sample 9 final 512 Name: Class: Date: Multiple Choice Identify the choice that best completes the statement or answers the question.

Transcription

1 Name: Class: Date: sample 9 final 512 Multiple Choice Identify the choice that best completes the statement or answers the question. 1. In each pair of triangles, parts are congruent as marked. Which pair of triangles is congruent by ASA? a. c. b. d. 1

2 Name: 2. What is the missing reason in the two-column proof? Given: AC bisects DAB and CA bisects DCB Prove: DAC ABC Statements Reasons 1. AC bisects DAB 1. Given 2. DAC BAC 2. Definition of angle bisector 3. AC AC 3. Reflexive property 4. CA bisects DCB 4. Given 5. DAC BCA 5. Definition of angle bisector 6. DAC BAC 6.? a. ASA Postulate c. SAS Postulate b. SSS Postulate d. AAS Theorem 2

3 Name: 3. Supply the missing reasons to complete the proof. Given: Q T and QR TR Prove: PR SR Statement 1. Q T and QR TR Reasons 1. Given 2. PRQ SRT 2. Vertical angles are congruent. 3. PRQ SRT 3.? 4. PR SR 4.? a. ASA; Substitution c. AAS; CPCTC b. SAS; CPCTC d. ASA; CPCTC 4. BE is the bisector of ABC and CD is the bisector of ACB. Also, XBA YCA. Which of AAS, SSS, SAS, or ASA would you use to help you prove BL CM? a. AAS b. SSS c. SAS d. ASA 5. Given a regular hexagon, find the measures of the angles formed by (a) two consecutive radii and (b) a radius and a side of the polygon. a. 40 ; 220 b. 60 ; 60 c. 36 ; 216 d. 45 ; The area of a regular hexagon is 35 in. 2. Find the length of a side. Round your answer to the nearest tenth. a. 3.7 in. b. 4.8 in. c. 6.4 in. d in. 7. The circumference of a circle is 60 cm. Find the diameter, the radius, and the length of an arc of 140. a. 60 cm; 30 cm; 23.3 cm c. 120 cm; 30 cm; 160 cm b. 60 cm; 120 cm; 11.7 cm d. 30 cm; 60 cm; 11.7 cm 3

4 Name: 8. Find the length of arc XPY. Leave your answer in terms of. 9. a. 24 m b. 12 m c. 4 m d. 720 m Find the area of the circle. Leave your answer in terms of. a m 2 b. 1.8 m 2 c m 2 d m The figure represents the overhead view of a deck surrounding a hot tub. What is the area of the deck? Round to the nearest tenth. a m 2 b m 2 c m 2 d m 2 4

5 Name: 11. Find the area of the shaded region. Leave your answer in terms of and in simplest radical form. a m 2 c m 2 b m 2 d. none of these 12. A model is made of a car. The car is 9 feet long and the model is 6 inches long. What is the ratio of the length of the car to the length of the model? a. 18 : 1 b. 1 : 18 c. 9 : 6 d. 6 : If a b 5, then 3a =. 3 a. 3b b. 10b c. 5b d. 6b 14. A map of Australia has a scale of 1 cm to 120 km. If the distance between Melbourne and Canberra is 463 km, how far apart are they on the map, to the nearest tenth of a centimeter? a. 0.4 cm b. 3.9 cm c cm d. 55,560 cm 15. You want to produce a scale drawing of your living room, which is 24 ft by 15 ft. If you use a scale of 4 in. = 6 ft, what will be the dimensions of your scale drawing? a. 24 in. by 144 in. c. 24 in. by 10 in. b. 16 in. by 10 in. d. 16 in. by 144 in. 16. State whether the triangles are similar. If so, write a similarity statement and the postulate or theorem you used. a. ABC MNO; SSS c. ABC MNO; AA b. ABC MNO; SAS d. The triangles are not similar. 5

6 Name: 17. a. ADB CDB; SAS c. ADB CDB; SSS b. ABD CDB; SAS d. The triangles are not similar. Explain why the triangles are similar. Then find the value of x. 18. a. SSS Postulate; c. SAS Postulate; b. AA Postulate; d. AA Postulate; Campsites F and G are on opposite sides of a lake. A survey crew made the measurements shown on the diagram. What is the distance between the two campsites? The diagram is not to scale. a m b m c m d m 6

7 Name: The figures are similar. The area of one figure is given. Find the area of the other figure to the nearest whole number. 20. The area of the larger triangle is 1589 ft 2. a ft 2 b ft 2 c ft 2 d ft Two trapezoids have areas 432 cm 2 and 48 cm 2. Find their ratio of similarity. a. 3 : 1 b. 9 : 1 c. 1 : 3 d. 1 : Find the slant height of the cone to the nearest whole number. a. 21 m b. 19 m c. 22 m d. 24 m 23. Find the surface area of a conical grain storage tank that has a height of 30 meters, a diameter of 20 meters, and a slant height of 32 meters. Round the answer to the nearest square meter. a m 2 b m 2 c m 2 d m 2 7

