Geometry End- of- Course Prep Packet

Transcription

1 Geometry End- of- Course Prep Packet TOPICS TESTED FOR GRADUATION PURPOSES Logic o If- then, converse, inverse, contrapositive o Proofs (example: prove that two triangles are congruent) o Postulates, undefined terms, axioms Triangles o Angles in a triangle add to 180 o Definitions of altitudes, medians, perpendicular bisectors, angle bisectors o Incenter, centroid, circumcenter, orthocenter o Triangle congruency proofs o and triangles o Pythagorean Theorem and its converse (showing that a triangle is a right triangle) Properties of parallelograms, including rhombuses, rectangles, and squares (diagonals in particular) Polygons how many degrees in the interior and exterior angles; basic properties Coordinate plane slopes of parallel and perpendicular lines; midpoints; applying properties of quadrilaterals Area of triangles and other polygons and of circles Basic trigonometry (sine, cosine, tangent) Unit conversion and degrees of precision in measurement TOPICS ON THE TEST BUT NOT COUNTED TOWARDS GRADUATION: Angles on parallel lines Compass and straightedge constructions Intersection of lines and planes in planes and space Triangle similarity Circles properties of chords, arcs, and angles; equations in the coordinate plane; arc length; sector area 3D shapes parallelpipids, etc vertices / shapes / cross section Equations of lines Transformations and symmetry Surface area and volume

2 EOC Test Taking Tips Avoid rounding wherever possible unless you are told specifically to do so. o If the question tells you a value is!, do not use 0.66 or or any other! similar approximation. o Do not do any rounding as you go when you are working through a problem. Keep exact values wherever possible; round only at the very end. Avoid using acronyms. For example, do not write CPCTC for Corresponding Parts of Congruent Triangles are Congruent. Use interval notation correctly. Never use a closed bracket with the infinity symbol. Example: o Correct: 3, OR, you could also say all real numbers x > 3 o Incorrect: (3, ] Define all variables you use, as specifically as possible. Use units wherever possible. Make sure your calculator is in degree mode, not radian mode. Check the problem type to see if you need to show work. Short Answer and Enhanced Multiple Choice problems require you to show your work. There is no penalty for guessing. Fill in ALL questions even if you are randomly guessing. Read the problem carefully make sure you know what it is asking. Take your time you have all the time you need! Make sure to get a good night s sleep the night before and to eat a good breakfast. Bring your calculator!

3 Description Formula Variables Arc Length Area of a Sector L = mbc 360 πd L: Arc Length B, C: End points of Arc d: Diameter of the circle m: the measure of A = mbc A: Area of a Sector 360 πr2 B, C: endpoints of intercepted arc r: Radius of the circle m: the measure of Cylinder SA = 2πr 2 + 2πrh SA: Surface Area r: radius of the base h: height V = πr 2 h V: Volume r: radius of the base h: height Cone SA = πr 2 + πrl SA: Surface Area r: Radius of the base l: slant height V = 1 3 Bh or V = 1 3 πr2 h V: Volume r: radius of the base h: height B: area of the base Prism V = Bh V: Volume B: area of the base h: height SA = 2B + Ph or SA = 2B + L SA: Surface Area B: area of the base P: perimeter of the base h: height L: Lateral Surface Area Pyramid Quadratic Formula x = b ± V = 1 3 Bh b2 4ac 2a V: Volume B: Area of the base h: height x: Solutions a, b, c: coefficients Sphere V = 4 3 πr3 SA = 4πr 2 V: Volume r: radius SA: Surface Area r: radius

4 Use at least two decimal place values when approximating square roots or trigonometric ratios. Special Right Triangles 30 2x x s s 45 Trigonometric Ratios sin(b) = b c b c cos(b) = a c a B tan(b) = b a

5 EOC Sample Geometry Problems 1. 2.

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13 19. 20) If the longer leg of a triangle measures 8 3 cm, find the length of the hypotenuse. [A] 16 cm [B] 8 cm [C] 16 3 cm [D]!"!! cm 21) 22)

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24 1. C 2. D 3. Statement#5: ABD EBC; Reason #6: SAS Congruence 4. C 5. B 6. B 7. (2, 1) 8. D 9. (1, - 2) B 12. B or 3 46 EOC Sample Geometry Problems Key 14. Possible answers: y = 10x + 70, y = 10 x 7, y 10 = 10(x 6) 15. (- 6, 1) See rubric below 19. See rubric below 20. A 21. C 22. B 23. D 24. D 25. A 26. B 27. C A or y = (2,1) or approximately See rubric below 38. See rubric below 39. See rubric below 40. See rubric below 41. See rubric below 42. See rubric below Scoring rubric for #18:

25 Scoring rubric for #19: Scoring rubric for #37: Scoring rubric for #38:

26 Scoring rubric for #39: Scoring rubric for #40: Scoring rubric for #41: Scoring rubric for #42: