California
Math
Grade 10 Math Courses - California Curriculum
Discover CA Grade 10 Math courses: Geometry and Mathematics II. Explore key concepts, problem-solving techniques, and prepare for advanced mathematical studies in line with California standards.
CA Grade 10 Math Curriculum - Geometry & Mathematics II
ID | Standard | StudyPug Topic |
|---|---|---|
CA.G.G.CO.1 | Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc. |
CA.G.G.CO.2 | Represent transformations in the plane using, e.g., transparencies and geometry software; describe transformations as functions that take points in the plane as inputs and give other points as outputs. Compare transformations that preserve distance and angle to those that do not. |
CA.G.G.CO.4 | Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments. |
CA.G.G.CO.6 | Use geometric descriptions of rigid motions to transform figures and to predict the effect of a given rigid motion on a given figure; given two figures, use the definition of congruence in terms of rigid motions to decide if they are congruent. |
CA.G.G.CO.8 | Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from the definition of congruence in terms of rigid motions. |
CA.G.G.CO.9 | Prove theorems about lines and angles. |
CA.G.G.CO.10 | Prove theorems about triangles. |
CA.G.G.SRT.1 | Verify experimentally the properties of dilations given by a center and a scale factor. |
CA.G.G.SRT.2 | Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar; explain using similarity transformations the meaning of similarity for triangles as the equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides. |
CA.G.G.SRT.4 | Prove theorems about triangles. |
CA.G.G.SRT.6 | Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles. |
CA.G.G.SRT.7 | Explain and use the relationship between the sine and cosine of complementary angles. |
CA.G.G.SRT.8 | Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems. |
CA.G.G.SRT.8.1 | Derive and use the trigonometric ratios for special right triangles (30°, 60°, 90° and 45°, 45°, 90°). |
CA.G.G.SRT.9 | (+) Derive the formula A = 1/2 ab sin(C) for the area of a triangle by drawing an auxiliary line from a vertex perpendicular to the opposite side. |
CA.G.G.SRT.10 | (+) Prove the Laws of Sines and Cosines and use them to solve problems. |
CA.G.G.SRT.11 | (+) Understand and apply the Law of Sines and the Law of Cosines to find unknown measurements in right and non-right triangles. |
CA.G.G.C.1 | Prove that all circles are similar. |
CA.G.G.C.2 | Identify and describe relationships among inscribed angles, radii, and chords. |
CA.G.G.C.3 | Construct the inscribed and circumscribed circles of a triangle, and prove properties of angles for a quadrilateral inscribed in a circle. |
CA.G.G.C.5 | Derive using similarity the fact that the length of the arc intercepted by an angle is proportional to the radius, and define the radian measure of the angle as the constant of proportionality; derive the formula for the area of a sector. Convert between degrees and radians. |
CA.G.G.GPE.1 | Derive the equation of a circle of given center and radius using the Pythagorean Theorem; complete the square to find the center and radius of a circle given by an equation. |
CA.G.G.GPE.2 | Derive the equation of a parabola given a focus and directrix. |
CA.G.G.GPE.4 | Use coordinates to prove simple geometric theorems algebraically. |
CA.G.G.GPE.5 | Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems. |
CA.G.G.GPE.6 | Find the point on a directed line segment between two given points that partitions the segment in a given ratio. |
CA.G.G.GMD.1 | Give an informal argument for the formulas for the circumference of a circle, area of a circle, volume of a cylinder, pyramid, and cone. |
CA.G.G.GMD.3 | Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems. |
CA.G.G.GMD.4 | Identify the shapes of two-dimensional cross-sections of three-dimensional objects, and identify three-dimensional objects generated by rotations of two-dimensional objects. |
CA.G.G.MG.3 | Apply geometric methods to solve design problems. |
CA.G.G.S.CP.1 | Describe events as subsets of a sample space (the set of outcomes) using characteristics (or categories) of the outcomes, or as unions, intersections, or complements of other events ("or," "and," "not"). |
CA.G.G.S.CP.2 | Understand that two events A and B are independent if the probability of A and B occurring together is the product of their probabilities, and use this characterization to determine if they are independent. |
CA.G.G.S.MD.6 | (+) Use probabilities to make fair decisions (e.g., drawing by lots, using a random number generator). |
CA.G.G.S.MD.7 | (+) Analyze decisions and strategies using probability concepts (e.g., product testing, medical testing, pulling a hockey goalie at the end of a game). |
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