8 Name: Find the volume of the given prism. Round to the nearest tenth if necessary. 24. a. 17 m 3 b. 34 m 3 c. 8.5 m 3 d. 1 m Find the volume of the composite space figure to the nearest whole number. a. 170 cm 3 b. 180 cm 3 c. 120 cm 3 d. 60 cm Find the volume of the composite space figure to the nearest whole number. a. 546 mm 3 b. 174 mm 3 c. 364 mm 3 d. 438 mm Cylinder A has radius 1 m and height 4 m. Cylinder B has radius 2 m and height 4 m. Find the ratio of the volume of cylinder A to the volume of cylinder B. a. 5 : 6 b. 1 : 4 c. 1 : 2 d. 1 : 1 8

9 Name: 28. Pentagon RSTUV is circumscribed about a circle. Solve for x for RS = 10, ST = 13, TU = 11, UV = 12, and VR = 12. The figure is not drawn to scale. 29. a. 4 b. 8 c. 11 d. 6 Find the value of x. If necessary, round your answer to the nearest tenth. The figure is not drawn to scale. a b. 120 c. 5.3 d. 12 9

10 Name: 30. AB = 20, BC = 6, and CD = a b c d. 15 a b c. 110 d Find m BAC. (The figure is not drawn to scale.) a. 114 b. 57 c. 132 d

11 Name: 33. Find the value of x for m(arc AB) = 46 and m(arc CD) = 25. (The figure is not drawn to scale.) a b c. 71 d Find m D for m B = 50. (The figure is not drawn to scale.) a. 80 b. 130 c. 65 d. 160 Short Answer 35. In NML, NL = NM, and the perimeter is 46 cm. A, B, and C are points of tangency to the circle. MC = 4 cm. Find NL. Explain your reasoning. (The figure is not drawn to scale.) 11

12 Name: 36. Given: m X = 150, WZ YZ, m Y = 92. Find each measurement. (The figure is not drawn to scale.) a. m Z b. m(arc WZ) c. m W d. m(arc WX) 37. Given: arc CF = arc DE Prove: CED DFC 12

13 Name: Essay 38. Write a two-column proof: Given: BAC DAC, DCA BCA Prove: BC CD 39. A log cabin is shaped like a rectangular prism. A model of the cabin has a scale of 1 centimeter to 0.5 meters. a. If the model is 14 cm by 20 cm by 7 cm, what are the dimensions of the actual log cabin? Explain how you find the dimensions. b. What is the volume of the actual log cabin? Explain how you find the volume. c. What is the ratio of the volume of the model of the cabin to the volume of the actual cabin? Explain your method for finding the ratio. Other 40. A parent group wants to double the area of a playground. The proposed diagram shows both the width and the length of the existing playground doubled. They ask you to comment on their proposal. What would you say? 41. Show that it is not possible for the lengths of the segments of two intersecting chords to be four consecutive integers. 13

14 sample 9 final 512 Answer Section MULTIPLE CHOICE 1. ANS: B PTS: 1 DIF: L1 REF: 4-3 Triangle Congruence by ASA and AAS OBJ: Using the ASA Postulate and the AAS Theorem NAT: NAEP G2e CAT5.LV20.56 IT.LV16.CP S9.TSK2.GM S10.TSK2.GM TV.LV20.14 TOP: 4-3 Example 1 KEY: ASA MSC: NAEP G2e CAT5.LV20.56 IT.LV16.CP S9.TSK2.GM S10.TSK2.GM TV.LV ANS: A PTS: 1 DIF: L1 REF: 4-3 Triangle Congruence by ASA and AAS OBJ: Using the ASA Postulate and the AAS Theorem NAT: NAEP G2e CAT5.LV20.56 IT.LV16.CP S9.TSK2.GM S10.TSK2.GM TV.LV20.14 TOP: 4-3 Example 2 KEY: ASA proof MSC: NAEP G2e CAT5.LV20.56 IT.LV16.CP S9.TSK2.GM S10.TSK2.GM TV.LV ANS: D PTS: 1 DIF: L1 REF: 4-4 Using Congruent Triangles: CPCTC OBJ: Proving Parts of Triangles Congruent NAT: NAEP G2e CAT5.LV20.56 IT.LV16.CP S9.TSK2.GM S10.TSK2.GM TV.LV20.14 TOP: 4-4 Example 1 KEY: ASA CPCTC proof MSC: NAEP G2e CAT5.LV20.56 IT.LV16.CP S9.TSK2.GM S10.TSK2.GM TV.LV ANS: D PTS: 1 DIF: L3 REF: 4-7 Using Corresponding Parts of Congruent Triangles OBJ: Using Overlapping Triangles in Proofs NAT: NAEP G3f CAT5.LV20.55 CAT5.LV20.56 IT.LV16.CP S9.TSK2.GM S10.TSK2.GM TV.LV20.13 TV.LV20.14 TOP: 4-7 Example 2 KEY: corresponding parts congruent figures ASA SAS AAS SSS reasoning MSC: NAEP G3f CAT5.LV20.55 CAT5.LV20.56 IT.LV16.CP S9.TSK2.GM S10.TSK2.GM TV.LV20.13 TV.LV ANS: B PTS: 1 DIF: L2 REF: 7-5 Areas of Regular Polygons OBJ: Areas of Regular Polygons NAT: NAEP M1h CAT5.LV20.50 CAT5.LV20.55 CAT5.LV20.56 IT.LV16.AM IT.LV16.CP S9.TSK2.GM S9.TSK2.PRA S10.TSK2.GM S10.TSK2.PRA TV.LV20.13 TV.LV20.14 TV.LV20.52 TOP: 7-5 Example 1 KEY: regular polygon multi-part question MSC: NAEP M1h CAT5.LV20.50 CAT5.LV20.55 CAT5.LV20.56 IT.LV16.AM IT.LV16.CP S9.TSK2.GM S9.TSK2.PRA S10.TSK2.GM S10.TSK2.PRA TV.LV20.13 TV.LV20.14 TV.LV ANS: A PTS: 1 DIF: L3 REF: 7-5 Areas of Regular Polygons OBJ: Areas of Regular Polygons NAT: NAEP M1h CAT5.LV20.50 CAT5.LV20.55 CAT5.LV20.56 IT.LV16.AM IT.LV16.CP S9.TSK2.GM S9.TSK2.PRA S10.TSK2.GM S10.TSK2.PRA TV.LV20.13 TV.LV20.14 TV.LV20.52 TOP: 7-5 Example 2 KEY: regular polygon hexagon area apothem radius MSC: NAEP M1h CAT5.LV20.50 CAT5.LV20.55 CAT5.LV20.56 IT.LV16.AM IT.LV16.CP S9.TSK2.GM S9.TSK2.PRA S10.TSK2.GM S10.TSK2.PRA TV.LV20.13 TV.LV20.14 TV.LV

