the alternative method to solve X = 3 + Y?

• Divide both sides by Y

• Subtract Y from both sides

• Add Y to both sides

• Multiply both sides by Y

What is the value of the expression √(M/X - 3) when M = -16 and X = -4?

• 1

• 2

• 3

• 4

How can the expression √(M/X - 3) be broken down using radicals?

• √(M) * √(X - 3)

• √(M) / √(X - 3)

• √(M) + √(X - 3)

• √(M) - √(X - 3)

In a made-up operation problem, what is the first step according to PEMDAS?

• Evaluate the expression inside the parentheses

• Add the numbers

• Solve the outer expression

• Multiply the numbers

What is the result of the operation 3 # 3 if the rule is (A + B)^A?

• 24

• 36

• 18

• 30