Algebra 2 Exam Flashcards

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Questions and Answers

What is the Compounded Interest Formula?

PERT, where P = Starting Amount, R = Interest Rate, T = Time (Years)

What is the Interest Formula?

P(1+r/n)^(nt), where P = Starting Amount, R = Interest Rate, N = Number of Times Per Year, T = Time (Years)

What is the Change of Base Formula?

logbA = logA/logB

What is the definition of a logarithm?

logbA = C, where b is the base number, A is the number affected by b, and C is the exponent that equals A Signup and view all the answers

What does it mean to exponentiate and reverse?

Putting everything as a power above a number to cancel out a logarithm, and vice versa. Signup and view all the answers

What is the formula for Direct Variation?

y = kx Signup and view all the answers

What is the formula for Inverse Variation?

y = k/x Signup and view all the answers

What is the formula for Join Variation?

z = kxy Signup and view all the answers

What are the Horizontal Asymptote Rules for Rational Functions?

For y = x^n / x^m: n > m (slant), n = m (y = n/m), n < m (y = 0) Signup and view all the answers

What are the steps to find the Distance Between Parallel Lines?

<ol> <li>Find a perpendicular line; 2. Find where it intersects each line; 3. Use the distance formula between the two points.</li> </ol> Signup and view all the answers

What is the Circle Formula?

(x-h)^2 + (y-k)^2 = r^2 Signup and view all the answers

What is the Parabola Formula?

y = 1/4p(x-h)^2 + k or x = 1/4p(y-k)^2 + h Signup and view all the answers

What is the formula for an Ellipse?

foci: c^2 = a^2 - b^2; horizontal: (x-h)^2/a^2 + (y-k)^2/b^2 = 1; vertical: (y-k)^2/a^2 + (x-h)^2/b^2 = 1 Signup and view all the answers

What is the formula for a Hyperbola?

foci: c^2 = a^2 + b^2; horizontal: (x-h)^2/a^2 - (y-k)^2/b^2 = 1; vertical: (y-k)^2/a^2 - (x-h)^2/b^2 = 1 Signup and view all the answers

What are the formulas for Arithmetic sequences?

Recursive: an = an-1 + d; Explicit: an = a1 + (n-1)d; Summation: sn = n/2 * (a1 + an) Signup and view all the answers

What are the formulas for Geometric sequences?

Recursive: an = r(an-1); Explicit: a1 * r^(n-1); Finite Sum: a1(1-r^n) / (1-r); Infinite Sum: a1 / (1-r) Signup and view all the answers

What is the Law of Sines?

sinA/a = sinB/b = sinC/c or a/sinA = b/sinB = c/sinC Signup and view all the answers

What is the Law of Cosines?

a^2 = b^2 + c^2 - 2bc cosA; b^2 = a^2 + c^2 - 2ac cosB; c^2 = a^2 + b^2 - 2ab cosC Signup and view all the answers

How many solutions can sine have?

For an obtuse angle: 1; For an acute angle: h > a none, h = a one, h < a b one Signup and view all the answers

What is the equation for a Sine Graph?

y = asinb(x-h) + k, where a = amplitude, 2π/b = period Signup and view all the answers

What is the equation for a Cosine Graph?

y = acosb(x-h) + k, where a = amplitude, 2π/b = period Signup and view all the answers

What is the equation for a Tangent Graph?

y = atanb(x-h) + k, where amplitude = 1 and the period = π/2 Signup and view all the answers

Study Notes

Compounded Interest

Formula: ( PERT ) where ( P ) is the starting amount, ( R ) is the interest rate, and ( T ) represents time in years.

Interest Calculation

Formula: ( P(1+\frac{r}{n})^{nt} )
Variables: ( P ) (starting amount), ( r ) (interest rate), ( n ) (payments per year), and ( t ) (time in years).

