Math Practice Problems Module 5


1. The altitude of a cone is equal to half the diameter of the sphere circumscribed about it. How many times is the volume of the sphere greater than that of the cones?
  1. ¼
  2. 2
  3. 4
  4. ½
2. Determine the volume of the spherical segment given its altitude equal to 4 cm and the radius of the base circle equal to 8 cm.
  1. 252p/3 cm3
  2. 342p/3 cm3
  3. 342p/3 cm3
  4. 416p/3 cm3
3. A ball whose radius is equal to 30 cm is provided with a cylindrical hole bored along its diameter. Compute the volume of the remaining portion if the radius of the cylindrical hole is equal to 18 cm.
  1. 20, 582p cm3
  2. 15, 325p cm3
  3. 18, 432p cm3
  4. 21, 153p cm3
4. The edge of a cube is equal to a. Find the radius of the circumscribed sphere.
  1. 9/2
  2. 2a
  3. aÖ3/2
  4. 4Ö2a
5. The perimeter of a rectangle is 22. If one of the rectangles is doubled and the other tripled, the perimeter would be 32 more than the perimeter of the original rectangle. What are the sides of the rectangle?
  1. 6 and 5
  2. 8 and 7
  3. 10 and 9
  4. 12 and 11
6. if a polygon has 54 diagonals, then it must have,
  1. 12 sides
  2. 10 sides
  3. 11 sides
  4. 13 sides
7. A trench is constructed so that its cross section is a trapezoid the area of which is 21 sq.ft. if the shorter base is 2 times its height and the longer base is 5 ft longer than its height. Find the length of the shorter base.
  1. 3
  2. 4
  3. 5
  4. 6
8. if the acute angles of a right triangle are in the ratio 1:2, then the number of degrees in the small angles is:
  1. 30
  2. 20
  3. 45
  4. 90


9. The length of a wire fence around a circular flowerbed is 10p feet. The area of the flowerbed in sq.ft is
  1. 100p
  2. 50p
  3. 25p
  4. 5p
10. The perimeter of rectangle is 28m and its diagonal is 10 m. find the area of the rectangle.
  1. 48 sq.m
  2. 38 sq.m
  3. 10 sq.m
  4. 28 sq.m
11. This conic section may be defined as the loci of appoint that moves in a plane so that the sum of its distances from two fixed points of the planes is a constant.
  1. hyperbola
  2. circle
  3. parabola
  4. ellipse
12. The graph of r=a(1+cosq) is a
  1. cardioid
  2. lemniscate
  3. limacon
  4. rose
13. The parabola y= 4-x2 opens
  1. to the right
  2. to the left
  3. upward
  4. downward
14. The equation r=a is the polar equation of
  1. an ellipse
  2. a parabola
  3. a hyperbola
  4. circle
15. The graph of x3+y3-3axy = 0 is called the
  1. cycloid
  2. strophoid
  3. folium of Descartes
  4. cissoids of diocles
16. The intersection of the medians of a triangle whose vertices are (-6, -8), (3, -5) and (4, -2) are at
  1. (0, 0)
  2. (-1/3, -5)
  3. (-1/3, 5)
  4. 1/3, -5)
17. Find the equation of the line, which passes through the point (-2, 9) and the sum of its intercepts equal to 10.
  1. 2x+3y-23 = 0
  2. 3x+2y-12 = 0
  3. 3x-2y+24 = 0
  4. 2x-3y+31 = 0
18. A parabola may be defined as the set of points that are equidistant from a fixed point and a fixed line. The fixed point is called the focus and the fixed line is called the
  1. asymptote
  2. latis rectum
  3. directrix
  4. tangent line





19. Find x if the lilneL1 through (-1, 3) and (-3, -2) is perpendicular to the line L2 through (-7, 4) and (x, 0).
  1. 6
  2. 3
  3. 4
  4. 2
20. The general equation of the parabola whose axis is parallel to the y-axis is
  1. Ax2+Cy2+Dx+Ey+F=0
  2. Ax2+Dx+Ey+F=0
  3. Ax2+Cy2+Dx+Ey+F=0 where A=C have the same sign
  4. None of the above
21. The point P divides the line segment P1P2 in the ratio r=P1P0/P1P2=3/10. if P0=(9, 2) and (6, 8), find P2.
  1. (15, -13)
  2. (16, -12)
  3. (17, -10)
  4. (18, -9)
22. The length of the latus rectum of 4x2+9y2+24x+36y+36=0 is
  1. 2.76
  2. 2.67
  3. 2.65
  4. 2.65
23. Find the angle from the line through (-2, -3) and 94, 3) to the line through (-1, 6) and (3, -2).
  1. arctan(1/2)
  2. arctan(1/3)
  3. arctan 3
  4. arctan 2
24. The graph of y2=x is
  1. a parabola
  2. a pair of intersecting lines
  3. a pair of parallel lines
  4. none of the above
25. The slope of the line 3x-2y = 4 is equal to
  1. 3/2
  2. 2/3
  3. –3
  4. none of the above
26. If the eccentricity of a conic section is greater than one, then it is
  1. an ellipse
  2. a circle
  3. a hyperbola
  4. a parabola
27. If the lines L1 and L2 with slopes m12 and m2 respectively, are perpendicular to each other, then
  1. m2=0
  2. m1=m2
  3. m1m2=-1
  4. m1 = -m2
28. The vertex of a parabola y2-4x+6y+13 = 0 is at
  1. (-3, 1)
  2. (1, -3)
  3. (0, 0)
  4. (1, 1)



