Virginia Mathematics Checkpoint Assessment GEOMETRY G.11. Topic: Polygons and Circles
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1 Virginia Mathematics Checkpoint Assessment GEOMETRY G.11 Topic: Polygons and Circles Standards of Learning Blueprint Summary Reporting Category Geometry SOL Number of Items Reasoning, Lines, and G.1(a-d), G.2(a-c), G.3(a-d), 18 Transformations G.4(a-g) Triangles G.5(a-d), G.6, G.7, G.8 14 Polygons, Circles, and Three- G.9, G.10, G.11(a-c), G.12, 18 Dimensional Figures G.13, G.14(a-d) Excluded from Testing None Number of Operational Items 50 Number of Field-Test Items 10 Total Number of Items on Test 60 Virginia Mathematics SOL Test Cut Scores Failing Scores Passing Scores Test Basic Proficient Advanced Minimum Minimum Minimum Minimum # correct % correct # correct % correct # correct % correct Math 3 16 of 40 40% 26 of 40 65% 36 of 40 90% Math 4 17 of 50 34% 31 of 50 62% 45 of 50 90% Math 5 18 of 50 36% 31 of 50 62% 45 of 50 90% Math 6 16 of 50 32% 28 of 50 56% 45 of 50 90% Math 7 17 of 50 34% 31 of 50 62% 45 of 50 90% Math 8 17 of 50 34% 31 of 50 62% 46 of 50 92% Algebra I n/a n/a 25 of 50 50% 45 of 50 90% Geometry n/a n/a 25 of 50 50% 44 of 50 88% Algebra II n/a n/a 27 of 50 54% 43 of 50 86% Geometry Checkpoint G.11 Page 1
2 Checkpoint Items 1. Directions: After showing your thinking, write your answer in the box. Find the value of x for the intersecting chords in the diagram. (3x + 10) 56 (5x 10) x = Geometry Checkpoint G.11 Page 2
3 2. Directions: After showing your thinking, circle the box you want to select. You must select all correct answers. Which angle measurements show the correct relationship between m ADC and m ABC (in that order) in circle D? A C D B 45, 45 60, 30 90, 45 50, , 44 86, 43 85, 95 35, 55 70, 35 Geometry Checkpoint G.11 Page 3
4 3. Directions: After showing your thinking, write your answer in the box. For the two secants, CB = 5, AB = 7 and CD = 6. What is the length of DE? A 7 B D 5 6 C E DE = Geometry Checkpoint G.11 Page 4
5 4. Directions: After showing your thinking, write your answer in the box. Your answer should be a decimal number to the nearest tenth. In the diagram QM is a secant and MR is a tangent segment. m QSR = 107 and m QT = 75. Find m TMR. Q R T S M m TMR = Geometry Checkpoint G.11 Page 5
6 5. Directions: After showing your thinking, write your answer in the box. Your answer should be rounded to the nearest whole number. Use π = The circles are concentric with center A. AB = 6 and BC = 4. Find the area of the shaded region if m CAE = 100. square units Geometry Checkpoint G.11 Page 6
7 6. Directions: After showing your thinking, write your answer in the box. Your answer should be a decimal rounded to the nearest tenth. Use π = In circle M, r = 5 and m AB = 80. Find the area of sector AMB. A M B square units Geometry Checkpoint G.11 Page 7
8 7. Directions: After showing your thinking, write your answers in the boxes. You must include the degree symbol with your answer. Find the values for x and y, given that the radius is 73 centimeters, the length of AD is 140 centimeters, and the length of CD is 191 centimeters. x and y represent the measure for central angles ABD and CBD. x = y = Geometry Checkpoint G.11 Page 8
9 8. Directions: After showing your thinking, write your answer in the box. A circular window will have a decorative design made of a wood strip surrounding it, formed by connecting tangent lines. How many inches of wood strip is needed to complete the design? 11 in 5 in 7 in inches Geometry Checkpoint G.11 Page 9
10 9. Directions: After showing your thinking, write your answer in the box. Your answer should be a decimal rounded to the nearest tenth. Use π = A bike tire is being measured for new tubing that will cover the outside rim. If the wheel is 26 inches (the diameter), how many inches of wheel tubing will be needed to go entirely around the wheel? inches of tubing Geometry Checkpoint G.11 Page 10
11 10. Directions: Complete the reasons column in the proof table below. Given: AF is a diameter, EG is a chord, and AF EG Prove: ED DG In the proof below, complete the missing reasons using the choices provided. Write your answers in the blank spaces in the table of the proof. Choices Reflexive property Transitive property Symmetric property All radii are congruent Side-Angle-Side Angle-Side-Angle Angle-Angle-Side Side-Side-Side Corresponding parts of congruent triangles are congruent Perpendicular lines form right angles Statement Reason 1. AF EG 1. Given 2. ADE and ADG are right 2. angles 3. ADE ADG 3. All right angles are congruent 4. AD AD AE AG ADE ADG ED DG 7. Geometry Checkpoint G.11 Page 11
12 Checkpoint Solutions SOL G.11 The student will use angles, arcs, chords, tangents, and secants to a) investigate, verify, and apply properties of circles; b) solve real-world problems involving properties of circles; and c) find arc lengths and areas of sectors in circles. Essential Knowledge and Skills a. Find lengths, angle measures, and arc measures associated with 1. two intersecting chords 2. two intersecting secants 3. an intersecting secant and tangent 4. two intersecting tangents 5. central and inscribed angles b. Calculate the area of a sector and the length of an arc of a circle, using proportions c. Solve real-world problems associated with circles, using properties of angles, lines, and arcs d. Verify properties of circles, using deductive reasoning, algebraic, and coordinate methods Item Answer/Solution SOL/EKS Code 1 14 G.11aa 2 G.11aa 3 4 G.11aa G.11aa Essential Knowledge and Skills Find lengths, angle measures, and arc measures associated with 1. two intersecting chords 2. two intersecting secants 3. an intersecting secant and tangent 4. two intersecting tangents 5. central and inscribed angles Find lengths, angle measures, and arc measures associated with 1. two intersecting chords 2. two intersecting secants 3. an intersecting secant and tangent 4. two intersecting tangents 5. central and inscribed angles Find lengths, angle measures, and arc measures associated with 1. two intersecting chords 2. two intersecting secants 3. an intersecting secant and tangent 4. two intersecting tangents 5. central and inscribed angles Find lengths, angle measures, and arc measures associated with 1. two intersecting chords 2. two intersecting secants 3. an intersecting secant and tangent 4. two intersecting tangents 5. central and inscribed angles Geometry Checkpoint G.11 Page 12
13 5 145 G.11cb G.11cb 7 x = 110, y = 150 G.11cb 8 36 G.11bc G.11bc Perpendicular lines form right angles 4. Reflexive property 5. All radii are congruent 6. Side-Angle-Side 7. Corresponding parts of congruent triangles are congruent G.11ad Calculate the area of a sector and the length of an arc of a circle, using proportions Calculate the area of a sector and the length of an arc of a circle, using proportions Calculate the area of a sector and the length of an arc of a circle, using proportions Solve real-world problems associated with circles, using properties of angles, lines, and arcs Solve real-world problems associated with circles, using properties of angles, lines, and arcs Verify properties of circles, using deductive reasoning, algebraic, and coordinate methods Geometry Checkpoint G.11 Page 13
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