Grade 11 Math

Grade 11 math builds on the concepts learned in Grade 10 and introduces more advanced topics, including functions, trigonometry, complex numbers, calculus, and probability. These concepts help develop strong analytical thinking and problem-solving skills.

Some real-life applications:

• Functions: Used to model relationships between quantities, like cab charges are related to distance.
• Trigonometry: Studies relationships between angles and sides of triangles, surveyors use trigonometry to measure the height of a mountain without climbing it.
• Probability: Measures the likelihood of events occurring, like predicting the chance of rain based on weather data.
• Statistics: Helps analyze and interpret data. For example, businesses analyze sales data to understand customer trends.

Algebra II

Most 11th graders take Algebra 2, builds on Algebra 1 & Geometry and covers advanced functions, polynomials, statistics, and an introduction to limits

1. Linear Functions & Systems

Linear Equations & Slope

• Linear Equations
• System of Linear Equations
• Graphical Method
• Substitution Method
• Elimination Method

Inverse & Piecewise Functions

• Functions in Maths
• Domain and Range of a Function
• Graphing Function
• Piecewise Function
• Absolute value functions & Inequalities

Systems & Inequalities

• Graphing Linear Inequalities
• Graphical Solution of Linear Inequalities (Two Variables)
• Matrix Solution of Systems

2. Quadratic Functions

Quadratic Forms & Graphing

• Quadratic Functions
• Graphing a Quadratic Function
• How to Find Vertex of a Quadratic Function
• Completing the Square Formula

Solving Quadratics

• Quadratic Equation
• Solving Quadratic Equations
• Quadratic Inequalities
• How to Solve Quadratic Inequalities
• Factorization of Quadratic Equations

Complex Numbers

• Complex Numbers
• Algebraic Operations on Complex Numbers
• Complex Conjugate
• Complex Solutions of Quadratic Equations

3. Polynomial Functions

Polynomial Operations

• Polynomials
• Dividing Polynomials (Long Division)
• Synthetic Division
• Factorization of Polynomial

Zeros & Theorems

• Remainder Theorem & Factor Theorem
• Fundamental Theorem of Algebra
• End Behavior & Degree Analysis
• Graphing Polynomial Functions

4. Rational & Radical Functions

Rational Expressions

• Rational Expression
• Addition and Subtraction of Rational Expressions
• Multiply and Divide Rational Expressions
• Rational Function

Radical Expressions & Functions

• Radical Expressions & Rational Exponents
• Vertical Asymptote
• Horizontal Asymptote

5. Exponential & Logarithmic Functions

Exponential Functions

• Exponential Functions
• Exponential Function Formula
• Exponential Graph
• Solving Exponential Equations Using Logs

Logarithmic Functions

• Introduction to Logarithms
• Logarithm Formulas
• Properties of Logarithms
• Logarithmic Function
• Natural Log (ln) & Euler's Number

6. Sequences & Series

Arithmetic & Geometric

• Intro to Sequences and Series
• Arithmetic Sequence
• Arithmetic Progression
• Sum of First n Terms in Arithmetic Sequence
• Geometric Progression
• Geometric Sequence Formulas
• Recursive Formula
• Harmonic Progression

Series & Sigma Notation

• Sigma (Summation) Notation
• Geometric Series
• Infinite Geometric Series

7. Trigonometric Functions

Trig Foundations

• Measuring Angles
• Radian Measure
• Unit Circle
• Radians to Degrees
• Trigonometric Functions
• Trigonometric Identities
• Trigonometric Graph
• Inverse Trigonometric Functions

Law of Sines & Cosines

• Law of Sines
• Law of Cosines
• Area of a Triangle Using Trig

8. Probability & Statistics

Probability

• Basic Concepts of Probability
• Events in Probability
• Conditional Probability
• Permutations and Combinations
• Principle of Counting
• Random Variable
• Binomial Distribution
• Discrete Probability Distribution

Statistics

• Statistics in Maths
• Descriptive Statistics
• Measures of Central Tendency
• Measures of Dispersion
• Frequency Distribution Table
• Scatter Plot
• Correlation Coefficient Formula
• Regression Analysis
• Normal Distribution & Z-Scores

9. Intro to Limits & Continuity

Limits

• Limits in Calculus
• Estimating Limits from Graphs
• Estimating Limits from Tables
• One-Sided Limits
• Limits at Infinity

Continuity

• Continuity of Functions
• Continuity at a Point
• Continuity and Discontinuity
• Intermediate Value Theorem

Precalculus

Combines algebra, trigonometry, and analytical concepts to prepare students for calculus and advanced mathematical studies.

1. Function Analysis

• Functions in Maths
• Domain and Range
• Graphing Functions
• Relations in Maths
• Function Composition
• Even/Odd Functions

2. Conic Sections

• Circles
• Center of Circle
• Equations of Circle
• Parabola
• Standard Equation
• Focus and Directrix
• Vertex
• Ellipse
• Hyperbola
• Eccentricity

3. Vectors & Parametric Equations

• Vector Magnitude
• Dot Product
• Parametric Equations

4. Matrices & Linear Systems

• Matrices
• Determinant
• Matrix inverse
• Cramer's Rule

5. Analytic Trigonometry

• Trig Identities & Equations
• Trigonometric Identities
• Inverse Trigonometric Functions
• Inverse Trigonometric Identities
• Sum/difference formulas
• Double- and half-angle formulas

6. Sequences, Series & Mathematical Induction

• Intro to Sequences and Series
• Arithmetic & Geometric
• Infinite geometric series
• Binomial theorem
• Mathematical induction

7. Intro to Calculus Concepts

• Derivatives
• Limits in Calculus
• One-Sided Limits
• Limits at Infinity
• Continuity of Functions
• Intermediate Value Theorem
• Average and Instantaneous Rate of Change

AP Statistics

Focuses on collecting, analyzing, and interpreting data to make informed predictions and decisions using statistical methods.

1. Exploring Data

• Graphical Representation
• Frequency Table
• Scatter Plot
• Descriptive Statistics
• Measure of Central tendency
• Measure of Spread
• Boxplots & Outliers

2. Describing Relationship

• Correlation Coefficient Formula
• Scatter Diagram (Correlation)
• Regression Analysis
• Residual Plots
• R-Squared Interpretation

3. Probability

• Basic Concepts of Probability
• Events in Probability
• Addition rule of Probability
• Conditional Probability
• Bayes' Theorem
• Permutation and Combination

4. Probability Distributions

• Random Variable
• Probability Distribution
• Discrete Probability Distribution
• Binomial Distribution
• Normal Distribution
• Geometric Distribution

5. Sampling Distributions & Inference

• Inferential Statistics
• Central Limit Theorem
• Confidence Intervals
• Z-test / T-test
• Chi-square test