29. If a line sklants upward to the right, then its slope is
  1. zero
  2. positive
  3. negative
  4. infinity
30. The graph of 3x2 –y = y2+6x is
  1. an ellipse
  2. a parabola
  3. a circle
  4. a hyperbola
31. The lines 3x+4y-10 = 0 and 4x-3y-1 = 0 are
  1. parallel
  2. coincident
  3. bisecting
  4. perpendicular
32. The equation of the line passing through (2, 2) and (4, 8) is y = ________
  1. x-4
  2. 3x-4
  3. 3x+2
  4. x+2
33. Given the curve Ax2+By2+F=0, passes through the points (4, 0) and (0, 3). Find the value of A.
  1. 9
  2. 3
  3. 4
  4. 5
34. The center of the circle 3x2+3y2-6x+10y+2 = 0 is at
  1. (1, 1)
  2. (2, 1/3)
  3. (1, -5/3)
  4. (0, 0)
35. The eccentricity of the ellipse x2/5 +y2/7 = 1 is
  1. 1/7Ö14
  2. 2/3
  3. 5/7
  4. 1
36. If the coefficient of the terms in x2 and y2 are unequal and of the same sign, then the conic is:
  1. parabola
  2. hyperbola
  3. ellipse
  4. circle
37. _________is the locus of appoint the absolute value of the difference of whose distances from two distinct fixed points is a positive constant
  1. ellipse
  2. parabola
  3. hyperbola
  4. circle
38. The slope of asymptotes of x2/a2 + y2/b2 = 1 is
  1. ±b/a
  2. ±a/b
  3. ±1
  4. 1-b/a
39. The locus of the parabola (x-5)2 = -12(y-1) is
  1. (5, 1)
  2. (5, -2)
  3. (1, -2)
  4. (1, -1)




40. The straight line equation y = x-5 passes through the points
  1. (6, 3)
  2. (3, 0)
  3. (2, 2)
  4. (0, -4)
41. The rectangular coordinates of a point are (Ö3, 1). The polar coordinates of this point are
  1. (4, p/6)
  2. (2, p/6)
  3. (4, p/3)
  4. (Ö3, 1)
42. The rectangular form of r=4 tan2qsecq is
  1. 4x3=y2
  2. x3=4y2
  3. 4x2=y3
  4. x2=4y3
43. The equation of the line passing through (0, 4) and parallel to the x-axis is
  1. y=4
  2. 4x+y = 0
  3. y = x2+4
  4. 4y-2=x
44. The graphs of the equations y = 2x+3 and y= x2-x-1intersect at two point. The coordinates of these points are
  1. (0, 3), (2, 1)
  2. (-1, 1), (4, 11)
  3. (-1, 1), (-6, 3)
  4. (1, 5), (2, 5)
45. The area of the triangle whose vertices are (-3, 8)(7, 4) and (5, -1) is
  1. 40 sq. units
  2. 29 sq. units
  3. 30 sq. units
  4. 60 sq. units
46. The curve xy = a2 is
  1. hyperbola
  2. parabola
  3. circle
  4. ellipse
47. The distance between two points P1(2, -1) and P2(6, 2) is
  1. 4
  2. 5
  3. 6
  4. 3
48. The polar form of xy = 3(x+y) is
  1. r = 6csc20(cosq+sinq)
  2. r2=6scs4q
  3. r=2sin2q
  4. r2=3cos3q
49. A quadrilateral whose four sides are equal and parallel with no angle equal to aright angle is called a
  1. parallelogram
  2. parallelepiped
  3. trapezoid
  4. rhombus
50. The graph of an equation of the form r = a ±b cosq is a limacon with a loop if
  1. 1
  2. a/b = 1
  3. 0,
2 £ a/b

1 comment:

  1. ANSWERS ARE FOUND AT THE "ANSWERS" SECTION OF THE WEBSITE. SEE "LABELS" AT RIGHT HAND SIDE ---->

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