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Math

Algebra

Algebraic Expressions

Equations

Inequalities

Linear Inequalities

One-variable Linear Inequalities

Representing Solutions Of Linear Inequalities In One Variable On A Number Line

Representing Solutions Of Absolute Value Inequalities On Number Lines

Solving/interpreting Linear Inequalities In One Variable

Solving And/or Interpreting Absolute Value Inequalities

Two-variable Linear Inequalities

Framing/writing Linear Inequalities In Two Variables

Framing Linear Inequalities In Two Variables

Graphing Linear Inequalities

Representing Solutions Of Linear Inequalities In Two Variables On A Graph

Graphing The Solution Set To A System Of Linear Inequalities In Two Variables As The Intersection Of The Half-planes

Representing Solutions Of Inequalities Of The Form Px + Qy ≤ R Or Px + Qy < R On Graphs

Representing Solutions Of Linear Inequalities In Two Variables On Graphs

Solutions In Equation Modeling

Solving/interpreting Linear Inequalities In Two Variables

Solving Real-world Problems Involving Multi-step Linear Inequalities In Two Variables

Non-linear Inequalities

Solving Multi-step Problems Using Non-linear Inequalities In One Variable

Solving Quadratic Inequalities In One Variable (algebraically Or Graphically)

Polynomials

Roots And Radicals

Understanding Roots

Applying Roots

Solving Problems Involving Nth Roots

Evaluating Roots

Evaluating Expressions Involving Cube Roots Of Positive/negative Numbers

Evaluating Expressions Involving Nth Roots

Evaluating Expressions Involving Square Roots Of Positive Numbers

Evaluating Nth Roots

Using Symbols For Solutions To Equations

Using The Cube Root Symbol For Solutions To Equations Of The Form X^3 = P

Using The Nth Root Symbol For Solutions To Equations Of The Form X^n = P

Using The Square Root Symbol For Solutions To Equations Of The Form X^2 = P

Sequences And Series

Sequences

Identifying And Writing Sequences

Identifying And Writing Rules For A Sequence When Given Some Terms Of The Sequence (including Arithmetic And Geometric Sequences)

Writing Terms Of A Sequence Recursively (including Arithmetic And Geometric Sequences)

Writing Terms Of A Sequence When Given The General Formula (including Arithmetic And Geometric Sequences)

Understanding And Applying Sequences

Using Arithmetic Sequences To Model Situations

Using Geometric Sequences To Model Situations

Series

Sum Of Finite Geometric Series Formula

Understanding And Applying Arithmetic Series

Applying The Formula For The Sum Of A Finite Arithmetic Series To Solve Problems

Understanding And Applying Geometric Series

Applying The Formula For The Sum Of A Finite Geometric Series To Solve Problems

Applying The Formula For The Sum Of An Infinite Geometric Series To Solve Problems

Functions

Advanced Functions

Advanced Function Analysis

Applying And Analysing Functions

Graphing Functions

Functions With Special Properties

Graphing Symbolic Functions & Key Features

Graphing Polynomial Functions & Identifying Zeros

Graphing Rational Functions With Zeros & Asymptotes

Graphing Root, Piecewise, Step & Absolute Value Functions

Understanding Sequences As Recursive Functions

Sequence Functions

Functions (sequence/series)

Arithmetic & Geometric Sequences: Recursive & Explicit

Exponential And Logarithmic Functions

Applications

Applying And Analysing Exponential And Logarithmic Functions

Applying The Laws Of Exponents To Interpret Expressions For Exponential Functions

Expressing The Solution Of Exponential Models (ab^(ct) = D) Where The Base Is B As Logarithms Using Technology

Observing That A Quantity Increasing As An Exponential Function Eventually Exceeds A Quantity Increasing As A Polynomial Function

Solving Real-world Problems Involving Exponential And/or Logarithmic Functions (including Modelling)

Understanding And Using The Inverse Relationship Between Exponential And Logarithmic Functions To Solve Problems

Comparing Function Types

Comparing Exponential & Polynomial Growth

Identifying Linear Vs Exponential Models

Identifying Constant Percent Growth/decay

Proving Growth Patterns In Linear & Exponential Functions

Recognizing Constant Rate Of Change

Exponential Functions

Graphing Exponential And Logarithmic Functions

Graphing Exponential Functions (including Growth/decay), Showing Intercepts And End Behavior

Performing Multiple Transformations On Different Exponential/logarithmic Functions (including Writing The Final Function)

Rewriting Exponential Functions To Reveal Properties

Interpreting Exponential Functions

Understanding Exponential And Logarithmic Functions

Identifying And Evaluating Exponential Functions

Proving That Exponential Functions Grow Or Decay By Equal Factors Over Equal Intervals

