Algebra 2 Pre-test Flashcards

Questions and Answers

What does it mean to evaluate a mathematical expression?

Simplify the expression

Solve for x

Find the graphical representation

Find the numerical value (correct)

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

-2

What does it mean to solve an equation?

Find the value of the unknown (correct)

Evaluate the expression

Find the graphical representation

Simplify the equation

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

x = 0 Signup and view all the answers

What does it mean to simplify an expression?

Combine like terms and reduce to lowest terms Signup and view all the answers

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

-2x + 8 Signup and view all the answers

What does factorial mean?

The product of all whole numbers starting with that number down to one Signup and view all the answers

What is 4! (Four factorial)?

24 Signup and view all the answers

What is the significance of permutations?

Order matters Signup and view all the answers

What is the permutation formula?

nPr = n! / (n-r)! Signup and view all the answers

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

120 possible outcomes Signup and view all the answers

What distinguishes a combination from a permutation?

Order does not matter in combinations Signup and view all the answers

What is the combination formula?

nCr = n! / (r! (n-r)!) Signup and view all the answers

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

nCr = 12 choose 8 Signup and view all the answers

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

Permutation Signup and view all the answers

What is the absolute value?

The distance a number is from zero Signup and view all the answers

What is the absolute value of -100?

100 Signup and view all the answers

What is the absolute value of 100?

100 Signup and view all the answers

What is the absolute value of -5?

-5 Signup and view all the answers

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

No solution Signup and view all the answers

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

x = 1 or x = -7 Signup and view all the answers

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

x < 5 Signup and view all the answers

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

FLIP THE SIGN Signup and view all the answers

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

Open Signup and view all the answers

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

Closed Signup and view all the answers

Study Notes

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.

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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.