Logarithmic Functions

Change of Base Formula: ( \log_b A = \frac{\log A}{\log B} )
Definition of a Logarithm: ( \log_b A = C ) implies ( b^C = A ) where ( b ) is the base, ( A ) the number, and ( C ) the exponent.

Exponential and Logarithmic Relationships

Exponentiation involves expressing terms as powers to eliminate logarithms.
Reversing the process puts terms back into logarithmic form to isolate exponents.

Variation Concepts

Direct Variation: ( y = kx ) where ( k ) is the constant of variation.
Inverse Variation: ( y = \frac{k}{x} ).
Joint Variation: ( z = kxy ) indicating dependency on multiple variables.

Analyzing Rational Functions

Asymptote Rules:
- ( n > m ): Slant asymptote, no horizontal asymptote.
- ( n = m ): Horizontal asymptote at ( y = \frac{n}{m} ).
- ( n < m ): Horizontal asymptote at ( y = 0 ).

Finding Distances

Distance Between Parallel Lines:
- Find a perpendicular line and its intersection points on each line.
- Use the distance formula to calculate the distance between these points.

Conics Formulas

Circle: ( (x-h)^2 + (y-k)^2 = r^2 ) where ( (h,k) ) is the center and ( r ) the radius.
Parabola:
- Vertical: ( y = \frac{1}{4p}(x-h)^2 + k )
- Horizontal: ( x = \frac{1}{4p}(y-k)^2 + h )
- Parameter ( p ) represents the focal distance.
Ellipse:
- Foci: ( c^2 = a^2 - b^2 )
- Horizontal form: ( \frac{(x-h)^2}{a^2} + \frac{(y-k)^2}{b^2} = 1 )
- Vertical form: ( \frac{(y-k)^2}{a^2} + \frac{(x-h)^2}{b^2} = 1 )
Hyperbola:
- Foci: ( c^2 = a^2 + b^2 )
- Horizontal form: ( \frac{(x-h)^2}{a^2} - \frac{(y-k)^2}{b^2} = 1 )
- Vertical form: ( \frac{(y-k)^2}{a^2} - \frac{(x-h)^2}{b^2} = 1 )

Sequences and Series

Arithmetic Sequence:
- Recursive: ( a_n = a_{n-1} + d )
- Explicit: ( a_n = a_1 + (n-1)d )
- Summation: ( S_n = \frac{n}{2}(a_1 + a_n) )
Geometric Sequence:
- Recursive: ( a_n = r \cdot a_{n-1} )
- Explicit: ( a_n = a_1 \cdot r^{n-1} )
- Finite Sum: ( S_n = \frac{a_1(1 - r^n)}{1 - r} ), Infinite Sum: ( S = \frac{a_1}{1 - r} )

Trigonometric Laws

Law of Sines: ( \frac{\sin A}{a} = \frac{\sin B}{b} = \frac{\sin C}{c} )
Area using sine: ( \text{Area} = \frac{1}{2}bc \sin A )
Law of Cosines:
- ( a^2 = b^2 + c^2 - 2bc \cos A )
- Similar formulas for ( b ) and ( c ).

Solutions in Triangle Geometry

Number of Solutions (Sine):
- For obtuse angle ( A ): one solution.
- For acute angle ( A ): conditions on height ( h ) determine the number of solutions.

Graphing Trigonometric Functions

Sine Graph: ( y = a \sin b(x-h) + k ) with amplitude ( a ) and period ( \frac{2\pi}{b} ), starts at 0.
Cosine Graph: ( y = a \cos b(x-h) + k ), starts at the highest or lowest point based on reflection.
Tangent Graph: ( y = a \tan b(x-h) + k ), has a period of ( \frac{\pi}{2} ) and numerous asymptotes.

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Test your understanding of key concepts in Algebra 2 with these flashcards. Covering topics such as the compounded interest formula and logarithmic functions, these cards are designed to help reinforce your knowledge for the upcoming exam.