Recognising Situations And Solving Problems In Which A Quantity Grows Or Decays By A Constant Percent Rate

Writing And Interpreting Exponential Functions

Constructing An Exponential Function (including Geometric Sequences) From A Description

Constructing An Exponential Function (including Geometric Sequences) From A Graph

Constructing An Exponential Function (including Geometric Sequences) From A Set Of Input-output Pairs

Interpreting The Parameters In An Exponential Function In Terms Of A Context

Function Relationships

Constructing Linear & Exponential Functions

Interpreting Parameters In Linear/exponential Functions

Understanding Inverse Of Exponents & Logarithms

Logarithmic Functions

Evaluating Logarithms In Exponential Models

Graphing Symbolic Functions

Graphing Exponential, Logarithmic & Trigonometric Functions

Graphing Logarithmic Functions, Showing Intercepts And End Behavior

Understanding Exponential And Logarithmic Functions

Applying The Laws Of Logarithms To Simplify/evaluate Expressions

Function Concepts

Linear Functions

Graphing Linear Functions

Graphing Linear Functions And Showing Intercepts

Transformations On Absolute Value Linear Functions

Transformations On Linear Functions

Understanding Linear Functions

Recognising Situations In Which One Quantity Changes At A Constant Rate With Respect To Another Quantity

Writing And Interpreting Linear Functions

Identifying/constructing A Linear Function (including Arithmetic Sequences) From A Description/equation

Identifying/constructing A Linear Function (including Arithmetic Sequences) From A Graph

Identifying/constructing A Linear Function (including Arithmetic Sequences) From A Set Of Input-output Pairs

Interpreting The Parameters Of A Linear Function In Terms Of A Context

Quadratic Functions

Applying And Analysing Quadratic Functions

Solving Real-world Problems Involving Quadratic Functions

Using The Process Of Factorisation/completing Square To Find/show Zeroes, Extreme Values And Symmetry On Graphs Of Quadratic Functions

Graphing Symbolic Quadratic Functions

Graphing Linear & Quadratic Functions

Graphing Quadratic Functions

Graphing Quadratic Functions (including Showing Intercepts, Maxima Or Minima)

Transformations On Quadratic Functions

Rewriting Quadratic Functions To Reveal Properties

Interpreting Quadratic Graphs Via Factoring

Understanding Quadratic Functions

Identifying Characteristics Of Quadratic Functions

Writing And Interpreting Quadratic Functions

Writing A Quadratic Function Under Specific Conditions

Trigonometric Functions

Graphing Trig Functions

Graphing Trigonometric Functions

Graphing The Sine And Cosine Functions (including Transformations)

Solving Trig Equations

Evaluating And Interpreting The Solutions To Trigonometric Equations In Real-world Contexts Using Technology

Solving Real-world Problems Involving Trigonometric Functions (including Frequencies And Modelling)

Using Inverse Functions To Solve Trigonometric Equations

Using Inverse Functions To Solve Trigonometric Equations Using Technology And/or Intrepret The Solutions

Trigonometric Applications

Modeling Periodic Phenomena With Trig Functions

Solving Trigonometric Equations With Inverse Functions

Understanding Inverse Of Restricted Trigonometric Functions

Trigonometric Basics

Extension Of Trig Functions Via Unit Circle

Understanding Radian Measure Of An Angle

Unit Circle: Symmetry & Periodicity In Trig Functions

Using Special Triangles & Unit Circle In Trigonometry

Trigonometric Identities

Applying And Analysing Trigonometric Functions

Proving & Applying Trig Addition/subtraction

Proving & Using Pythagorean Trigonometric Identity

Understanding Trig Functions

Understanding Trigonometric Functions

Understanding And Using The Unit Circle To Extend Trigonometric Functions To All Real Numbers (both Degrees And Radians)

Geometry

Area And Volume

Area

Measuring And Estimating Area Of Miscellaneous Shapes

Calculating Areas Of Irregular Polygons

Volume

Basic Geometry

Expressing Properties With Equations

Solving Geometry Problems With Line Slopes

Fundamental Concepts

Proving Theorems: Lines & Angles

Understanding Basic Geometry Definitions

Understanding And Measuring Angles

Understanding That An Angle That Turns Through 'n' One-degree Angles Has An Angle Measure Of 'n' Degrees

