United States · Common Core State Standards
10th Grade Mathematics
This course bridges the gap between foundational algebra and advanced geometric reasoning. Students explore the intersection of algebraic modeling and spatial relationships while developing rigorous proof-based logic and statistical analysis skills.
The Language of Proof and Logic
Students move beyond intuitive understanding to formalize geometric relationships using inductive and deductive reasoning.
Exploring the structure of mathematical arguments through if-then statements, converses, and contrapositives.
Investigating the unique angle relationships formed when parallel lines are intersected by a transversal.
Developing the ability to write two-column and flow proofs to justify geometric theorems.
Transformations and Congruence
Students utilize rigid motions to define congruence and explore the properties of triangles and quadrilaterals.
Defining congruence through the lenses of translations, reflections, and rotations.
Establishing the minimum requirements for proving two triangles are identical.
Classifying four-sided figures based on their symmetry, side lengths, and angle properties.
Similarity and Trigonometry
Applying dilations to understand similarity and introducing right triangle trigonometry as a tool for indirect measurement.
Exploring how scale factors affect length and area in proportional figures.
Defining sine, cosine, and tangent as ratios of side lengths in right triangles.
Extending trigonometric principles to solve for missing parts of non-right triangles.
Quadratic Functions and Modeling
Students master the various forms of quadratic equations and use them to model parabolic motion and optimization.
Comparing standard, vertex, and factored forms of quadratic functions.
Mastering methods including factoring, completing the square, and the quadratic formula.
Applying quadratic functions to solve problems involving projectile motion and area optimization.
Circles and Conic Sections
Exploring the geometric properties of circles, including arcs, chords, tangents, and the derivation of the circle equation.
Investigating the relationships between angles, arcs, and segments within and outside circles.
Deriving and applying the standard form equation of a circle using the Pythagorean Theorem.
Calculating portions of a circle's circumference and area using proportional reasoning.
Probability and Decision Making
Utilizing conditional probability and independence to analyze complex events and make informed predictions.
Calculating the likelihood of events occurring given that other events have already taken place.
Using the Addition Rule and Multiplication Rule to solve complex probability problems.
Evaluating the long term outcomes of probabilistic scenarios and games of chance.