10th grade math is typically Geometry, where students move from calculating to proving. They study congruence, similarity, trigonometry, circles, volume and probability, and learn to justify each step with clear reasoning.

Key Topics Covered:

Transformations, congruence and similarity, geometric proof, right triangle trigonometry, circles, area and volume, coordinate geometry, conditional probability and statistics in the media.

Parent Tip:

Geometry rewards students who can explain why, not only how. Strong proof and trigonometry skills prepare students for Algebra 2, the PSAT, SAT and ACT, and many state end-of-course exams.

Use transformations, congruence and similarity to solve and prove

Write logical proofs about lines, angles, triangles and quadrilaterals

Solve right and non-right triangles with trigonometry

Find arc length, sector area and equations of circles

Find volume and surface area of composite solids

Find and interpret conditional probability

Student learning 10th grade math online with a live tutor at home in the USA

No.	Topic	What We Cover
01	Points, Lines, Planes and Segments	Use precise geometry vocabulary and notation and work with segment lengths.
02	Angle Relationships	Use complementary, supplementary, vertical and parallel-line angles to find unknowns.
03	Distance, Midpoint and Slope	Use coordinate formulas to find lengths, midpoints and parallel or perpendicular lines.
04	Rigid Motions	Describe translations, reflections and rotations as functions on the plane.
05	Dilations and Scale Factor	Dilate figures and explain how size and angle measures change.
06	Congruent Triangles	Use rigid motions and the SSS, SAS, ASA and AAS criteria to prove triangles congruent.
07	Logic and Deductive Reasoning	Write conditional statements, converses and counterexamples, and build a logical argument.
08	Two-Column and Paragraph Proofs	Prove theorems about lines, angles and triangles in two-column and paragraph form.
09	Triangle Theorems	Prove and use theorems about isosceles triangles, medians, midsegments and angle bisectors.
10	Quarter 1 Review	Review geometry foundations and proof. A mock test and parent report follow.

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Student in a tutoring session with their tutor

Warm-up (5 min)

Quick mental math and a review of the previous session

Core Teaching (25 min)

New concept from the lesson eBook, with examples and guided practice

Guided Practice (15 min)

Student works through problems with tutor support

Independent Practice (10 min)

Student completes the in-class quiz independently

Wrap-up (5 min)

Summary, 2 take-home quizzes and a preview of the next session

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No.	Topic	What We Cover
11	Similar Triangles	Use similarity criteria AA, SAS and SSS to decide whether triangles are similar.
12	Similarity Theorems and Proportion	Prove and use the triangle proportionality and side-splitter theorems.
13	The Pythagorean Theorem in Space	Solve 2D and 3D problems with right triangles, such as the diagonal of a box.
14	Special Right Triangles	Use 45-45-90 and 30-60-90 relationships to find exact lengths.
15	Trigonometric Ratios	Define sine, cosine and tangent as ratios of sides in right triangles.
16	Solving Right Triangles	Find missing sides and angles using trig ratios and inverse functions.
17	Angles of Elevation and Depression	Solve real problems with ladders, ramps, towers and lines of sight.
18	Law of Sines and Law of Cosines	Extend trigonometry to non-right triangles and decide which law to use.
19	Trigonometry Problem Solving	Model real-world navigation and surveying problems and justify the method.
20	Quarter 2 Review	Review similarity and trigonometry. A mock test and parent report follow.

No.	Topic	What We Cover
21	Quadrilaterals and Parallelogram Proofs	Prove properties of parallelograms, rectangles, rhombuses and trapezoids.
22	Polygons and Coordinate Proofs	Use coordinates and algebra to prove that a figure is a given shape.
23	Circles: Central and Inscribed Angles	Find angle and arc measures and prove relationships among them.
24	Chords, Tangents and Secants	Use properties of tangents, chords and secants to solve for lengths and angles.
25	Arc Length and Sector Area	Find arc length and sector area from the central angle.
26	Equations of Circles	Write and graph circle equations and complete the square to find the center and radius.
27	Area and Perimeter of Composite Figures	Combine and subtract shapes to find area and perimeter, such as a track or a garden.
28	Volume of Prisms, Cylinders, Pyramids, Cones and Spheres	Use volume formulas and cross-sections, with real-world units.
29	Composite Surface Area and Volume	Find surface area and volume of combined solids and solve design problems.
30	Quarter 3 Review	Review circles, area and volume. A mock test and parent report follow.

No.	Topic	What We Cover
31	Sample Spaces and Set Notation	List outcomes, describe events with unions, intersections and complements, and use Venn diagrams.
32	Independent Events	Decide whether events are independent and use the multiplication rule.
33	Conditional Probability	Find and interpret P(A given B) with tables, trees and formulas.
34	Two-Way Tables and Conditional Probability	Use two-way tables to find conditional probabilities and test independence.
35	The Addition Rule	Find P(A or B) for inclusive and mutually exclusive events.
36	Permutations and Combinations	Count arrangements and selections and use them in probability.
37	Probability Simulations	Run simulations with digital tools and compare results with theory.
38	Geometric Modeling	Use area, density and volume to model real objects and make design decisions.
39	Statistics in the Media	Judge claims, graphs and polls for bias, sampling and misleading displays.
40	Grade 10 Review and Algebra 2 Readiness	Review the year's key skills, including end-of-course exam practice, and preview Algebra 2. A mock test and parent report follow.

10th Grade Math Tutoring in the USA

By Quarter 4 of 10th Grade Math, Your Child Will...

10th Grade Math Curriculum, Quarter by Quarter

Try a Free Lesson to See the Full Program

Try a Free Lesson to See the Full Program

Try a Free Lesson to See the Full Program

Try a Free Lesson to See the Full Program