Geo - CH11 Practice Test

Transcription

1 Geo - H11 Practice Test Multiple hoice Identify the choice that best completes the statement or answers the question. 1. Identify the secant that intersects ñ. a. c. b. l d. 2. satellite rotates 50 miles above Earth s atmosphere. n astronaut works on the satellite and sees the sun rise over Earth. To the nearest mile, what is the distance from the astronaut to the horizon? (Hint: Earth s radius is about 4,000 miles.) a. 634 mi c. 630 mi b. 402,500 mi d. 397,500 mi 3. and are tangent to ñp. Find. a. = 11 2 c. = 2 b. = 1 2 d. = The circle graph shows the colors of automobiles sold at a car dealership. Find m(arc).

2 a. m(arc) = 36 c. m(arc) = 170 b. m(arc) = 10 d. m(arc) = Jenny s birthday cake is circular and has a 30 cm radius. Her slice creates an arc with a central angle of 120. What is the area of Jenny s slice of cake? Give your answer in terms of π. a. 300π cm 2 c. 150π cm 2 b. 10π cm 2 d. 3600π cm 2 6. Find the arc length of an arc with measure 130º in a circle with radius 2 in. Round to the nearest tenth. a. 4.5 in 2 c in 2 b. 2.3 in 2 d. 0.5 in 2 7. Find m(arc). a. m(arc) = 30 c. m(arc) = 20

3 b. m(arc) = 15 d. m(arc) = Meteorologists are planning the location of a new weather station. To optimize radar coverage, the station must be equidistant from three cities located at ( 16, 1), (1, 6), and (1, 18). What are the coordinates where the station should be built? a. ( 7.5, 2.5) c. ( 4.3, 4.3) b. ( 7, 9.5) d. ( 4, 6) 9. Identify the point (3, 300 ). a. M c. O b. N d. P 10. Graph r = 1.5. a. c.

4 b. d. Numeric Response 11. ñj has center J(4, 3) and radius 5. What is the measure, in degrees, of the arc with endpoints (9, 3) and (4, 2)? 12. What is the area of the sector, in square units, determined by an arc with a measure 75 in a circle with radius 10? Round to the nearest hundredth. 13. GHK subtends the semicircle. Find the measure of arc HK to the nearest degree. 14. In ñs, the measure of arc is 129 and m F = 36. Find the degree measure of arc.

5 15. Find the value of k. Round to the nearest hundredth. Matching Match each vocabulary term with its definition. a. chord b. arc c. point of tangency d. secant e. tangent of a circle f. interior of a circle g. common tangent h. sector of a circle i. exterior of a circle 16. the set of all points outside a circle 17. a line that is in the same plane as a circle and intersects the circle at exactly one point 18. a segment whose endpoints lie on a circle 19. a line that intersects a circle at two points 20. a line that is tangent to two circles Match each vocabulary term with its definition. a. adjacent arcs

6 b. arc c. arc length d. congruent arcs e. subtend f. minor arc g. intercepted arc h. half arc i. major arc 21. an arc of a circle whose points are on or in the exterior of a central angle 22. an unbroken part of a circle consisting of two points on the circle called the endpoints and all the points of the circle between them 23. an arc of a circle whose points are on or in the interior of a central angle 24. the distance along an arc measured in linear units 25. two arcs of the same circle that intersect at exactly one point

7 Geo - H11 Practice Test nswer Section MULTIPLE HOIE 1. NS: secant is a line that intersects a circle at two points. is the secant that intersects ñ. orrect! This is a tangent. secant is a line that intersects the circle at two points. This is a diameter and a chord. secant is a line. This is a radius. secant is a line that intersects the circle at two points. PTS: 1 IF: asic REF: Page 746 OJ: Identifying Lines and Segments That Intersect ircles NT: e TOP: 11-1 Lines That Intersect ircles 2. NS: Step 2 raw a sketch. Let be the center of Earth, F be the satellite, and H be a point on the horizon. FH is tangent to ñ at H, so FH H because a line tangent to a circle is perpendicular to the radius at the point of tangency. This means ΔHF is a right triangle. Use the Pythagorean Theorem to find the length of FH. Step 3 Solve. F = 50 mi F = + F = 4, = 4050 mi F 2 = FH 2 + H 2 Pythagorean Theorem (4,050) 2 = FH 2 + (4, 000) 2 Substitute 4,050 for F and 4,000 for H. 402, 500 FH 2 Subtract (4, 000) 2 from both sides. 634 mi FH Take the square root of both sides. orrect! Take the square root of this result. Round to the nearest mile, not nearest ten miles. dd 50 mi to 4,000 mi to obtain the hypotenuse of a right triangle. Using 4,000

8 mi as one leg of the right triangle, use the Pythagorean Theorem to find the distance to the horizon. PTS: 1 IF: verage REF: Page 749 OJ: Problem-Solving pplication NT: e TOP: 11-1 Lines That Intersect ircles 3. NS: = Theorem: If two segments are tangent to a circle from the same exterior point, then the segments are congruent. 3y + 4 = 11y Substitute. 4 = 8y Subtract 3y from both sides. y = 1 2 = 3ÊÁ Ë 1 2 ˆ + 4 Substitute. = 11 2 Simplify. ivide both sides by 2. orrect! Substitute this value for y and solve for segment. heck your algebra. If two segments are tangent to a circle from the same exterior point, then the segments are congruent. PTS: 1 IF: verage REF: Page 750 OJ: Using Properties of Tangents TOP: 11-1 Lines That Intersect ircles 4. NS: m(arc) = m P m(arc) = 0.10(360 ) m P is 10% of 360. m(arc) = 36 NT: e Theorem: The measure of a minor arc is equal to the measure of its central angle. orrect! The measure of a minor arc is equal to the measure of its central angle. The measure of a minor arc is equal to the measure of its central angle. The measure of a minor arc is equal to the measure of its central angle. PTS: 1 IF: verage REF: Page 756 OJ: pplication NT: e TOP: 11-2 rcs and hords 5. NS:

9 = πr 2 ÊÁ Ë m ˆ 360 Formula for area of a sector = π(30) 2 ÊÁ Ë 120 ˆ 360 Substitute the given values. = 300π cm 2 Simplify. orrect! Use the formula for finding the area of a sector. Use the formula for finding the area of a sector. The area of a sector is equal to pi times radius squared times the measure of the arc divided by 360 degrees. PTS: 1 IF: verage REF: Page 765 OJ: pplication NT: h TOP: 11-3 Sector rea and rc Length 6. NS: m L = 2πrÊ Ë Á 360 ˆ Formula for arc length 130 = 2π(2) Ê Ë Á 360 ˆ Substitute. = 13 9 π in in 2 Simplify. orrect! Use the formula for finding the distance along an arc. The arc length is equal to 2 times pi times the radius times the measure of the arc divided by 360 degrees. Use the formula for finding the distance along an arc. PTS: 1 IF: verage REF: Page 766 OJ: Finding rc Length NT: e TOP: 11-3 Sector rea and rc Length 7. NS: Inscribed ngle Theorem m = 1 2 m(arc)

10 15 = 1 2 m(arc) Substitute 15º for m. m(arc) = 30 Multiply both sides by 2. orrect! Use the Inscribed ngle Theorem. The measure of an inscribed angle is half the measure of its intercepted arc. The measure of the inscribed angle is half the measure of the intercepted arc, not twice the measure of the intercepted arc. PTS: 1 IF: asic REF: Page 773 OJ: Finding Measures of rcs and Inscribed ngles TOP: 11-4 Inscribed ngles 8. NS: Step 1 Plot the 3 points. NT: e Step 2 onnect,, and to form a triangle. Step 3 Find a point that is equidistant from the 3 points by constructing the perpendicular bisectors of two of the sides of Δ. The perpendicular bisectors intersect in a point that is equidistant from,, and.

11 The intersection of the perpendicular bisectors is at the point P( 4, 6). P is the center of the circle that passes through,, and. Find the perpendicular bisectors of the sides connecting the points. The center is the intersection point of the perpendicular bisectors. Find the perpendicular bisectors of the sides connecting the points. The center is the intersection point of the perpendicular bisectors. Find the perpendicular bisectors of the sides connecting the points. The center is the intersection point of the perpendicular bisectors. orrect! PTS: 1 IF: verage REF: Page 801 OJ: pplication NT: e TOP: 11-7 ircles in the oordinate Plane 9. NS: Step 1 Measure 300 counterclockwise from the polar axis. Step 2 Locate the point on the ray that is 3 units from the origin.

12 orrect! Measure 300 degrees counterclockwise from the polar axis. Measure 300 degrees counterclockwise from the polar axis. Measure 300 degrees counterclockwise from the polar axis. PTS: 1 IF: verage REF: Page 809 OJ: 11-Ext.3 Plotting Polar oordinates oordinates 10. NS: Make a table of values and plot the points. TOP: 11-Ext Polar θ r Make a table of values and plot the points. orrect! Make a table of values and plot the points. Make a table of values and plot the points. PTS: 1 IF: verage REF: Page 809 OJ: 11-Ext.4 Graphing Polar Equations TOP: 11-Ext Polar oordinates NUMERI RESPONSE 11. NS: 90 PTS: 1 IF: dvanced TOP: 11-2 rcs and hords 12. NS: PTS: 1 IF: dvanced TOP: 11-3 Sector rea and rc Length

13 13. NS: 143 PTS: 1 IF: dvanced TOP: 11-4 Inscribed ngles 14. NS: 57 PTS: 1 IF: verage TOP: 11-5 ngle Relationships in ircles 15. NS: 2.29 PTS: 1 IF: verage TOP: 11-6 Segment Relationships in ircles MTHING 16. NS: I PTS: 1 IF: asic REF: Page 746 TOP: 11-1 Lines That Intersect ircles 17. NS: E PTS: 1 IF: asic REF: Page 746 TOP: 11-1 Lines That Intersect ircles 18. NS: PTS: 1 IF: asic REF: Page 746 TOP: 11-1 Lines That Intersect ircles 19. NS: PTS: 1 IF: asic REF: Page 746 TOP: 11-1 Lines That Intersect ircles 20. NS: G PTS: 1 IF: asic REF: Page 748 TOP: 11-1 Lines That Intersect ircles 21. NS: I PTS: 1 IF: asic REF: Page 756 TOP: 11-2 rcs and hords 22. NS: PTS: 1 IF: asic REF: Page 756 TOP: 11-2 rcs and hords 23. NS: F PTS: 1 IF: asic REF: Page 756 TOP: 11-2 rcs and hords 24. NS: PTS: 1 IF: asic REF: Page 766 TOP: 11-3 Sector rea and rc Length 25. NS: PTS: 1 IF: asic REF: Page 757 TOP: 11-2 rcs and hords