Laureta - Math10-Gat-Q2-W5

`MATHEMATICS 10
SUMMATIVE TEST and PERFORMANCE TASK

Quarter 2 Week 5
I. SUMMATIVE TEST
Multiple Choice. Read the statements carefully and select the letter of the best answer from the choices given.
Write your answer in your answer sheet.
1. A _______ to a circle is a line coplanar with the circle and intersects it in one and only one point. B
A. secant B. tangent C. perpendicular D. parallel
2. If a line is tangent to a circle, then it is perpendicular to the ____ drawn at the point of tangency. C
A. diameter B. chord C. radius D. angle
3. A common tangent is a line that is tangent to two _____ in the same plane. A
A. circles B. lines C. radius D. angles
4. Common ______tangents do not intersect the segment joining the centers of the two circles. B
A. internal B. external C. interior D. exterior
5. A _____ is a line that intersects a circle at exactly two points. A secant contains a chord of a circle. A
A. secant B. tangent C. perpendicular D. parallel
6. If two secants intersect in the exterior of a circle, then the measure of the angle formed is _____
the positive difference of the measures of the intercepted arcs. C
A. equal B. twice C. one-half D. not equal
7. A ______of a circle is the region bounded by an arc of the circle and the two radii to the endpoints of the arc. C
A. segment B. interior C. sector D. exterior
8. If two secant segments are drawn to a circle from an exterior point, then the product of the lengths of one
secant segment and its external secant segment is ____ to the product of the lengths of the other secant
segment and its external secant segment. A
A. Equal B. twice C. one-half D. not equal
9. Catherine designed a pendant. It is a regular hexagon set in a circle. Suppose the opposite vertices are
connected by line segments and meet at the center of the circle. What is the measure of each angle formed
at the center? C
A. 22.5° B. 45° C. 60° D. 72°
10. At a given point on the circle, how many lines can be drawn that is tangent to a circle? B
A. none B. one C. two D. three
11. What is the length of x in the figure on the right? A
3 4
A. 6 B. 7 C. 8 D. 9 x 8
12. In the figure on the right, m XY = 150 and m MN = 30. What is the m < XPY? A
A. 60 B. 90 C. 120 D. 180
13. The top view of a circular table shown below has a radius of 120 cm. Find the area of N P
the smaller segment of the table (shaded region) determined by a 60° arc. C M
A. (2400 π - 3600√ 3 ¿ cm2 X
B. 3600√ 3cm2 60°
C. 2400 π cm2 120 cm
Y
D. (14400 π - 3600√ 3 ¿ cm 2
14. In circle C on the right, m AB = 60, and its radius is 6 cm. What is the area of the shaded region in
terms of π? A A
A. 6 π cm C. 10 π cm 60
B. 8 π cm D. 12 π cm C 6 cm °B
15. A dart board has diameter of 40 cm and is divided into 20 congruent sectors. What is the area of each sector? A
A. 20 π cm2 B. 40 π cm2 C. 80 π cm2 D. 800 π cm2
For items no. 16 – 20. Consider the figure on the right.
16. Which line is tangent to circle A? A
A. Line DE C. line AD
B. line BC D. line EC E B
17. What is the point of tangency? D
A. Pt. A C. pt. B
B. Pt. C D. pt. D
A F
18. Which line is a secant to circle A? C D
A. Line DE C. line AD H
B. line BC D. line EC
C
19. What is the relation of line DE and line segment AD? B
A. Tangent C. parallel G
B. Perpendicular D. no relation
20. Which segment is bisected by line segment BC? B
A. Line segment AB C. line segment AD
B. Line segment FG D. line segment AC
For items no. 21-25. Consider the figure on the right.
21. What is the measure of < TSQ? B
A. 60 ° C. 80°
B. 70° D. 40°
140°
22. Which arc measures 80°? A
40°
A. Arc RS C. arc TS
B. Arc RT D. arc RST
23. What is the measure of <TPQ? D
A. 40° C. 80°
B. 60° D. 30°
24. What is the measure of arc RT? A
A. 140 ° C. 80°
B. 60° D. 30°
25. What is the measure of arc TRS? C
A. 280 ° B. 180° C. 220° D. 240°
II. PERFORMANCE TASK . Solve the problem.

A bicycle chain fits tightly around two gears. What is the distance between the centers of the gears if the radii of
the bigger and smaller gears are 9.3 inches and 2.4 inches respectively, and the portion of the chain tangent to the
two gears is 26. 5 inches long. ( HINT: Draw a right triangle and use the Pythagorean Theorem)
13.25 in.
9.3 in. 2.4 in.

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`MATHEMATICS 10

SUMMATIVE TEST and PERFORMANCE TASK

II. PERFORMANCE TASK . Solve the problem.

9.3 in. 2.4 in.

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