High School Math Syllabus

High school math is a fundamental part of the education system, but it can be a source of confusion and anxiety for many students and parents. In this article, we aim to break down the high school math syllabus into simple, understandable terms.

High school math doesn’t follow a stringent track. Candidates are free to choose their own tracks to complete the high school math core curriculum according to their personal interests and career needs.

Whether you’re a student trying to make sense of your coursework or a parent looking to support your child’s learning, this guide will provide you with a clear overview of what to expect. 

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Here you go with the high school math syllabus in order: 

High School math curriculum

There are different tracks to choose your own math curriculum from 9th grade onwards. Students may begin their high school math education with either Geometry, Pre-Algebra, or Algebra I, depending on their chosen track i.e. Advanced, Remedial, or Average.

The best way is to choose a high school math curriculum that aligns with your future goals and studies. If you’re having difficulty in selecting the courses, please talk to a high school math tutor.

Advanced math level

Students taking advanced placement mathematics begin their high school math education in seventh or eighth grade by taking Algebra I or Geometry. This frees up time for them to study more advanced math in their senior year. Freshmen on the advanced track start high school with Algebra II or Geometry, depending on which math course they took in junior high.

The average math level

Students on the average track begin high school with Algebra I, followed by Geometry in sophomore year, Algebra II in junior year, and Pre-Calculus or Trigonometry in senior year. 

Remedial math level

Students in the remedial track start with Pre-Algebra in ninth grade, followed by Algebra I in tenth, Geometry in eleventh, and Algebra II in senior year.

High school math core concepts

Now that you know the different tracks you can take to complete the syllabus, let’s walk through the important topics and concepts taught in the specific high school math subjects:

Algebra 1

Expressions, equations, and functions

• Expressions, variables, and operations
• Composing expressions
• Composing equations and inequalities
• Representing functions as rules and graphs

Exploring real numbers

• Number system
• Integers and real numbers
• Properties of real numbers

Linear equations, functions, visualization

• Basics of solving equations
• Ratios and proportions
• The slope of a line
• Calculate the rate of change of a linear function
• Similar figures
• Graphs, coordinate plane, sole, and intercept

Functions and real-world problems

• Definition of functions
• Input and output to a function
• domain and range values 
• Graphs

Solving Linear inequalities

• Solving compound inequalities
• Absolute value equations and inequalities
• Linear inequalities in two variables

Systems of linear inequalities and equations

• Systems of linear inequalities
• Substitution and elimination methods

Exponents and exponential functions

• Interpret and write exponential functions in the form f(x) = ax
• Exponential functions with real-world problem
• Exponential functions – growth and decay

Factoring and polynomials

• Monomials and polynomials
• Special products of polynomials
• Factorization of polynomials

Quadratic equations

• Determine the domain and range of quadratic functions
• Graph quadratic functions on the coordinate plane
• Solve quadratic equations having real solutions by factoring, taking square roots
• Estimation and prediction using quadratic equations

Radical Expressions

• Simplify radical expressions
• Radical functions, graphs
• Pythagorean theorem
• Distance and midpoint formulas

Rational Expressions

• Simplify rational expressions
• Multiply rational expressions
• Add, subtraction and division of polynomials
• Solving rational expressions

Algebra 2

Equations and inequalities

• Simplify expressions and equations
• Absolute and Modulus values
• Solving inequalities

Functions and linear equations

• Solving linear equations, functions
• Slope and intercept, graphs
• Graph inequalities

Solving system of linear equations

• Solving systems of equations in two variables
• Solving systems of equations in three variables

Matrices

• Introduction of Matrices
• Operations with Matrices
• Determinants
• Using matrices when solving a system of equations

Polynomials 

• Simplify expressions
• Factoring polynomials
• Polynomials function
• Remainder and factor theorems
• Roots and zeros 

Quadratic functions and inequalities

• Solving quadratic equations
• Roots and coefficients
• Real-world problems with Quadratic equations

Exponential and logarithmic functions

• Exponential function
• Logarithm functions and properties

Arithmetic sequences and series

• Arithmetic sequences and series
• Geometric sequences and series
• Binomial theorem

