Below are the topics taught in each level of math with the grades associated with each level. However, students will be placed at their acceptable level based upon ability and not grade or age (yes, we actually have an 8th grader sitting in the Algebra II and Geometry classes).
Looking forward, the SAT (critical for college acceptance and taken at the end of a student's junior year of high school), is roughly divided by questions from the following levels:
Pre-algebra 1: 5%
Pre-algebra 2: 5%
Algebra I: 40%
Algebra II: 40%
Pre-algebra I: Generally 4th and 5th Grade.
a). addition, subtraction, multiplication.
b). translating. division.
c). exponents/powers. order of operations. scientific notation.
Pre-algebra II: Generally 6th and 7th Grade.
a). properties. algebraic inequalities.
b). 1st degree/1st variable. coordinate planes.
c). plane geometry. pythagorean theorem.
Algebra I: Generally 8th and 9th Grade.
a). expressions, equations, and functions. real numbers. linear equations.
b). linear functions. linear equalities. systems of linear functions and inequalities.
c). exponents. factoring and polynomials. quadratic functions.
d). radical expressions. rational expressions.
Algebra II: Generally 10th and 11th Grade.
a). equations and inequalities. graph functions and linear equations. matrices.
b). polynomials and radical expressions. quadratic functions and inequalities. conic sections.
c). polynomials functions. rational expressions. exponential and logarithmic functions.
d). sequences and series. discrete mathematics and probability. basic triginometry.
Geometry: Generally 10th and 11th Grade.
a). points, lines, and angles. proof. perpendicular and parallel.
b). triangles. similarity. right triangles and trigonometry. Quadrilaterals.
c). transformations. circles. area.