Algebra 2 Pre-test Flashcards

What does it mean to evaluate a mathematical expression?

What is the result of evaluating -2(5-4)?

What does it mean to solve an equation?

What is the solution for the equation x - 13 = -13?

What does it mean to simplify an expression?

What is the simplified form of 3x - 2 - 5x + 10?

What does factorial mean?

What is 4! (Four factorial)?

What is the significance of permutations?

What is the permutation formula?

How many possible outcomes are there if you have 6 books and can put 3 at a time?

What distinguishes a combination from a permutation?

What is the combination formula?

If you can get 12 books a year but choose 8, how many outcomes do you have?

Is the scenario with 5 officers and 10 members a permutation or combination?

What is the absolute value?

What is the absolute value of -100?

What is the absolute value of 100?

What is the absolute value of -5?

What is the solution for |x + 3| = -6?

How do you solve the equation -10 + |x + 3| = -6?

What is the inequality -3x > -15 solved for x?

What happens when you multiply or divide by a negative number in an inequality?

When graphing, is the graph closed or open for < or >?

When graphing, is the graph closed or open for ≤ or ≥?

Key Algebra Concepts

Evaluate: Determine the numerical value of an expression.
Example: Evaluate -2(5-4) results in -2.
Solve: Find the unknown value in an equation.
Example: Solving x - 13 = -13 yields x = 0.
Simplify: Combine like terms or reduce expressions to their simplest form.
Example: Simplifying 3x - 2 - 5x + 10 gives -2x + 8.

Factorials and Permutations

Factorial: The product of all whole numbers from a given number down to one.
Example: 4! = 4 x 3 x 2 x 1 = 24.
Permutation: Arrangement where order matters. Denoted as nPr.
Permutation Formula: nPr = n! / (n - r)!
Example: For 6 books taken 3 at a time: nPr = 6P3 = 6! / (6-3)! = 120 outcomes.

Combinations

Combination: Arrangement where order does not matter. Denoted as nCr.
Combination Formula: nCr = n! / [r!(n - r)!]
Example: Choosing 8 books from 12 gives the outcomes determined by nCr.

Absolute Value

Absolute Value: The distance of a number from zero on the number line.
Example: | -100 | = 100 and | 100 | = 100.

Solving Absolute Value Equations

Absolute value equations can potentially have no solution.
Example: |x + 3| = -6 has no solution since absolute values are non-negative.
Another example with a solvable absolute value: -10 + |x + 3| = -6 leads to two possible solutions: x = 1 and x = -7.

Inequalities and Signs

When solving inequalities, if you multiply or divide by a negative number, flip the inequality sign.
Example: From -3x > -15, dividing by -3 results in x < 5.
Open vs. Closed Circles:
- Open for < or >
- Closed for ≤ or ≥

These notes encapsulate fundamental algebraic concepts and their applications in problem-solving, helpful for exam preparation and understanding key terms and processes.

Prepare for your Algebra 2 exam with these pre-test flashcards. Each card includes a key term along with its definition and examples to help reinforce your understanding of essential concepts. Perfect for quick reviews and self-assessment before the test.