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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 Inequalities 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

One-variable 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

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

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

Function Concepts

Specific Functions

Advanced Functions

Graphing Complex Functions

Graphing Symbolic Functions & Key Features

Graphing Polynomial Functions & Identifying Zeros

Graphing Rational Functions With Zeros & Asymptotes

Graphing Root, Piecewise, Step & Absolute Value Functions

Graphing Functions

Graphing Various Function Types

Identifying Effects Of Transformations On Graphs

Identifying Function Families

Identifying/finding Turning Points

Recursive Functions

Functions (sequence/series)

Arithmetic & Geometric Sequences: Recursive & Explicit

Understanding Sequences As Recursive Functions

Exponential And Logarithmic Functions

Applications Of Exponential And Logarithmic Functions

Applying And Analysing Exponential And Logarithmic Functions

Applying The Laws Of Exponents To Interpret Expressions For Exponential Functions

Comparing Exponential And Polynomial Growth Rates

Expressing Solutions Of Exponential Models Using Logarithms

Solving Real-world Problems With Exponential/logarithmic Functions

Using The Inverse Relationship Between Exponential And Logarithmic Functions

Understanding Exponential And Logarithmic Functions

Applying The Laws Of Logarithms

Identifying And Evaluating Exponential Functions

Proving Properties Of Exponential Growth/decay

Recognising Situations Involving Constant Percent Rates

Writing And Interpreting Exponential Functions

Constructing Exponential Functions From Various Representations

Interpreting Parameters In Exponential Contexts

Exponential Models

Comparing Exponential & Polynomial Growth

Constructing Linear & Exponential Functions

Identifying Linear Vs Exponential Models

Identifying Constant Percent Growth/decay

Proving Growth Patterns In Linear & Exponential Functions

Recognizing Constant Rate Of Change

Interpreting Parameters In Linear/exponential Functions

Rewriting Exponential Functions To Reveal Properties

Interpreting Exponential Functions

Logarithmic Functions

Evaluating Logarithms In Exponential Models

Graphing Exponential And Logarithmic Functions

Graphing Exponential Functions (including Growth/decay)

Graphing Logarithmic Functions

Performing Multiple Transformations On Functions

Understanding Inverse Of Exponents & Logarithms

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 From Different Representations

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

Quadratic Functions

Expressions In Equivalent Forms

Quadratic Equations

Factoring Quadratics

Max/min Of Quadratic Functions

Transforming Exponential Functions

Graphing And Analyzing Quadratics

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

Working With 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

Understanding Quadratic Functions

Identifying Characteristics Of Quadratic Functions

Writing And Interpreting Quadratic Functions

Writing A Quadratic Function Under Specific Conditions

Trigonometric Functions

Applications Of Trigonometric Functions

Applying And Analysing Trigonometric Functions

Applying The Unit Circle To Explain Symmetry And Periodicity

Applying Trigonometric Identities And Formulas

Evaluating And Interpreting Trigonometric Equation Solutions

Solving Real-world Problems With Trigonometric Functions

Using Inverse Functions To Solve Trigonometric Equations

Understanding Trigonometric Functions

Extension Of Trig Functions Via Unit Circle

Understanding Radian Measure Of An Angle

Understanding Trigonometric Functions

Understanding And Using The Unit Circle To Extend Trigonometric Functions To All Real Numbers

Unit Circle: Symmetry & Periodicity In Trig Functions

Using Special Triangles & Unit Circle In Trigonometry

Working With Trigonometric Functions

Graphing Trigonometric Functions

Graphing The Sine And Cosine Functions (including Transformations)

