Algebra 2 - Science and Math Projects

Unit 1: Functions and Equations

Domain, range, transformations, quadratics, and complex numbers

Weeks 1-6

Unit 2: Polynomials

Graphing, operations, factoring, and solving polynomial equations

Weeks 7-11

Unit 3: Rational & Radical Functions

Rational exponents, inverse functions, and radical equations

Weeks 12-15

Unit 4: Exponentials & Logarithms

Growth, decay, compound interest, and logarithmic properties

Weeks 16-20

Unit 5: Rational Functions

Asymptotes, operations, and rational equations

Weeks 21-23

Unit 6: Sequences & Series

Explicit and recursive formulas, arithmetic and geometric sequences

Weeks 24-25

Unit 7: Trigonometric Functions

Unit circle, identities, and trigonometric graphs

Weeks 26-29

Unit 8: Probability

Compound events, conditional probability, and Bayes' theorem

Weeks 30-31

Unit 9: Statistics

Data distributions, binomial probability, and empirical rule

Week 32

Function Type:

Analysis Results:

Function Type:

Analysis Results:

a (vertical stretch): 1

h (horizontal shift): 0

k (vertical shift): 0

Transformation Info:

Complex Number 1:

Complex Number 2:

Operation:

Operation Results:

a coefficient:

b coefficient:

c coefficient:

Quadratic Info:

Solution Results:

Equation 1: ax + by = c

Equation 2: ax + by = c

System Solution:

Polynomial Degree:

Leading Coefficient: 1

Constant Term: 0

Polynomial Analysis:

Polynomial P(x):

Polynomial Q(x):

Operation:

Operation Results:

Polynomial to Factor:

Factoring Method:

Factoring Results:

Dividend P(x):

Divisor D(x):

Division Method:

Division Results:

Polynomial Equation:

Solution Method:

Solution Results:

Numerator:

Denominator:

Analysis Results:

Radical Type:

Horizontal Shift: 0

Vertical Shift: 0

Radical Analysis:

Function:

Inverse Analysis:

Radical Equation:

Solution Results:

Base:

Numerator (m):

Denominator (n):

Exponent Results:

Base (a): 2

Vertical Shift: 0

Exponential Analysis:

Base:

Horizontal Shift: 0

Logarithmic Analysis:

Exponential Equation:

Solution Method:

Solution Results:

Logarithmic Equation:

Solution Method:

Solution Results:

Application Type:

Initial Value:

Rate/Time Parameter:

Application Results:

Function Type:

Function Analysis:

Asymptote Type:

Asymptote Analysis:

Operation Type:

Operation Example:

Example Equation:

Solution Steps:

First Term (a₁):

Common Difference (d):

Sequence Analysis:

First Term (a₁):

Common Ratio (r):

Sequence Analysis:

First Term (a₁):

Common Ratio (r):

Series Analysis:

Angle (degrees): 0° (0 rad)

Trigonometric Values:

Function Type:

Amplitude (A):

Period (B):

Phase Shift (C):

Vertical Shift (D):

Function Analysis:

Graph Type:

Frequency: 1

Amplitude: 1

Graph Properties:

Trigonometric Identities

Essential trigonometric identities for Algebra 2

Identity Name	Formula	Description

About Trigonometric Identities

Trigonometric identities are equations that are true for all values of the variables involved. They are used to simplify trigonometric expressions and solve trigonometric equations.

Trigonometric Applications

Real-world applications of trigonometry in Algebra 2

Example 1: Height of a Building

You are standing 100 meters away from a building. The angle of elevation to the top of the building is 30 degrees. How tall is the building?

Example 2: Distance Between Two Ships

Two ships are sailing in the ocean. Ship A is 500 meters north of Ship B. The angle between the direction of Ship A and the north is 45 degrees. The angle between the direction of Ship B and the north is 60 degrees. What is the distance between the two ships?

About Trigonometric Applications

Trigonometry has numerous real-world applications. It is used in fields such as engineering, physics, and navigation to solve problems involving angles and distances.

Probability Visualization

Probability is the measure of the likelihood that an event will occur. It is quantified as a number between 0 and 1, where 0 indicates impossibility and 1 indicates certainty.

Formula: P(Event) = Favorable Outcomes / Total Outcomes

Experiment Type:

Probability Results:

Permutations and Combinations

Permutations are arrangements where order matters.

Combinations are selections where order does not matter.

These concepts are fundamental in probability and combinatorics.

Total Items (n):

Items to Select (r):

Results:

Birthday Paradox

The birthday paradox is a probability problem that demonstrates how our intuition about probability can be misleading. It asks: What is the probability that in a group of people, at least two share the same birthday?

Surprisingly, in a group of just 23 people, the probability exceeds 50%!

Number of People:

Birthday Paradox Results:

Conditional Probability

Conditional probability is the probability of an event occurring given that another event has already occurred.

Formula: P(A|B) = P(A ∩ B) / P(B)

Where P(A|B) is the probability of event A given that event B has occurred.

Example Scenario:

Conditional Probability Results:

Bayes' Theorem

Bayes' theorem describes the probability of an event based on prior knowledge of conditions that might be related to the event.

Formula: P(A|B) = [P(B|A) × P(A)] / P(B)

This theorem is fundamental in statistical inference and machine learning.

Medical Test Example:

Disease Prevalence (%):

Test Sensitivity (%):

Test Specificity (%):

Bayes' Theorem Results:

Distribution Type:

Mean (μ): 0

Standard Deviation (σ): 1

Zoom Controls:

Statistical Analysis:

Number of Trials (n):

Number of Successes (k):

Probability of Success (p):

Binomial Probability:

Data Value (x):

Mean (μ):

Standard Deviation (σ):

Normal Distribution Analysis:

Understanding Algebra 2 Concepts

Algebra 2 builds upon fundamental algebraic concepts to explore more complex functions, equations, and mathematical relationships. This comprehensive course covers essential topics for college preparation and standardized testing.

Functions and Equations form the foundation, teaching students to analyze domain, range, and transformations while solving quadratic equations and working with complex numbers.

Polynomial Functions introduce higher-degree equations, factoring techniques, and polynomial division methods essential for advanced mathematics.

Exponential and Logarithmic Functions model real-world growth and decay phenomena, with applications in science, finance, and population studies.

Trigonometric Functions connect algebra with geometry, introducing periodic functions and their applications in modeling cyclical behavior.

Probability and Statistics provide essential skills for data analysis and decision-making in an increasingly data-driven world.