Geometric Elements

Drawing And Identifying Geometric Elements

Drawing And Understanding Skew Lines And Planes

Drawing And Identifying Pairs Of Lines

Drawing And Identifying Parallel And/or Perpendicular Lines

Geometric Properties

Proving And Using Geometric Properties

Using The Angle Bisector Theorem To Solve Problems

Using The Perpendicular Bisector Theorem To Solve Problems

Geometric Terminology

Naming Geometric Elements

Naming Points, Line Segments, Rays, Lines And Planes

Understanding Key Terms

Knowing Precise Definitions Of Line Segments, Perpendicular Lines And Parallel Lines

Circles And Conic Sections

Congruence And Similarity

Applications

Applying Congruency And/or Similarity To Solve Problems

Use Congruency Criteria To Solve Problems

Use Similarity Criteria To Solve Problems

Congruence

Congruence Of Triangles Via Rigid Motions

Transforming Figures & Determining Congruence

Triangle Congruence Via Rigid Motions

Understanding Congruency

Establishing The Conditions Necessary For Two Triangles To Be Congruent

Reasoning How Two Figures Are Congruent Using Transformations

Similarity

Establishing Aa Criterion For Similar Triangles

Identifying Similarity In Triangles Using Transformations

Triangle Congruence & Similarity Problem Solving

Understanding Similarity

Describing A Sequence Of Transformations To Demonstrate Similarity Between Two Figures

Establishing The Conditions Necessary For Two Triangles To Be Similar

Identifying Similar Figures

Coordinate Geometry

Geometric Constructions

Advanced Constructions

Construct Shapes Inscribed In A Circle

Constructing Tangent Line To Circle

Geometric Constructions Using Various Tools

Using Constructions

Performing And Using Constructions Involving Circles

Using The Circumcenter Of A Triangle To Solve Geometric Problems

Using The Incenter Of A Triangle To Solve Geometric Problems

Perimeter And Circumference

Circle Perimeter

Applying The Understanding Of The Circumference Of A Circle To Solve Problems

Describing An Informal Argument For The Formula For The Circumference Of A Circle

Polygons

Quadrilaterals

Applying Properties Of Parallelograms

Applying Properties Of Special Parallelograms (square, Rectangle And Rhombus) To Solve Geometric Problems

Applying Properties Related To Angles And/or Sides And/or Diagonals In A Parallelogram To Solve Geometric Problems

Proving Theorems On Parallelograms

Understanding Quadrilaterals

Proving And Using The Properties Of Angles For A Quadrilateral

Triangles

Applying Properties Of Triangles

Applying Properties Based On The Relationship Between Side Lengths And Angle Measures To Solve Geometric Problems

Applying Properties Related To Altitudes To Solve Geometric Problems

Applying Properties Related To Medians To Solve Geometric Problems

Applying The Triangle Midsegment Theorem (intercept Theorem Or Basic Proportionality Theorem) To Solve Geometric Problems

Proving Triangle Theorems

Solid Geometry

3d Geometric Models

Applying Geometric Concepts In Modelling

Applying Concepts Of Density Based On Volume In Modeling Situations

Using Geometric Shapes (including Their Measures And Properties) To Describe Real-life Objects

Shapes

Applying Geometry In Design Problem Solving

Describing Objects Using Geometric Shapes

Identifying 2d Cross-sections & 3d Rotations

Reasoning With Three-dimensional Shapes And Their Attributes

Describing The Two-dimensional Figures That Result From Slicing Cones

Describing The Two-dimensional Figures That Result From Slicing Cylinders

Describing The Two-dimensional Figures That Result From Slicing Right Rectangular Prisms

Describing The Two-dimensional Figures That Result From Slicing Right Rectangular Pyramids

Surface Area

Transformations

Trigonometry

Advanced Trigonometry

Applying Law Of Sines & Cosines In Triangles

Applying Trigonometric Ratios Along With Other Mathematical Concepts

Deriving And Using The Formula For The Area Of A Triangle In Terms Of Sides And The Sine Ratio

Using The Law Of Sines And/or Cosines In Triangles To Solve Problems

Deriving Triangle Area Formula With Auxiliary Line

Proving & Applying Sine And Cosine Laws

Right Triangle Trigonometry

Applying Trigonometric Ratios

Solving Problems Involving Trigonometric Ratios In Right Triangles

Defining And Understanding Trigonometric Ratios

Defining The Six Fundamental Ratios For Acute Angles

Explaining And Using The Relationship Between The Sine And Cosine Of Complementary Angles