Modeling Periodic Phenomena With Trig Functions

Proving & Applying Trig Addition/subtraction

Proving & Using Pythagorean Trigonometric Identity

Solving Trigonometric Equations With Inverse Functions

Understanding Inverse Of Restricted Trigonometric Functions

Geometry

Area And Volume

Area

Measuring And Estimating Area Of Miscellaneous Shapes

Calculating Areas Of Irregular Polygons

Volume

Basic Geometry

Geometric Elements

Drawing And Identifying Geometric Elements

Drawing And Identifying Pairs Of Lines

Drawing And Identifying Parallel And/or Perpendicular Lines

Circles And Conic Sections

Congruence And Similarity

Congruence

Applying Congruency To Solve Problems

Use Congruency Criteria To Solve Problems

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

Applying Similarity To Solve Problems

Use Similarity Criteria To Solve Problems

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

Constructions

Geometric Constructions

Construct Shapes Inscribed In A Circle

Constructing Tangent Line To Circle

Geometric Constructions Using Various Tools

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

Coordinate Geometry

Geometric Constructions

Measurement And Dimension

Area

Measuring And Estimating Area Of Miscellaneous Shapes

Calculating Areas Of Irregular Polygons

Surface Area

Surface Area Of Basic Solids

Solving Mathematical And Real-world Problems Involving Surface Area Of Cubes And Cuboids

Solving Mathematical And/or Real-world Problems Involving Surface Area Of Cubes And Cuboids

Surface Area Of Complex Solids

Solving Mathematical And Real-world Problems Involving Surface Area Of Composite Solids

Applying The Formulae For The Surface Area Of Cylinders, Prisms, Pyramids And/or Cones To Real-world Problems Involving Composite Solids

Solving Mathematical And Real-world Problems Involving Surface Area Of Cones

Solving Mathematical And/or Real-world Problems Involving Surface Area Of Cones

Solving Mathematical And Real-world Problems Involving Surface Area Of Cylinders

Solving Mathematical And/or Real-world Problems Involving Surface Area Of Cylinders

Volume

Volume Applications

Measuring And Estimating Volume Of Cones

Solving Mathematical And/or Real-world Problems Involving Volume Of Cones

Measuring And Estimating Volume Of Cylinders

Solving Mathematical And/or Real-world Problems Involving Volume Of Cylinders

Measuring And Estimating Volume Of Miscellaneous Shapes

Applying The Formulae For The Volumes Of Cones, Cylinders And Spheres To Real-world Problems Involving Composite Solids

Measuring And Estimating Volume Of Pyramids

Solving Problems Involving Volume Of Pyramids

Measuring And Estimating Volume Of Spheres

Solving Mathematical And/or Real-world Problems Involving Volume Of Spheres

Volume Concepts And Formulas

Argument For Formulas Of Circles & 3d Shapes

Cavalieri's Principle: Volume Formulas Argument

Density Concepts In Area & Volume Modeling

Solving Problems Using Volume Formulas

Perimeter And Circumference

Plane Geometry

Angles

Proving And Using Geometric Properties

Using The Angle Bisector Theorem To Solve Problems

Using The Perpendicular Bisector Theorem To Solve Problems

Understanding And Measuring Angles

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

Basic Geometry

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

Naming Geometric Elements

Naming Points, Line Segments, Rays, Lines And Planes

Proving Theorems: Lines & Angles

Understanding Basic Geometry Definitions

Understanding Key Terms

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

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 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

Geometric Modeling

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

Surface Area

Transformations

Trigonometry

General Triangles

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

Modeling And Tools

Appropriate Tool Selection

Mathematical Models

Technology Use In Mathematics

Problem Solving

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

Complex Numbers In The Coordinate Plane

Complex Plane: Distance & Midpoint Calculation

Geometric Representation Of Complex Numbers

Proving Fundamental Theorem Of Algebra

Representing Complex Numbers In Different Forms

Solving Quadratics With Complex Solutions

Operations With Complex Numbers

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

Multiplying Complex Numbers

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

Understanding Complex Numbers

Extend Polynomial Identities To Complex Numbers

Finding Conjugates & Moduli Of Complex Numbers

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

Understanding Complex Numbers And I² = -1

Understanding And Applying Conjugates Of Complex Numbers

Applying Conjugates To Find Quotients

Finding The Conjugate Of A Complex Number

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

Matrices

Matrix Applications

2x2 Matrix Transformations & Determinant Area

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 Concepts

Understanding Role Of Zero, Identity Matrices & Determinants

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

Matrix Multiplication With Vectors

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

Measurement And Dimensional Analysis

Working With Units

Defining Quantities For Descriptive Modeling

Interpreting Units & Scales In Problem Solving

Selecting Accuracy Level For Quantity Reporting

Numerical Expressions

Real Numbers

Vectors

Vector Concepts

Understanding And Representing Vector Quantities

Understanding, Representing And Using Vectors

Vector Operations

Statistics And Probability

Bivariate Statistics

Scatter Plots

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

Analyzing Residuals To Assess Model Fit

Distinguishing Between Correlation And Causation

Finding And Interpreting Correlation Coefficients

Fitting Lines And Functions To Data

Interpolating And Extrapolating With Linear Models

Using Fitted Functions To Solve Contextual Problems

Two-way Tables

Identifying And Interpreting Patterns Of Association

Calculating And Interpreting Relative Frequencies

Describing Possible Associations In Data

Interpreting Two-way Tables For Categorical Variables

Investigating Patterns In Scatter Plots

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

Basic Statistical Concepts

Understanding Statistical Variability (qualitative)

Recognising A Statistical Question

Data Representation

Data Representation On Real Number Line

Interpreting Data

Choosing And Interpreting The Scale In Graphs And Data Displays

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

Measures Of Variability

Estimating Measures Of Variability

Calculating Interquartile Range And Mean Absolute Deviation

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

Probability

Applying Probability

Analyzing Strategies Using Probability Concepts

Calculating Expected Values In Decision Making

Calculate Expected Payoff In Chance Game

Comparing Strategies Via Expected Values

Developing And Using Probability Models

Evaluating And Comparing Strategies Based On Expected Values

Finding Expected Payoffs For Games Of Chance

Using Probability Concepts For Decision-making

Basic Probability Concepts

Describing Events In Sample Space Using Set Theory

Determining Independence Of Two Events

Interpreting Conditional Probability Of A Given B

Making Fair Decisions Using Probabilities

Understanding Conditional Probability & Independence

Understanding And Applying Conditional Probability

Understanding And Working With Different Types Of Events

Calculating Probability

Applying & Interpreting Addition Rule In Model

Applying Multiplication Rule In Probability Model

Calculating Probabilities With Permutations & Combinations

Estimating Probabilities Of Compound Events

Two-way Frequency Tables & Conditional Probabilities

Understanding And Applying Theoretical Probability

Calculating Theoretical Probabilities In The Context Of Area Models

Probability Distributions

Calculating Expected Value & Interpreting Mean

Defining & Graphing Random Variables In Probability

Developing Probability Distribution & Expected Value

Empirical Probability Distribution & Expected Value

Understanding And Using Probability Distributions

Calculating And Interpreting Expected Values

Developing Probability Distributions For Random Variables

Statistics

Normal Distributions

Understanding And Applying Normal Distributions

Fitting Data To Normal Distributions Using Mean And Standard Deviation

Recognising Limitations Of Normal Distribution Models

Using Tables/technology For Normal Curve Calculations

Statistical Analysis

Analyzing Data Sets: Shape, Center, Spread & Outliers

Comparing Data Sets Using Statistics

Describing And Understanding Distributions

Comparing Distributions By Shape, Center, And Spread

Describing Patterns And Deviations In Data

Relating Measures Of Central Tendency To Distribution Shape

Relating Measures Of Variability To Distribution Shape

Estimating Population Percentages Using Mean & Sd

Statistical Inference

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11th Grade

Math

Statistics And Probability

Probability

11th Grade Probability Passages

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Understanding Distribution Shapes - Skewness & Normal Distribution - Statistics & Probability

11th Grade

Math

Examine distribution shapes with a focus on skewness and normal curves. Develop skills in interpreting probability distributions and analyzing statistical data. Enhance understanding of statistical concepts and improve the ability to assess and interpret data distributions effectively.

9th Grade - 12th Grade

Understanding Divisibility - Prime and Composite Numbers - Basic Arithmetic Skills

Passage

Understanding Divisibility - Prime and Composite Numbers - Basic Arithmetic Skills

9th Grade - 12th Grade

Math

Focus is given to understanding divisibility, identifying and distinguishing between prime and composite numbers, and developing fundamental arithmetic skills. Learners will strengthen their problem-solving and logical reasoning abilities.

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1. 2021 survey of 800+ teachers conducted by Wayground

2. Journal of Education and e-Learning Research (Source)

3. International Online Journal of Education and Teaching (Source)

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