Probability

• Probabilities
• Permutations and combinations

Trigonometry

• Trigonometric functions
• Lines and Angles
• Circular functions
• Inverse functions

Geometry

Lines and Angles

• Line
• Line segment and Ray
• Angle
• Type of angles

Parallel Lines

• Transversal
• Parallel lines and relation between different angles formed by transversal and parallel lines

Triangles

• Triangle
• Basic properties of triangle
• Angle sum property and different types of Triangles

Congruence of triangles

• Congruency
• SSS, SAS, ASA, AAS, and RHS congruence of triangles

Concurrent lines in Triangles

• Median-Centroid
• Altitude-Orthocentre
• Angular bisector-Incentre.

Polygons

• Polygon
• Different types of Polygons
• Interior angle Sum
• Exterior angle sum and No.Of diagonals.

Quadrilateral

• Quadrilateral
• Angle sum properties of Quadrilateral and basic properties of Quadrilateral
• Types of Quadrilateral

Various theorems in Quadrilateral

• Mid-Point theorem
• Converse of Mid-Point theorem and Intercept theorem

Similar Triangles

• Similarity
• Properties of Similar Polygons
• Basic Proportionality theorem and its Converse
• Vertical Angle bisector theorem and its Converse

Criteria for Similarity of Triangles

• Areas and Perimeters of Similar Triangles
• Right triangle and Pythagorean theorem
• Right triangle-Trigonometry

Circles

• Circle
• Circle theorems
• Perimeter and Area
• Volume and Surface area

PreCalculus

Functions

• Functions and Relations
• Domain and Range
• Even and odd functions
• Transformation of functions
• Trigonometric equations 

Trigonometry

• Graphs of Sine and cosine
• Transformations of sine and cosine
• Inverse trigonometric functions
• Sinusoidal equations and models
• Angle Addition
• Using trigonometric identities

Polynomials

• Addition and subtraction of polynomials 
• Division of polynomials
• Binomial theorem
• Graphs of polynomial functions  and solving equations
• Graphing rational functions and reciprocal functions

Exponential and Logarithms

• Applications of exponential functions
• Logarithms
• Solving exponential and logarithmic equations
• Graphing logarithmic functions

Conic sections

• Feature of a circle
• Equations of a circle
• Center, radii, foci of an ellipse
• Focus and directrix of a parabola
• Hyperbola

Vectors

• Introduction to vectors
• Operations with vectors
• Applications of vectors

Complex numbers

• Complex numbers and imaginary numbers
• The complex plane: Complex numbers
• Addition, Subtraction, and Multiplication of complex numbers
• Distance and midpoint of complex numbers
• Complex conjugates and dividing complex numbers
• Identities with complex numbers
• Absolute value and angle of complex numbers
• The polar form of complex numbers, multiplication, and division

Matrices

• Introduction
• Representing linear systems of equations with augmented matrices
• Matrix row operations
• Row-echelon form and Gaussian elimination
• Addition, Subtraction, Multiplication of Matrices
• Multiplying matrices by scalars
• Properties of matrix addition & scalar multiplication
• Properties of matrix multiplication
• Matrices as transformations
• The determinant of a 2×2 matrix
• Finding the inverse of a matrix using its determinant
• Solving equations with inverse matrices
• Model real-world situations with matrices

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Key takeaway on High School math syllabus

The High School curriculum choice is up to the student and should be based on their academic level and understanding. There are three different math tracks to choose from: advanced, average, and remedial.

• Advanced track: Students begin their high school math education in 7th or 8th grade and take Algebra I or Geometry. This frees up time for them to study more advanced math in their senior year.
• Average track: Students begin high school with Algebra I, followed by Geometry, Algebra II, and Pre-Calculus or Trigonometry.
• Remedial track: Students begin high school with Pre-Algebra, followed by Algebra I, Geometry, and Algebra II.

Students need to choose the track that is right for them, as this will help them to succeed in math and prepare for college and careers.