15 7. ANS: A PTS: 1 DIF: L2 REF: 7-6 Circles and Arcs OBJ: Circumference and Arc Length NAT: NAEP M1h CAT5.LV20.55 CAT5.LV20.56 IT.LV16.CP S9.TSK2.GM S10.TSK2.GM TV.LV20.13 TV.LV20.14 TOP: 7-6 Example 4 KEY: circumference radius MSC: NAEP M1h CAT5.LV20.55 CAT5.LV20.56 IT.LV16.CP S9.TSK2.GM S10.TSK2.GM TV.LV20.13 TV.LV ANS: B PTS: 1 DIF: L1 REF: 7-6 Circles and Arcs OBJ: Circumference and Arc Length NAT: NAEP M1h CAT5.LV20.55 CAT5.LV20.56 IT.LV16.CP S9.TSK2.GM S10.TSK2.GM TV.LV20.13 TV.LV20.14 TOP: 7-6 Example 5 KEY: arc circumference MSC: NAEP M1h CAT5.LV20.55 CAT5.LV20.56 IT.LV16.CP S9.TSK2.GM S10.TSK2.GM TV.LV20.13 TV.LV ANS: C PTS: 1 DIF: L1 REF: 7-7 Areas of Circles and Sectors OBJ: Finding Areas of Circles and Parts of Circles NAT: NAEP M1h CAT5.LV20.50 CAT5.LV20.55 CAT5.LV20.56 IT.LV16.AM IT.LV16.CP S9.TSK2.GM S9.TSK2.PRA S10.TSK2.GM S10.TSK2.PRA TV.LV20.13 TV.LV20.14 TV.LV20.52 TOP: 7-7 Example 1 KEY: area of a circle radius MSC: NAEP M1h CAT5.LV20.50 CAT5.LV20.55 CAT5.LV20.56 IT.LV16.AM IT.LV16.CP S9.TSK2.GM S9.TSK2.PRA S10.TSK2.GM S10.TSK2.PRA TV.LV20.13 TV.LV20.14 TV.LV ANS: B PTS: 1 DIF: L2 REF: 7-7 Areas of Circles and Sectors OBJ: Finding Areas of Circles and Parts of Circles NAT: NAEP M1h CAT5.LV20.50 CAT5.LV20.55 CAT5.LV20.56 IT.LV16.AM IT.LV16.CP S9.TSK2.GM S9.TSK2.PRA S10.TSK2.GM S10.TSK2.PRA TV.LV20.13 TV.LV20.14 TV.LV20.52 TOP: 7-7 Example 1 KEY: area of a circle radius MSC: NAEP M1h CAT5.LV20.50 CAT5.LV20.55 CAT5.LV20.56 IT.LV16.AM IT.LV16.CP S9.TSK2.GM S9.TSK2.PRA S10.TSK2.GM S10.TSK2.PRA TV.LV20.13 TV.LV20.14 TV.LV ANS: C PTS: 1 DIF: L2 REF: 7-7 Areas of Circles and Sectors OBJ: Finding Areas of Circles and Parts of Circles NAT: NAEP M1h CAT5.LV20.50 CAT5.LV20.55 CAT5.LV20.56 IT.LV16.AM IT.LV16.CP S9.TSK2.GM S9.TSK2.PRA S10.TSK2.GM S10.TSK2.PRA TV.LV20.13 TV.LV20.14 TV.LV20.52 TOP: 7-7 Example 3 KEY: sector circle area central angle MSC: NAEP M1h CAT5.LV20.50 CAT5.LV20.55 CAT5.LV20.56 IT.LV16.AM IT.LV16.CP S9.TSK2.GM S9.TSK2.PRA S10.TSK2.GM S10.TSK2.PRA TV.LV20.13 TV.LV20.14 TV.LV ANS: A PTS: 1 DIF: L1 REF: 8-1 Ratios and Proportions OBJ: Using Ratios and Proportions NAT: NAEP N4c CAT5.LV20.46 CAT5.LV20.54 CAT5.LV20.55 IT.LV16.CP IT.LV16.FR S9.TSK2.GM S9.TSK2.NS S10.TSK2.GM S10.TSK2.NS TV.LV20.10 TV.LV20.13 TOP: 8-1 Example 1 KEY: ratio word problem MSC: NAEP N4c CAT5.LV20.46 CAT5.LV20.54 CAT5.LV20.55 IT.LV16.CP IT.LV16.FR S9.TSK2.GM S9.TSK2.NS S10.TSK2.GM S10.TSK2.NS TV.LV20.10 TV.LV ANS: C PTS: 1 DIF: L1 REF: 8-1 Ratios and Proportions OBJ: Using Ratios and Proportions NAT: NAEP N4c CAT5.LV20.46 CAT5.LV20.54 CAT5.LV20.55 IT.LV16.CP IT.LV16.FR S9.TSK2.GM S9.TSK2.NS S10.TSK2.GM S10.TSK2.NS TV.LV20.10 TV.LV20.13 TOP: 8-1 Example 2 KEY: proportion Cross-Product Property MSC: NAEP N4c CAT5.LV20.46 CAT5.LV20.54 CAT5.LV20.55 IT.LV16.CP IT.LV16.FR S9.TSK2.GM S9.TSK2.NS S10.TSK2.GM S10.TSK2.NS TV.LV20.10 TV.LV

16 14. ANS: B PTS: 1 DIF: L1 REF: 8-1 Ratios and Proportions OBJ: Using Ratios and Proportions NAT: NAEP N4c CAT5.LV20.46 CAT5.LV20.54 CAT5.LV20.55 IT.LV16.CP IT.LV16.FR S9.TSK2.GM S9.TSK2.NS S10.TSK2.GM S10.TSK2.NS TV.LV20.10 TV.LV20.13 TOP: 8-1 Example 4 KEY: proportion Cross-Product Property word problem MSC: NAEP N4c CAT5.LV20.46 CAT5.LV20.54 CAT5.LV20.55 IT.LV16.CP IT.LV16.FR S9.TSK2.GM S9.TSK2.NS S10.TSK2.GM S10.TSK2.NS TV.LV20.10 TV.LV ANS: B PTS: 1 DIF: L1 REF: 8-1 Ratios and Proportions OBJ: Using Ratios and Proportions NAT: NAEP N4c CAT5.LV20.46 CAT5.LV20.54 CAT5.LV20.55 IT.LV16.CP IT.LV16.FR S9.TSK2.GM S9.TSK2.NS S10.TSK2.GM S10.TSK2.NS TV.LV20.10 TV.LV20.13 TOP: 8-1 Example 4 KEY: proportion Cross-Product Property word problem MSC: NAEP N4c CAT5.LV20.46 CAT5.LV20.54 CAT5.LV20.55 IT.LV16.CP IT.LV16.FR S9.TSK2.GM S9.TSK2.NS S10.TSK2.GM S10.TSK2.NS TV.LV20.10 TV.LV ANS: A PTS: 1 DIF: L1 REF: 8-3 Proving Triangles Similar OBJ: The AA Postulate and the SAS and SSS Theorems NAT: NAEP G2e CAT5.LV20.55 CAT5.LV20.56 IT.LV16.CP S9.TSK2.GM S10.TSK2.GM TV.LV20.13 TV.LV20.14 TOP: 8-3 Example 2 KEY: Side-Side-Side Similarity Theorem MSC: NAEP G2e CAT5.LV20.55 CAT5.LV20.56 IT.LV16.CP S9.TSK2.GM S10.TSK2.GM TV.LV20.13 TV.LV ANS: A PTS: 1 DIF: L1 REF: 8-3 Proving Triangles Similar OBJ: The AA Postulate and the SAS and SSS Theorems NAT: NAEP G2e CAT5.LV20.55 CAT5.LV20.56 IT.LV16.CP S9.TSK2.GM S10.TSK2.GM TV.LV20.13 TV.LV20.14 TOP: 8-3 Example 2 KEY: Side-Angle-Side Similarity Theorem corresponding sides MSC: NAEP G2e CAT5.LV20.55 CAT5.LV20.56 IT.LV16.CP S9.TSK2.GM S10.TSK2.GM TV.LV20.13 TV.LV ANS: D PTS: 1 DIF: L1 REF: 8-3 Proving Triangles Similar OBJ: Applying AA, SAS, and SSS Similarity NAT: NAEP G2e CAT5.LV20.55 CAT5.LV20.56 IT.LV16.CP S9.TSK2.GM S10.TSK2.GM TV.LV20.13 TV.LV20.14 TOP: 8-3 Example 3 KEY: Angle-Angle Similarity Postulate MSC: NAEP G2e CAT5.LV20.55 CAT5.LV20.56 IT.LV16.CP S9.TSK2.GM S10.TSK2.GM TV.LV20.13 TV.LV ANS: A PTS: 1 DIF: L1 REF: 8-3 Proving Triangles Similar OBJ: Applying AA, SAS, and SSS Similarity NAT: NAEP G2e CAT5.LV20.55 CAT5.LV20.56 IT.LV16.CP S9.TSK2.GM S10.TSK2.GM TV.LV20.13 TV.LV20.14 TOP: 8-3 Example 4 KEY: Side-Angle-Side Similarity Theorem word problem MSC: NAEP G2e CAT5.LV20.55 CAT5.LV20.56 IT.LV16.CP S9.TSK2.GM S10.TSK2.GM TV.LV20.13 TV.LV

17 20. ANS: A PTS: 1 DIF: L1 REF: 8-6 Perimeters and Areas of Similar Figures OBJ: Finding Perimeters and Areas of Similar Figures NAT: NAEP M2g NAEP N4c CAT5.LV20.50 CAT5.LV20.55 CAT5.LV20.56 IT.LV16.AM IT.LV16.CP S9.TSK2.GM S9.TSK2.PRA S10.TSK2.GM S10.TSK2.PRA TV.LV20.13 TV.LV20.14 TV.LV20.52 TOP: 8-6 Example 2 KEY: similar figures area MSC: NAEP M2g NAEP N4c CAT5.LV20.50 CAT5.LV20.55 CAT5.LV20.56 IT.LV16.AM IT.LV16.CP S9.TSK2.GM S9.TSK2.PRA S10.TSK2.GM S10.TSK2.PRA TV.LV20.13 TV.LV20.14 TV.LV ANS: A PTS: 1 DIF: L1 REF: 8-6 Perimeters and Areas of Similar Figures OBJ: Finding Perimeters and Areas of Similar Figures NAT: NAEP M2g NAEP N4c CAT5.LV20.50 CAT5.LV20.55 CAT5.LV20.56 IT.LV16.AM IT.LV16.CP S9.TSK2.GM S9.TSK2.PRA S10.TSK2.GM S10.TSK2.PRA TV.LV20.13 TV.LV20.14 TV.LV20.52 TOP: 8-6 Example 4 KEY: similar figures area MSC: NAEP M2g NAEP N4c CAT5.LV20.50 CAT5.LV20.55 CAT5.LV20.56 IT.LV16.AM IT.LV16.CP S9.TSK2.GM S9.TSK2.PRA S10.TSK2.GM S10.TSK2.PRA TV.LV20.13 TV.LV20.14 TV.LV ANS: A PTS: 1 DIF: L1 REF: 10-4 Surface Areas of Pyramids and Cones OBJ: Finding Surface Area of a Cone NAT: NAEP M1j CAT5.LV20.50 CAT5.LV20.55 CAT5.LV20.56 IT.LV16.AM IT.LV16.CP TOP: 10-4 Example 4 KEY: cone slant height of a cone Pythagorean Theorem MSC: NAEP M1j CAT5.LV20.50 CAT5.LV20.55 CAT5.LV20.56 IT.LV16.AM IT.LV16.CP 23. ANS: B PTS: 1 DIF: L2 REF: 10-4 Surface Areas of Pyramids and Cones OBJ: Finding Surface Area of a Cone NAT: NAEP M1j CAT5.LV20.50 CAT5.LV20.55 CAT5.LV20.56 IT.LV16.AM IT.LV16.CP TOP: 10-4 Example 4 KEY: cone surface area of a cone problem solving word problem surface area formulas surface area MSC: NAEP M1j CAT5.LV20.50 CAT5.LV20.55 CAT5.LV20.56 IT.LV16.AM IT.LV16.CP 24. ANS: A PTS: 1 DIF: L2 REF: 10-5 Volumes of Prisms and Cylinders OBJ: Finding Volume of a Prism NAT: NAEP M1j CAT5.LV20.50 CAT5.LV20.55 CAT5.LV20.56 IT.LV16.AM IT.LV16.CP IT.LV16.PS S9.TSK2.GM S9.TSK2.PRA S10.TSK2.GM S10.TSK2.PRA TV.LV20.13 TV.LV20.14 TV.LV20.16 TV.LV20.17 TOP: 10-5 Example 2 KEY: volume of a triangular prism volume formulas volume prism MSC: NAEP M1j CAT5.LV20.50 CAT5.LV20.55 CAT5.LV20.56 IT.LV16.AM IT.LV16.CP IT.LV16.PS S9.TSK2.GM S9.TSK2.PRA S10.TSK2.GM S10.TSK2.PRA TV.LV20.13 TV.LV20.14 TV.LV20.16 TV.LV

18 25. ANS: B PTS: 1 DIF: L2 REF: 10-5 Volumes of Prisms and Cylinders OBJ: Finding Volume of a Prism NAT: NAEP M1j CAT5.LV20.50 CAT5.LV20.55 CAT5.LV20.56 IT.LV16.AM IT.LV16.CP IT.LV16.PS S9.TSK2.GM S9.TSK2.PRA S10.TSK2.GM S10.TSK2.PRA TV.LV20.13 TV.LV20.14 TV.LV20.16 TV.LV20.17 TOP: 10-5 Example 1 KEY: volume of a rectangular prism problem solving volume formulas volume MSC: NAEP M1j CAT5.LV20.50 CAT5.LV20.55 CAT5.LV20.56 IT.LV16.AM IT.LV16.CP IT.LV16.PS S9.TSK2.GM S9.TSK2.PRA S10.TSK2.GM S10.TSK2.PRA TV.LV20.13 TV.LV20.14 TV.LV20.16 TV.LV ANS: D PTS: 1 DIF: L1 REF: 10-5 Volumes of Prisms and Cylinders OBJ: Finding Volume of a Cylinder NAT: NAEP M1j CAT5.LV20.50 CAT5.LV20.55 CAT5.LV20.56 IT.LV16.AM IT.LV16.CP IT.LV16.PS S9.TSK2.GM S9.TSK2.PRA S10.TSK2.GM S10.TSK2.PRA TV.LV20.13 TV.LV20.14 TV.LV20.16 TV.LV20.17 TOP: 10-5 Example 4 KEY: volume of a composite figure cylinder volume of a cylinder volume of a rectangular prism volume formulas volume prism MSC: NAEP M1j CAT5.LV20.50 CAT5.LV20.55 CAT5.LV20.56 IT.LV16.AM IT.LV16.CP IT.LV16.PS S9.TSK2.GM S9.TSK2.PRA S10.TSK2.GM S10.TSK2.PRA TV.LV20.13 TV.LV20.14 TV.LV20.16 TV.LV ANS: B PTS: 1 DIF: L2 REF: 10-5 Volumes of Prisms and Cylinders OBJ: Finding Volume of a Cylinder NAT: NAEP M1j CAT5.LV20.50 CAT5.LV20.55 CAT5.LV20.56 IT.LV16.AM IT.LV16.CP IT.LV16.PS S9.TSK2.GM S9.TSK2.PRA S10.TSK2.GM S10.TSK2.PRA TV.LV20.13 TV.LV20.14 TV.LV20.16 TV.LV20.17 TOP: 10-5 Example 3 KEY: cylinder volume of a cylinder volume formulas volume word problem problem solving MSC: NAEP M1j CAT5.LV20.50 CAT5.LV20.55 CAT5.LV20.56 IT.LV16.AM IT.LV16.CP IT.LV16.PS S9.TSK2.GM S9.TSK2.PRA S10.TSK2.GM S10.TSK2.PRA TV.LV20.13 TV.LV20.14 TV.LV20.16 TV.LV ANS: A PTS: 1 DIF: L2 REF: 11-1 Tangent Lines OBJ: Using Multiple Tangents NAT: NAEP G3e CAT5.LV20.50 CAT5.LV20.55 CAT5.LV20.56 IT.LV16.AM IT.LV16.CP TV.LV20.52 TOP: 11-1 Example 5 KEY: properties of tangents tangent to a circle pentagon MSC: NAEP G3e CAT5.LV20.50 CAT5.LV20.55 CAT5.LV20.56 IT.LV16.AM IT.LV16.CP TV.LV ANS: D PTS: 1 DIF: L1 REF: 11-4 Angle Measures and Segment Lengths OBJ: Finding Segment Lengths NAT: NAEP G3e CAT5.LV20.50 CAT5.LV20.55 CAT5.LV20.56 IT.LV16.AM IT.LV16.CP TOP: 11-4 Example 3 KEY: circle chord intersection inside the circle MSC: NAEP G3e CAT5.LV20.50 CAT5.LV20.55 CAT5.LV20.56 IT.LV16.AM IT.LV16.CP 5

19 30. ANS: B PTS: 1 DIF: L1 REF: 11-4 Angle Measures and Segment Lengths OBJ: Finding Segment Lengths NAT: NAEP G3e CAT5.LV20.50 CAT5.LV20.55 CAT5.LV20.56 IT.LV16.AM IT.LV16.CP TOP: 11-4 Example 3 KEY: circle intersection outside the circle secant MSC: NAEP G3e CAT5.LV20.50 CAT5.LV20.55 CAT5.LV20.56 IT.LV16.AM IT.LV16.CP 31. ANS: B PTS: 1 DIF: L1 REF: 11-4 Angle Measures and Segment Lengths OBJ: Finding Segment Lengths NAT: NAEP G3e CAT5.LV20.50 CAT5.LV20.55 CAT5.LV20.56 IT.LV16.AM IT.LV16.CP TOP: 11-4 Example 3 KEY: segment length tangent secant MSC: NAEP G3e CAT5.LV20.50 CAT5.LV20.55 CAT5.LV20.56 IT.LV16.AM IT.LV16.CP 32. ANS: B PTS: 1 DIF: L1 REF: 11-3 Inscribed Angles OBJ: Finding the Measure of an Inscribed Angle NAT: NAEP G3e CAT5.LV20.50 CAT5.LV20.55 CAT5.LV20.56 IT.LV16.AM IT.LV16.CP TOP: 11-3 Example 2 KEY: circle inscribed angle central angle intercepted arc MSC: NAEP G3e CAT5.LV20.50 CAT5.LV20.55 CAT5.LV20.56 IT.LV16.AM IT.LV16.CP 33. ANS: A PTS: 1 DIF: L1 REF: 11-4 Angle Measures and Segment Lengths OBJ: Finding Angle Measures NAT: NAEP G3e CAT5.LV20.50 CAT5.LV20.55 CAT5.LV20.56 IT.LV16.AM IT.LV16.CP TOP: 11-4 Example 1 KEY: circle secant angle measure arc measure intersection inside the circle MSC: NAEP G3e CAT5.LV20.50 CAT5.LV20.55 CAT5.LV20.56 IT.LV16.AM IT.LV16.CP 34. ANS: A PTS: 1 DIF: L2 REF: 11-4 Angle Measures and Segment Lengths OBJ: Finding Angle Measures NAT: NAEP G3e CAT5.LV20.50 CAT5.LV20.55 CAT5.LV20.56 IT.LV16.AM IT.LV16.CP TOP: 11-4 Example 1 KEY: circle chord angle measure arc measure intersection on the circle intersection outside the circle MSC: NAEP G3e CAT5.LV20.50 CAT5.LV20.55 CAT5.LV20.56 IT.LV16.AM IT.LV16.CP 6

20 SHORT ANSWER 35. ANS: NM NL and, by the Tangent Theorem, NC = NA. By subtraction, MC LA. Also by the Tangent Theorem, MC MB and LA LB, so 4 MC MB LB LA. The perimeter is 46 cm, so 46 NC MC MB LB LA NA. By substitution, 46 NA NA, so NA 15. Since NL NA LA, NL 15 cm 4 cm, or 19 cm. PTS: 1 DIF: L2 REF: 11-1 Tangent Lines OBJ: Using Multiple Tangents NAT: NAEP G3e CAT5.LV20.50 CAT5.LV20.55 CAT5.LV20.56 IT.LV16.AM IT.LV16.CP TV.LV20.52 TOP: 11-1 Example 5 KEY: reasoning tangent to a circle tangent properties of tangents Tangent Theorem MSC: NAEP G3e CAT5.LV20.50 CAT5.LV20.55 CAT5.LV20.56 IT.LV16.AM IT.LV16.CP TV.LV ANS: a. 30 b. 150 c. 88 d. 34 PTS: 1 DIF: L2 REF: 11-3 Inscribed Angles OBJ: Finding the Measure of an Inscribed Angle NAT: NAEP G3e CAT5.LV20.50 CAT5.LV20.55 CAT5.LV20.56 IT.LV16.AM IT.LV16.CP TOP: 11-3 Example 1 KEY: chord inscribed angle-arc relationship circle MSC: NAEP G3e CAT5.LV20.50 CAT5.LV20.55 CAT5.LV20.56 IT.LV16.AM IT.LV16.CP 7

21 37. ANS: Statements Reasons 1. F E 1. Inscribed angles intersecting the same arc are. 2. arc CF arc DE 2. Given 3. m CDF 1 m(arc CF) 2 m DCE 1 m(arc DE) 2 3. Inscribed Angle Theorem 4. m CDF 1 m(arc CF) 2 4. Substitution m DCE 1 m(arc CF) 2 5. m CDF m DCE 5. Substitution 6. CDF DCE 6. Definition of congruence 7. CD DC 7. Reflexive property 8. CED DFC 8. AAS PTS: 1 DIF: L3 REF: 11-3 Inscribed Angles OBJ: Finding the Measure of an Inscribed Angle NAT: NAEP G3e CAT5.LV20.50 CAT5.LV20.55 CAT5.LV20.56 IT.LV16.AM IT.LV16.CP TOP: 11-3 Example 2 KEY: chord inscribed angle-arc relationship circle proof MSC: NAEP G3e CAT5.LV20.50 CAT5.LV20.55 CAT5.LV20.56 IT.LV16.AM IT.LV16.CP ESSAY 38. ANS: [4] Statement Reason 1. BAC DAC and DCA BCA 1. Given 2. CA CA 2. Reflexive Property 3. CBA CDA 3. ASA 4. BC CD 4. CPCTC [3] correct idea, some details inaccurate [2] correct idea, not well organized [1] correct idea, one or more significant steps omitted PTS: 1 DIF: L3 REF: 4-4 Using Congruent Triangles: CPCTC OBJ: Proving Parts of Triangles Congruent NAT: NAEP G2e CAT5.LV20.56 IT.LV16.CP S9.TSK2.GM S10.TSK2.GM TV.LV20.14 KEY: ASA CPCTC congruent figures corresponding parts rubric-based question extended response proof MSC: NAEP G2e CAT5.LV20.56 IT.LV16.CP S9.TSK2.GM S10.TSK2.GM TV.LV

22 39. ANS: [4] a. To find the actual dimensions, you must use the scale of 1 cm to 0.5 meters. A quick way to find the dimensions is to divide each value of a measure by 2 and then that is the number of meters in the dimension for the cabin = 7, so this is 7 meters = 10, so this is 10 meters. 7 2 = 3.5, so this is 3.5 meters. The dimensions of the actual cabin are 7 m by 10 m by 3.5 m. b. To find the volume of the cabin, use the formula for volume of a prism. V = Bh Use the formula for volume. = B = 245 The volume of the cabin is 245 cubic meters. c. To find the ratio, you must know the volume of each cabin in the same units. The volume of the model is 14 cm 20 cm 7 cm 1960 cubic centimeters. The volume of the actual cabin is 245 cm cm m 100 cm m 100 cm m = 245,000,000 cubic centimeters, since each meter is 100 centimeters ratio of model to actual 245, 000, , 000 The ratio of the volumes is 1 to 125,000. [3] one mathematical error or correct answers with incomplete explanations [2] two mathematical errors or correct answers with errors in explanation [1] correct answers with no explanation PTS: 1 DIF: L2 REF: 10-5 Volumes of Prisms and Cylinders OBJ: Finding Volume of a Prism NAT: NAEP M1j CAT5.LV20.50 CAT5.LV20.55 CAT5.LV20.56 IT.LV16.AM IT.LV16.CP IT.LV16.PS S9.TSK2.GM S9.TSK2.PRA S10.TSK2.GM S10.TSK2.PRA TV.LV20.13 TV.LV20.14 TV.LV20.16 TV.LV20.17 KEY: extended response volume of a rectangular prism prism problem solving word problem rubric-based question volume formulas volume MSC: NAEP M1j CAT5.LV20.50 CAT5.LV20.55 CAT5.LV20.56 IT.LV16.AM IT.LV16.CP IT.LV16.PS S9.TSK2.GM S9.TSK2.PRA S10.TSK2.GM S10.TSK2.PRA TV.LV20.13 TV.LV20.14 TV.LV20.16 TV.LV

23 OTHER 40. ANS: Answers may vary. Sample: Since both the width and the length are doubled, the area will be quadrupled. To double the area, you only need to double one of the dimensions. PTS: 1 DIF: L2 REF: 8-6 Perimeters and Areas of Similar Figures OBJ: Finding Perimeters and Areas of Similar Figures NAT: NAEP M2g NAEP N4c CAT5.LV20.50 CAT5.LV20.55 CAT5.LV20.56 IT.LV16.AM IT.LV16.CP S9.TSK2.GM S9.TSK2.PRA S10.TSK2.GM S10.TSK2.PRA TV.LV20.13 TV.LV20.14 TV.LV20.52 KEY: area perimeter writing in math reasoning word problem MSC: NAEP M2g NAEP N4c CAT5.LV20.50 CAT5.LV20.55 CAT5.LV20.56 IT.LV16.AM IT.LV16.CP S9.TSK2.GM S9.TSK2.PRA S10.TSK2.GM S10.TSK2.PRA TV.LV20.13 TV.LV20.14 TV.LV ANS: Let m, m + 1, m + 2, and m + 3 represent the four consecutive numbers. Then the product of the greatest and least numbers will equal the product of the two consecutive middle numbers. Solving the equation m(m + 3) = (m + 1)(m + 2) for m results in m 2 + 3m = m 2 + 3m + 2, or 0 = 2, which is false. PTS: 1 DIF: L3 REF: 11-4 Angle Measures and Segment Lengths OBJ: Finding Angle Measures NAT: NAEP G3e CAT5.LV20.50 CAT5.LV20.55 CAT5.LV20.56 IT.LV16.AM IT.LV16.CP TOP: 11-4 Example 3 KEY: circle intersection inside the circle segment length algebra proof reasoning MSC: NAEP G3e CAT5.LV20.50 CAT5.LV20.55 CAT5.LV20.56 IT.LV16.AM IT.LV16.CP 10

24 sample 9 final 512 [Answer Strip] A 2. D 3. B 8. C 11. B 1. C 9. A 12. C 13. B 14. B 10. B 15. D 4. A 16. B 5. A 6. A 7.

25 sample 9 final 512 [Answer Strip] A 17. A 28. B 30. A 20. A 24. D 18. A 21. A 22. B 25. B 31. D 29. A 19. D 26. B 23. B 32. B 27.

26 sample 9 final 512 [Answer Strip] A 33. A 34.