Sine-cosine Relationship In Complementary Angles

Solving Right Triangles With Trig & Pythagoras

Understanding Trigonometric Ratios In Right Triangles

Mathematical Practices

Mathematical Communication

Explaining Solution Processes

Mathematical Vocabulary

Representing Mathematical Ideas

Modeling And Tools

Appropriate Tool Selection

Mathematical Models

Technology Use In Mathematics

Problem Solving

Multi-step Problems

Problem-solving Strategies

Real-world Applications

Reasoning And Proof

Logical Reasoning

Mathematical Arguments

Pattern Recognition

Number System

Complex Numbers

Applications Of Complex Numbers

Proving Fundamental Theorem Of Algebra

Solving Quadratics With Complex Solutions

Understanding And Applying Conjugates Of Complex Numbers

Applying Conjugates To Find Quotients

Finding The Conjugate Of A Complex Number

Complex Number Fundamentals

Extend Polynomial Identities To Complex Numbers

Understanding Complex Numbers And I² = -1

Understanding And Using Complex Number Notation

Finding The Square Root Of A Negative Number

Knowing The Existence Of A Complex Number I And That I^2 = –1

Understanding That Every Complex Number Has The Form Of A + Bi Where A And B Are Real Numbers

Complex Number Operations

Adding And Subtracting Complex Numbers

Using Different Properties (commutative, Associative) To Add And/or Subtract Complex Numbers

Adding, Subtracting & Multiplying Complex Numbers

Applying Properties Of Operations On Complex Numbers To Solve Problems

Calculating The Distance Between Complex Numbers

Extending Algebraic Polynomial Identities To Complex Numbers

Finding The Midpoint Of A Segment Connecting Two Complex Numbers

Knowing The Fundamental Theorem Of Algebra

Solving Problems Involving A Mix Of Addition, Subtraction, Multiplication And/or Division Of Complex Numbers

Finding Conjugates & Moduli Of Complex Numbers

Multiplying Complex Numbers

Using I^2 = –1 And Different Properties (commutative, Associative, Distributive) To Multiply Complex Numbers (including Cases Where Addition/subtraction Are Involved)

Complex Numbers In The Coordinate Plane

Complex Plane: Distance & Midpoint Calculation

Geometric Representation Of Complex Numbers

Representing Complex Numbers In Different Forms

Representing Complex Numbers

Finding The Modulus And/or Argument Of A Complex Number

Representing Complex Numbers In The Polar Form

Representing Complex Numbers In The Rectangular Form

Understanding Why The Rectangular And Polar Forms Of A Complex Number Represent The Same Number

Matrices

Matrix Applications

Data Manipulation Using Matrices

Solving Problems Involving Mixed Operations

Solving Problems Involving A Mix Of Addition, Subtraction And/or Multiplication Of Matrices

Understanding And Applying Determinants

Finding The Inverse Of A Matrix (if It Exists)

Understanding And Using Matrices

Representing And Manipulating Data Through Matrices

Matrix Operations

Add, Subtract, Multiply Matrices

Adding And Subtracting Matrices

Adding And/or Subtracting Matrices Of Appropriate Dimensions

Multiplying Matrices By Scalars

Multiplying Matrices

Multiplying A Vector (column Matrix) By A Matrix To Produce Another Vector

Multiplying Matrices By Scalars

Multiplying Two Matrices Of Appropriate Dimensions

Understanding That Matrix Multiplication Is Associative And Distributive

Understanding That Matrix Multiplication Is Associative And Distributive But Not Commutative

Understanding The Role Of The Identity Matrix In Matrix Multiplication

Non-commutative Matrix Multiplication

Matrix Properties

2x2 Matrix Transformations & Determinant Area

Matrix Multiplication With Vectors

Understanding Role Of Zero, Identity Matrices & Determinants

Numerical Expressions

Laws Of Exponents

Understanding And Applying The Laws Of Exponents To Numerical Expressions (integral Exponents)

Understanding And Applying Laws Of Exponents (product Law, Quotient Law And Power Law) To Numerical Expressions For Exponents >0.

Understanding And Using Zero And Negative Exponents, Applying Law Of Exponents To Numerical Expressions Where Exponent Is Zero Or Negative.

Understanding And Applying The Laws Of Exponents To Numerical Expressions (rational Exponents)

Simplifying Expressions Involving Rational Exponents Using The Laws Of Exponents

Understanding That The Definition Of Rational Exponents Follows From Extending Understanding Of Integer Exponents

