Grade 10: Math
Start with a unit whose prerequisites fit. Work through the lessons, use the study guide to review, and try the new cases before continuing.
- Unit 1 · 4 lessons
Geometry: Claims, Converses, and Proof
Geometry arguments connect definitions, givens and established properties. A conclusion needs a chain of reasons; an attractive diagram may suggest a relation but does not establish every length, angle or universal claim.
Before you begin: Recognize squares, rectangles and triangles; distinguish a statement from its supporting reason.
- Unit 2 · 4 lessons
Geometry: Angle Theorems and Triangle Constraints
Parallel-line and triangle theorems connect geometric conditions to numerical equations. Some side and angle values are impossible, so reasoning must check the defining configuration rather than rely only on arithmetic.
Before you begin: Understand straight and triangle angle totals; compare sums and differences.
- Unit 3 · 4 lessons
Geometry: Congruence and Bisector Reasoning
Congruence fixes a figure’s shape and size, while correspondence identifies matching vertices and sides. Perpendicular and angle bisectors encode equidistance or equal-angle properties that can be used and checked in a construction.
Before you begin: Read named triangle vertices; know perpendicular lines and equal angle measures.
- Unit 4 · 4 lessons
Geometry: Similarity and Right-Triangle Ratios
Similarity preserves angle measures and corresponding length ratios. Right triangles with the same acute angle are similar, explaining why sine, cosine and tangent depend on an angle rather than the triangle’s overall size.
Before you begin: Use ratios and proportions; identify opposite leg, adjacent leg and hypotenuse.
- Unit 5 · 4 lessons
Geometry: Quadrilaterals and Coordinate Reasons
Geometric properties can be expressed through coordinates as well as diagrams. Parallelogram angle and diagonal theorems, midpoint coordinates, perpendicular slopes and perpendicular base-height relationships provide exact arguments about figures.
Before you begin: Evaluate midpoint averages and signed fractions; know parallelograms and triangle area.
- Unit 6 · 4 lessons
Geometry: Circle Theorems, Arcs, and Sectors
Circle angle theorems distinguish central, inscribed and tangent configurations. A sector or arc occupies a stated fraction of the whole circle, but its area and length use different whole-circle measures and units.
Before you begin: Identify radius, arc and circumference; use fractions of totals; distinguish degrees from length.
- Unit 7 · 4 lessons
Geometry: Curved Solids and Volume Scaling
Three-dimensional formulas relate solid shapes to base areas, heights and radii. Similar solids change every corresponding length together, making volume respond to the cube of a scale factor rather than its first power.
Before you begin: Compute circle area; evaluate squares and cubes; use fractions in formulas.
- Unit 8 · 4 lessons
Geometry: Regions, Capacity, and Probability Models
Geometry can support probability, material, density and layout models when the assumptions are explicit. Ratios and decompositions must use nonoverlapping regions, consistent dimensions and the correct uniformity or exact-fit conditions.
Before you begin: Compute rectangular area; divide labeled quantities; interpret uniform choice and exact grid arrangements.
- Unit 9 · 4 lessons
Build and Use a Quadratic Area Model
Create a constrained area rule, inspect its changes, find a maximum, and solve a target-area equation.
Before you begin: Expand and factor simple expressions. · Solve linear equations, evaluate squares, and use rectangle perimeter and area.
Check what you can explain
The subject test uses additional supplied cases across these units. Its feedback links back to the relevant lessons. Use it to plan practice; a score on these questions is not a school grade or proof of complete subject mastery.
Open the subject test