Common Core State Standards for Mathematics Accelerated Geometry (V09)  Semester Two 


Domain: Circles (GC: GCA or GCB)  
Learning Standard: Understand and apply theorems about circles  Test Questions 
GCA0912.01 Prove that all circles are similar.  14, 15 
GCA0912.02 Identify and describe relationships among inscribed angles, radii, and chords. Include the relationship between central, inscribed, and circumscribed angles; inscribed angles on a diameter are right angles; the radius of a circle is perpendicular to the tangent where the radius intersects the circle.  16, 17, 18, 19, 20, 21, 22 
GCA0912.03 Construct the inscribed and circumscribed circles of a triangle, and prove properties of angles for a quadrilateral inscribed in a circle  23 
Learning Standard: Find arc lengths and areas of sectors of circles  Test Questions 
GCB0912.05 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  24, 25, FR3 
Domain: Congruence (GCO)  
Learning Standard: Prove geometric theorems  Test Questions 
GCO0912.11 Prove theorems about parallelograms. Theorems include: opposite sides are congruent, opposite angles are congruent, the diagonals of a parallelogram bisect each other, and conversely, rectangles are parallelograms with congruent diagonals.  7 
Learning Standard: Make geometric constructions  Test Questions 
GCO0912.13 Construct an equilateral triangle, a square, and a regular hexagon inscribed in a circle.  12 
Domain: Geometric Measurement and Dimension (GGMD)  
Learning Standard: Explain volume formulas and use them to solve problems  Test Questions 
GGMD0912.01 Give an informal argument for the formulas for the circumference of a circle, area of a circle, volume of a cylinder, pyramid, and cone. Use dissection arguments, Cavalieri’s principle, and informal limit arguments.  13 
GGMD0912.03 Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.  31, 32, 33, 34, 35 
Learning Standard: Visualize relationships between twodimensional and threedimensional objects  Test Questions 
GGMD0912.04 Identify the shapes of twodimensional crosssections of threedimensional objects, and identify threedimensional objects generated by rotations of twodimensional objects.  36, 37, 38 
Domain: Expressing Geometric Properties with Equations (GGPE)  
Learning Standard: Translate between the geometric description and the equation for a conic section  Test Questions 
GGPE0912.01 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.  26, 27 
Learning Standard: Use coordinates to prove simple geometric theorems algebraically  Test Questions 
GGPE0912.04 Use coordinates to prove simple geometric theorems algebraically. For example, prove or disprove that a figure defined by four given points in the coordinate plane is a rectangle; prove or disprove that the point (1, √3) lies on the circle centered at the origin and containing the point (0, 2).  9, 10, 11 FR2 
GGPE0912.07 Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula.  28, 29, 30 
Domain: Modeling with Geometry (GMG)  
Learning Standard: Apply geometric concepts in modeling situations  Test Questions 
GMG0912.01 Use geometric shapes, their measures, and their properties to describe objects (e.g., modeling a tree trunk or a human torso as a cylinder).  39 
GMG0912.02 Apply concepts of density based on area and volume in modeling situations (e.g., persons per square mile, BTUs per cubic foot).  FR4 
Domain: Similarity, Right Triangles, & Trigonometry (GSRT)  
Learning Standard: Prove theorems involving similarity  Test Questions 
GSRT0912.05 Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.  8 
Learning Standard: Define trigonometric ratios and solve problems involving right triangles  Test Questions 
GSRT0912.07 Explain and use the relationship between the sine and cosine of complementary angles  1, 2 
GSRT0912.08 Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.  3, 4 FR1 
Learning Standard: Apply trigonometry to general triangles  Test Questions 
GSRT0912.11 Understand and apply the Law of Sines and the Law of Cosines to find unknown measurements in right and nonright triangles (e.g., surveying problems, resultant forces)  5, 6 
Domain: Conditional Probability & the Rules of Probability (SCP)  
Learning Standard: Understand independence and conditional probability and use them to interpret data  Test Questions 
SCP0912.01 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”).  40, 41 
SCP0912.02 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.  42 
SCP0912.03 Understand the conditional probability of A given B as P(A and B)/P(B), and interpret independence of A and B as saying that the conditional probability of A given B is the same as the probability of A, and the conditional probability of B given A is the same as the probability of B.  45 
SCP0912.04 Construct and interpret twoway frequency tables of data when two categories are associated with each object being classified. Use the twoway table as a sample space to decide if events are independent and to approximate conditional probabilities. For example, collect data from a random sample of students in your school on their favorite subject among math, science, and English. Estimate the probability that a randomly selected student from your school will favor science given that the student is in tenth grade. Do the same for other subjects and compare the results.  43, 44, FR5 
SCP0912.05 Recognize and explain the concepts of conditional probability and independence in everyday language and everyday situations. For example, compare the chance of having lung cancer if you are a smoker with the chance of being a smoker if you have lung cancer.  46 
Learning Standard: Use the rules of probability to compute probabilities of compound events in a uniform probability model  Test Questions 
SCP0912.06 Find the conditional probability of A given B as the fraction of B’s outcomes that also belong to A, and interpret the answer in terms of the model.  47 
SCP0912.07 Apply the Addition Rule, P(A or B) = P(A) + P(B) – P(A and B), and interpret the answer in terms of the model.  48, 49 
Total: 49 points
Free Response: 24 points
Overall: 73 points