SURPRISE EVALUATION EXAM 02

Multiple Choice
Identify the choice that best completes the statement or answers the question.

1) Ten less than four times a certain number is 14. Determine the number.
A) 6 B) 7 C) 8 D) 9

2) Find the area of a regular pentagon whose side is 25 m and apothem is 17.2 m
A) 1075 sq. m B) 1085 sq. m C) 1080 sq. m D) 1095 sq. m

3) The area of a circle is 89.42 sq. inches. What is the length of the side of a regular hexagon inscribed in a circle?
A) 5.533 in. B) 5.335 in. C) 6.335 in. D) 7.335 in.

4) A trapezoid has an area of 36 sq. m and an altitude of 2 m. Its two bases have ratio of 4:5. What is the lengths of
the bases?
A) 12, 15 B) 7, 11 C) 8, 10 D) 16, 20

5) The sides of a triangle are 5, 8, 10, respectively. Find the lengths of the medians.
A) 10.703, 8.819, 6.416 B) 9.703, 7.819, 5.416 C) 7.703, 5.819, 3.516 D) 8.703, 6.819, 4.416

6) Given a sphere of a diameter, d. What is the percentage increase in its diameter when the surface area is
increases by 21%?
A) 5% B) 10% C) 21% D) 33%

7) Find the area of a regular octagon inscribed in a circle of radius 10 cm.

A) 148.91 cm2 B) 186.48 cm2 C) 166.24 cm2 D) 282.24 cm2

8) Supplementary chords are two chords which join a point on the circle to the endpoints of a diameter.
The supplemental chords subtend a/an ____ angle.
A) acute B) right C) obtuse D) reflex

9) A chord is 24 cm long and its midpoint is 8 cm from the midpoint of its shorter arc. Find the radius of the circle.
A) 14 B) 15 C) 13 D) 16

10) As the area of the circle increases, the ratio of its circumference to its diameter
A) increases B) remains constant C) decreases D) will be equal to 1

11) Formed by intersection of rays from one point reflected or refracted from a curvature surface.
A) Envelop B) Caustic C) Evolute D) Pencil

12) Find the area of a quadrilateral have sides 12 m, 20 m, 8 m, and 16.97 m if the sum of the opposite angles is
equal to 2250, find the area of the quadrilateral
A) 100 sq. m B) 124 sq. m C) 168 sq. m D) 158 sq. m

13) the apothem of a polygon is ___ of its inscribed circle.

A) radius B) circumference C) diameter D) length

14) A ____ of a circle in the figure bounded by two radii and the intercepted arc.
A) major arc B) minor arc C) segment D) sector
15) The face of a regular dodecahedron is a
A) square B) pentagon C) hexagon D) triangle

16) Find the area of zone of sphere of radius 20 cm if the altitude of the zone is 7 cm.
A) 208 ? sq. cm B) 280 ? sq. cm C) 802 ? sq. cm D) 820 ? sq. cm

17) Determine the volume of a right truncated triangular prism with the following definitions: let the corners of the
triangular base be defined by A, B and C. The length of AB = 10 ft., BC = 9 ft., and CA = 12 ft. The sides A, B and
C are perpendicular to the triangular base and have the height of 8.6 ft, 7.1 ft, 5.5 ft, respectively.
A) 413 sq. ft B) 311 sq. ft C) 313 sq. ft D) 391 sq. ft

18) A regular pentagon has sides of 20 cm. An inner pentagon with sides of 10 cm is inside and concentric to the
larger pentagon. Determine the area inside and concentric to the larger pentagon but outside of the smaller
pentagon.
A) 430.70 sq. cm B) 573.26 sq. cm C) 473.77 sq. cm D) 516.14 sq. cm

19) Determine the area of a regular 6-star polygon if the inner regular hexagon has 10 cm sides.
A) 441.66 sq. cm B) 467.64 sq. cm C) 519.60 sq. cm D) 493.62 sq. cm

20) How many times do the volume of a sphere increases if the radius is doubled?
A) 4 times B) 2 times C) 6 times D) 8 times

21) A circle whose radius is 10 cm is inscribed inn a hexagon, find hte area of the hexagon.
A) 346 B) 364 C) 634 D) 436

22) The face of a regular icosahedron is a

A) square B) pentagon C) hexagon D) triangle

23) Determine the area of the quadrilateral shown, OB = 80 cm, AO = 120 cm, OD = 150 cm and ? = 250
A) 2721.66 sq. cm B) 2271.66 sq. cm C) 2172.66 sq. cm D) 2217.66 sq. cm

24) The volume of the frustum of a cone which is 25 cm high and whose base radii are 7.5 cm annd 5 cm respectively is:
A) 3181 B) 3802 C) 3109 D) 8311

25) Prisms are named according to their

A) diagonals B) sides C) vertices D) bases

26) A swimming pool is constructed in the shape of two partially overlapping identical circles. Each of the circles has a
radius of 9 m and each circle passes through the center of the other. Find the area of the swimming pool.
A) 380 sq. m B) 390 sq. m C) 400 sq. m D) 410 sq. m

27) The angle of a sector is 300 and the radius is 15 cm. What is the area of the sector in sq. cm?
A) 59.8 B) 89.5 C) 58.9 D) 85.9

28) In a circle of a diameter of 10 m, a regular five-pointed star touching its circumference is inscribed. What is the
area of that part not covered by the star?
A) 40.5 sq. m B) 45.5 sq. m C) 50.5 sq. m D) 55.5 sq. m

29) A bookstore purchased a best selling price book at P 200.00 per copy. At what price should this book be sold so
that giving a 20% discount, the profit is 30%?
 A) P 450 B) P 500 C) P 357 D) P 400

30) A man 38 years old has a son of ten years old. In how many years will the father be three times as old as his
son?
A) 2 B) 3 C) 4 D) 5

31) It is a polyhedron of which two faces are equal polygons in parallel planes and the other faces are
parallelograms.
A) tetrahedron B) prism C) frustum D) prismatoid

32) How many sides has a polygon if the sum of its interior angles equals the sum of its exterior angles?
A) 3 B) 6 C) 4 D) 5

33) A portion of the surface of a sphere included between two parallel planes.
A) Spherical excess B) Spherical segment C) Zone D) Lune

34) Two pipes running simultaneously can fill a certain tank l in 6 hrs. If both pipes run for 3 hrs, and the first pipe
is shut off, it requires 4 hrs more for the second pipe to fill the tank . How long does it take each pipe running
separately to fill the pool.
A) 8 & 34 days B) 12 & 18 days C) 10 & 25 days D) 8 & 24 days

35) A circle of radius R has a curvature of

A) R2 B) 1/R C) 2R D) sqrt(r)?

36) Each side of a cube is increased by 1%. By what percent is the volume of the cube increased?
A) 1.21% B) 2.8% C) 3.03% D) 3.5%

37) Find the area of a sector of a circle of radius 6 and a central angle of 60 degrees.
A) 16.72 B) 18.85 C) 20.12 D) 14.83

38) Jojo bought a second hand Betamax VCR and then sold it to Rudy at a profit of 40%. Rudy then sold the VCR to
Noel at a profit of 20%. If Noel paid P 2,856 more than it cost to Jojo, how much did Jojo paid for the unit?
A) P 4,000 B) P 4,100 C) P 4,200 D) P 4,300

39) The area of a triangle is 8346 sq. m and two of its interior angles are 37025’ and 56017’. What is the length of the
longest side?
A) 171.5 m B) 181.5 m C) 191.5 m D) 200.5 m

40) How many edges are there in .a dodecagon?

A) 6 B) 12 C) 30 D) 8

41) The arc length equal to the radius of the circle is called
A) radian B) quarter sector C) sector D) semicircle

42) Another term for gon.

A) Grad B) Mil C) Centesimal degree D) A and C

43) One-fourth of a great circle is called

A) cone B) sector C) quadrant D) arc

44) Each angle of regular dodecagon is equal to

 A) 135 B) 150 C) 125 D) 105

45) Given two solids and a plane. Supposed that every plane parallel to the given plane intersecting one
of the two solids, also intersects the other and gives cross sections with the same area, then the two
solids have the same volume. This is known as the.
A) unit postulate B) plane postulate C) parallel postulate D) cavalieri’s postulate

46) If R is the radius of the sphere and h is the distance between two parallel plane, the area of the
zone is
A) 2pi*Rh B) 4pi*Rh C) rh2(3R-h)/3 D) 4pi*(R-h)

47) What is the angle of pi and less than 2pi?

A) straight line B) obtuse angle C) oblique angle D) acute angle

48) Compute the lateral surface area of the cone having a slant height of 5 cm and a diameter of 6 cm
A) 38.86 cm2 B) 47.12 cm2 C) 30.24 cm2 D) 25.64 cm2

49) What is the value in degrees of 1 radian?

A) 90° B) 57.3° C) 60° D) 33°

50) A rhombus has diagonals of 32 and 20 inches. Determine its area.

A) 360 sq. in B) 280 sq. in C) 320 sq. in D) 400 sq. in

51) Find the area of a quadrilateral having sides AB = 10 cm, BC = 5 cm, CD = 14.14 cm and DA = 15 cm, if the sum
of the opposite angles is equal to 2250
A) 96 sq. m B) 100 sq. m C) 94 sq. m D) 98 sq. m

52) If an arc length is 12 m subtends a central angle A in a circle of radius 3, find the measure of A in terms of radian.
A) 3 B) 4 C) 5 D) 6

53) Two sides of a triangle are 13 and 21, respectively, and its area is 126 sq. units. Find the third side.
A) 40, 48.6 B) 30, 38.6 C) 10, 18.6 D) 20 , 28.6

54) The center of the inscribed circle of a triangle is known as known as _____ of the triangle.
A) circumcenter B) incenter (correct) C) excenter D) orthocenter

55) What is the area in sq. m of the zone of a spherical segment having a volume of 1470.265 cu. M if the diameter of
the sphere is 30 m?
A) 465.5 sq. m B) 565.5 sq. m C) 665.5 sq. m D) 656.5 sq. m

56) A circle having an area of 452 sq. m is cut into two segments by a chord which is 6 m from the center of the circle.
Compute the area of the bigger segment.
A) 354.89 sq. m B) 363.68 sq m C) 378.42 sq m D) 383.64 sq m

57) Which of the following is NOT a property of a circle?

A) Through 3 points not in a straight lines only one circle can be drawn. B) A tangent to a circle is
perpendicular to the radius at the point of tangency and conversely. C) An inscribed angle is
measured by one half of the Intercepted arc. D) The arcs of two circles subtended by equal central
angles are always equal.

58) If x varies directly as y and inversely as z, and x=14 when y=7 and z=2, find the value of x when y=16 and z=4.
A) 14 B) 4 C) 16 D) 6
59) A polyhedron having bases two polygons in parallel planes and for lateral faces triangles or
trapezoids with one side lying on the other base of the polyhedron.
A) Pyramid B) Cone C) Prismatoid D) Truncated prism

60) Given a sphere of a diameter, d. What is the percentage increase in its volume when the surface area is increases
by 21%?
A) 5% B) 10% C) 21% D) 33%

61) A rectangle ABCD which measures 18 cm by 24 cm. is folded once, perpendicular to diagonal AC, so that the
opposite vertices A and C coincide. Find the length of the fold.
A) 20.5 cm B) 21.5 cm C) 22.5 cm D) 23.5 cm

62) The distance between the centers of the three circles which are mutually tangent to each other externally are 10,
12 and 14 units. The area of the largest circle is
A) 72π B) 23π C) 64π D) 16π

63) Find the area in sq. cm of a regular octagon inscribed in a circle of radius 10 cm?
A) 283 B) 289 C) 298 D) 238

64) The volume of a circular cylinder is equal to the product of its base and altitude
A) axiom B) postulate C) theorem D) corollary

65) Body or space bounded by surface every point of which is equidistant from a point within.
A) Circle B) Sphere C) Spheroid D) Ellipsoid

66) Find the area of a regular octagon inscribed in a circle whose radius is 10 cm.
A) 283 B) 229 C) 883 D) 829

67) A oblique-angled parallelogram with four sides equal is called

A) rhombus B) diamond C) lozenge D) all of the above

68) Find the difference of the area of the square inscribed in a semi-circle having a radius of 15 m. The base of the
square lies on the diameter of the semi-circle.
A) 171.5 sq. cm B) 172.5 sq. cm C) 173.5 sq. cm D) 174.5 sq. cm

69) Six times the middle digit of a three-digit number is the sum of the other two. If the number is divided by the
sum of its digits, the answer is 51 and the remainder is 11. If the digits are reversed, the number becomes
smaller by 198. Find the number.
A) 725 B) 275 C) 752 D) 572

70) Compute the weight of a piece of lumber 400 mm by 600mm, 6.00 m long, if the lumber weights 960 kg/m3.
A) 1,324.8 kg B) 1,382.4 kg C) 1,283.4 kg D) 1,832.4 kg

71) Two perpendicular chords both 5 cm from the center of a circle divide the circle into four parts. If the radius of the
circle is 13 cm, find the area of the smallest part.
A) 30 sq. cm B) 31 sq. cm C) 32 sq. cm D) 33 sq. cm

72) The area of a regular hexagon inscribed in a circle of radius 1 is

A) 1.316 B) 2.945 C) 2.598 D) 3.816
73) Each of the faces of a regular hexahedron is a
A) square B) triangle C) rectangle D) hexagon

74) A regular hexagon is inscribed in a circle whose diameter is 20 m. Find the area of the 6 segments of the circle
formed by the sides of the hexagon.
A) 36.45 sq. m B) 63.54 sq. m C) 45.63 sq. m D) 54. 36 sq. m

75) A line segment that is divided into two segments, a greater a and a smaller b such that the length of
a+b is to a and a is to b. such division is known as
A) Golden segment B) golden ratio C) golden proportion D) all of the above

76) A man is three times as old as his son. In ten years, he will be twice as old as the son. How old was the father
seven years ago?
A) 25 years old B) 18 years old C) 23 years old D) 28 years old

77) The arc of a sector is 9 units and its radius is 3 units. What is the area of the sector in square units?
A) 12.5 B) 13.5 C) 14.5 D) 15.5

78) A sphere having a diameter of 30 cm is cut into 2 segments. The altitude of the first segment is 6 cm. What is the
ratio of the area of the second segment to that of the first?
A) 4:1 B) 3:1 C) 2:1 D) 3:2

79) A Solid cut of a given solid by two non parallel planes is called
A) frustum B) prism C) truncated prism D) prismatoid
SURPRISE EVALUATION EXAM 02
Answer Section

MULTIPLE CHOICE

1) A

2) A

3) B

4) D

5) D

6) B

7) D

8) B

9) C

10) B

11) B

12) C

13) A

14) D

15) B

16) B

17) B

18) D

19) C

20) D

21) A
22) D

23) A

24) C

25) D

26) D

27) C

28) C

29) C

30) C

31) B

32) C

33) D

34) D

35) B

36) C

37) B

38) C

39) B

40) C

41) A

42) D

43) C

44) B

45) D
46) A

47) C

48) B

49) B

50) C

51) B

52) B

53) D

54) B

55) B

56) B

57) D

58) C

59) C

60) D

61) C

62) C

63) A

64) C

65) B

66) A

67) D

68) C

69) A
70) B

71) B

72) C

73) A

74) D

75) B

76) C

77) B

78) A

79) C