Measurement Applications

Working With Units

Defining Quantities For Descriptive Modeling

Interpreting Units & Scales In Problem Solving

Selecting Accuracy Level For Quantity Reporting

Real Numbers

Vectors

Vector Concepts

Understanding And Representing Vector Quantities

Understanding, Representing And Using Vectors

Vector Operations

Statistics And Probability

Bivariate Data

Scatter Plots And Correlation

Calculate & Interpret Correlation Coefficient

Correlation Vs Causation Distinction

Interpreting Frequencies & Trends In Data

Interpreting Slope & Intercept In Data Context

Scatter Plot Representation & Variable Relation

Assessing Function Fit Via Residual Analysis

Fit & Use Functions To Solve Data Problems

Fit Linear Function For Scatter Plot

Understanding And Applying Scatter Plots

Two-way Tables

Identifying And Interpreting Patterns Of Association

Data Analysis

Data Representation

Data Visualization

Data Representation On Real Number Line

Organising And Representing Data

Distinguishing Between Qualitative And Quantitative Data

Investigating And Describing Patterns Such As Clustering And Outliers

Representing Data Using Box-and-whisker Plots

Representing Data Using Dot Plots

Representing Data Using Histograms

Interpreting Data Displays

Interpreting Data

Choosing And Interpreting The Scale In Graphs And Data Displays

Probability

Sampling And Inference

Sampling Techniques

Using Random Sampling To Draw Inferences

Developing A Margin Of Error Through The Use Of Simulation Models

Explaining How Randomisation Relates To Sample Surveys, Experiments And Observational Studies

Recognising The Purposes Of And Differences Among Sample Surveys, Experiments And Observational Studies

Understanding Representative Samples And The Idea That Examining A Sample Can Lead To Useful Information About The Population

Using Data From A Sample Survey To Estimate A Population Mean Or Proportion

Statistical Estimation

Comparing Treatments & Parameters Via Data

Estimating Population Mean & Margin Of Error

Evaluating Data-based Reports

Statistical Inference Concepts

Assessing Model Consistency With Data Process

Understanding Inferences In Statistics

Understanding Surveys, Experiments & Randomization

Statistical Foundations

Basic Statistics

Understanding Statistical Variability (qualitative)

Recognising A Statistical Question

Ela

Language

Reading

Research And Media Literacy

Speaking And Listening

Writing

Science

Biology

Chemistry

Environmental Science

Physics

Scientific Methods And Applications

Data Analysis

Bioinformatics

Biological Network Analysis

Genome Annotation

Phylogenetic Analysis

Sequence Analysis

Structural Bioinformatics

Computational Methods

Algorithm Development

Data Mining

Machine Learning Applications

Network Analysis

Scientific Computing

Modeling And Simulation

Differential Equation Models

Monte Carlo Methods

Multi-scale Modeling

Parameter Estimation

System Dynamics

Statistics

Bayesian Statistics

General Linear Models

Mixed Effects Models

Multivariate Analysis

Time Series Analysis

Interdisciplinary Research

Collaborative Research

Collaborative Authorship

Cross-disciplinary Communication

Integrating Diverse Methodologies

Interdisciplinary Team Building

Managing Disciplinary Differences

Convergence Research

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Socio-technical Systems

Translational Research

Integrative Research Design

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Systems Thinking

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Emergent Properties

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System Boundaries And Interfaces

Research Ethics And Integrity

Ethical Dimensions Of Science

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Research Priorities And Values

Science Advocacy Ethics

Societal Implications Of Research

Research Compliance

Animal Care And Use

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Research Skills

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Data Curation

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High-throughput Methods

Microscopy And Imaging

Specialized Laboratory Procedures

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Critical Literature Analysis

Methodology Justification

Research Question Refinement

Timeline Planning

Research Project Management

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Research Documentation

Resource Allocation

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Team Coordination

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Advanced Presentation Skills

Conference Presentations

Defending Scientific Work

Interdisciplinary Communication

Research Seminar Preparation

Visual Representation Of Complex Data

Peer Review Process

Editorial Decisions

Open Peer Review

Publication Ethics

Responding To Reviewers

Reviewing Manuscripts

Public Engagement

Citizen Science Program Design

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Science Communication For Public

Science Policy Communication

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Social-studies

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Passages

12th Grade

Math

Mathematical Practices

12th Grade Mathematical Practices Passages

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Linear System Solutions - Problem Solving Applications - Algebra

9th Grade - 12th Grade

Math

Study the application of solving linear systems in real-world scenarios to enhance algebraic problem-solving proficiency. Develop the ability to efficiently determine unique and infinite solutions through mastery of key techniques.

9th Grade - 12th Grade

Understanding Congruence - Proving Triangles and Angles - Geometry Theorems

Passage

Understanding Congruence - Proving Triangles and Angles - Geometry Theorems

9th Grade - 12th Grade

Math

Develop a deep understanding of key theorems related to triangle and angle congruence, including CPCTC (Corresponding Parts of Congruent Triangles are Congruent) and the SAS (Side-Angle-Side) Postulate. Build skills to effectively prove geometric relationships through a comprehensive grasp of these concepts.

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