Once I heard a student remark "I get it when they have x and y in a equation; but when they add a, b and c, not sure what is going on!!" Trust me over 45% students abhor algebra because of its bad reputation of an abstruse math topic that combines alphabets and numerals. However, once they start appreciating the need and the value of a variable (the unknown!) or variables, their algebra journey takes a fascinating twist!
Besides that lingering algebra fear in many, I have also seen parents getting confused with the various kinds of algebra topics their kids have to go through. Advanced students cover higher algebra earlier while others follow the prescribed level or a lower level algebra. So, I think a good list of topics involved in various algebra courses may be of great help to most of us, if not all. It may also help you know where your son or daughter is on the algebra route.
As a tutor and a father of a 9th grade daughter and a 4th grade son, I cannot stress enough the need to build a solid foundation of algebraic concepts. If you are a student who needs help with any algebra topic or a parent looking for assistance, you can reach me out by visiting my WyzAnt profile. Algebra is so profound and enriching - once you get involved, you just stay involved!
Here we go:
Pre-Algebra (Middle School - Typically 6th and 7th grade)
Integers and Absolute Value
Comparing and ordering Integers
Multiplying rational numbers
Dividing rational numbers
Adding and subtracting fractions and mixed numbers
Arithmetic & Geometric Sequences
The Distributive Property
Simplifying Algebraic Expressions
Solving equations adding or subtracting
Solving equations multiplying or dividing
Solving two-step equations
Writing two-step equations
Order of operations (Number and Expressions)
Variables and Expressions
Variables and Equations
Permutations and Combinations
Algebra-1 (Middle School - 8th Grade typically. Sometimes 9th grade)
Positive and Negative Numbers
Relations and Functions
Systems of Equations
Algebra-2 (High School. Typically 10th or 11th grade)
Solve equations and inequalities.
Graph points, lines, and functions.
Solve systems of equations.
Combine, multiply, and factor polynomials.
Manipulate fractional algebraic Expression.
Manipulate algebraic powers and roots.
Graph and solve equations involving complex numbers.
Solve quadratic equations.
Graph quadratic functions.
Graph circles, ellipses, hyperbolas, and systems of equations.
Graph exponential functions and solve logarithmic equations.
Solve problems involving permutations, combinations, and basic probability.
Perform addition, subtraction, and multiplication with matrices.
NOTE - I collected this information by visiting various websites outlining the courses and topics covered in Pre-Algebra, Algebra-1 and Algebra-2 -- this is just a brief "compilation" and is not guaranteed to list out EVERY single topic that may be covered under those courses. However, it should give you a fair assessment of the nature of topics covered.
Enjoy your Algebra! :-)