Content

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.

**Looking to Learn High School Math? Book a Free Trial Lesson and match with top High School Math Tutors for Concepts, Homework Help, and Test Prep.**

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

**👍🔍 Recommended Reading 📚📖**

- Where to Learn High-School Math? [Best Math Resources and Tutorials]
- What is the Hardest Math in High school?
- Which is the Easiest High School Math?

**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.

Written by by

Medha PandeyReviewed by by

Prerit Jain