Algebra 2 VA SOL Review Flashcards

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Questions and Answers

What is the inverse of f(x)?

Switch x and y

What do you need to do to solve a problem involving normally distributed data with a mean and standard deviation?

Draw the curve and label the bottom, using the 68, 95, 99.7 rule.

How do you factor 8x^3 + 27?

(2x + 3)(4x^2 - 6x + 9)

What do the terms roots, zeros, and solutions refer to?

X-intercepts Signup and view all the answers

Can you crush this test?

Heck yeah! Signup and view all the answers

What is the equation when Y varies proportionally with another variable?

y=kx Signup and view all the answers

Where should you look on the graph for the end behavior of f(x) as x approaches negative infinity?

Look at the left arrow on the graph. Signup and view all the answers

Where should you look on the graph for the end behavior of f(x) as x approaches infinity?

Look at the right arrow on the graph. Signup and view all the answers

What does 'find the solution set' mean?

Solve the equation. Signup and view all the answers

What does the notation { } mean?

No solution is one of your options. Signup and view all the answers

What should you do if you have no idea how to start a problem?

Read all the words slowly and look for familiar terms. Signup and view all the answers

What should you do if you seriously have no clue what to do?

Skip it and find a problem you know how to solve. Signup and view all the answers

Should you ever zone out during an S.O.L?

Yes, but then zone back in and keep going. Signup and view all the answers

What does 'domain' refer to?

Left to right. Signup and view all the answers

What does 'range' refer to?

Down to top. Signup and view all the answers

What is a horizontal asymptote?

y = # Signup and view all the answers

What is a vertical asymptote?

x = # Signup and view all the answers

What do you do if you see f(g(2))?

First plug 2 into g( ), then plug that number into f( ). Signup and view all the answers

What should you look for when finding the solution set for a system of equations on a graph?

Intersections of two lines. Signup and view all the answers

How do you find the best model for a table of numbers?

Use your calculator to analyze the data. Signup and view all the answers

What is the constant of proportionality?

K = the constant. Signup and view all the answers

Study Notes

Inverse Functions

The inverse of f(x) is found by switching x and y coordinates.

Probability and Normal Distribution

For normally distributed problems, draw a curve and label the x-axis.
Place the mean in the center, add and subtract standard deviations three times for intervals.
Apply the 68-95-99.7 rule to evaluate probability ranges.

Factoring Techniques

Factor the polynomial 8x^3 + 27 using SOAP (Sum of Cubes).
The factorization results in (2x + 3)(4x² - 6x + 9).

Understanding Roots and Zeros

Roots, zeros, and solutions refer to x-intercepts where f(x) = 0.
For systems of equations, identify intersection points (x, y) instead.

Confidence in Testing

Maintain a positive attitude; preparation is key for success.

Direct Variation

When “Y varies proportionally with...” appears, use the equation y = k.
Inverse relationships place the constant on the bottom; jointly varies involves multiplication.

Analyzing End Behavior

For end behavior as x approaches negative infinity, observe the left end of the graph.
The graph's upward trend indicates f(x) approaches infinity, downward indicates negative infinity.

Analyzing End Behavior (Continued)

For end behavior as x approaches infinity, look at the right end of the graph.
Similar trends apply for upward or downward movement of f(x).

Solution Set Interpretation

"Find the solution set" means to solve the equation, which may yield multiple or no solutions.

Recognition of No Solution

The symbol { } signifies that no solution is an option; verify results by substituting back into the original equation.

Strategies for Unknown Problems

If unsure how to start, read the problem thoroughly, identify familiar terms, and consult the formula sheet.

Dealing with Tough Problems

If completely lost, skip the problem; focus on questions that are manageable.

Staying Engaged During Tests

It’s acceptable to zone out briefly during an S.O.L.; regroup and continue with concentration.

Domain and Range

Domain refers to the input values of a function (left to right).
Range refers to the output values (down to top).

Asymptotes

Horizontal asymptotes are expressed as y = constant; they determine the function’s behavior at extremes.
Vertical asymptotes are expressed as x = constant; they show restrictions in the domain of the function.

Function Composition

To evaluate f(g(2)), first substitute 2 into g, then take that result to evaluate f.

Solving Systems of Equations Graphically

Look for the intersection points of two lines on the graph to find the solution set.

Modeling Data

To find the best model for a set of numerical data, utilize a calculator.
Enter the data under STAT → Edit, then use STAT → Calc to assess regression options based on the highest r² value.

Constant of Proportionality

In problems involving variation, K represents the constant of proportionality in the equation y = kx.

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Description

Review key concepts in Algebra 2 with these flashcards, perfect for the Virginia Standards of Learning. Each card covers critical topics such as inverse functions, normal distribution, and factoring polynomials to help reinforce your understanding. Ideal for exam preparation and self-assessment.