PPDC Lecture
Week 2
1.) The segment from (-1, 4) to (2, -2)
is extended three times its own length.
The terminal point is?
2.) The midpoint of the line segment
between (x, y) and (-2, 4) is (2, -1).
Find the coordinate, x and y.
3.) Find the area of triangle whose vertices
are A(-3, -1), B(5, 3) and C(2, -8)
4.) Find the distance from the point (2, 0)
to the line 3x+4y+9=0
5.) Find the slope of the line 3x+2y+5=0
6.) One line passes through the points (1, 9)
and (2, 6), another line passes through (3, 3)
and (-1, 5). The acute angle between the two
lines is:
7.) Find the shortest distance from the point (1, 2)
to a point on the circumference of the circle
defined by the equation x^2+y^2+10x+6y+30=0
8.) Determine the length of the chord common to
the circles x^2+y^2 = 64 and x^2+y^2-16x = 0.
9.) The vertex of the parabola y^2-2x+6y+3=0.
10.) The curve y = -x^2+x+1 opens:
11.) The area of the ellipse 9x^2+25y^2-36x189=0 is equal to?
12.) What is the radius of the sphere with center
at origin and which passes through the point
(8, 1, 6)?
13.) The graph y = (x-1)/(x+2) is not defined at:
14.) Point C(5, 7, z) and D(4, 1, 6) are 7.28 cm
apart. Find the value of z.
15.) Find the equation of the ellipse whose center
is at (-3, -1), vertex at (2, -1) and focus at (1, -1).
16.) If the edge of a cube is doubled, which of the
following is incorrect?
a. Lateral area will be quadrupled
b. the volume is increased 8 times
c. the diagonal is doubled
d. the weight is doubled
17.) The space diagonal of a cube is 4√3. Find its
volume.
18.) A trough has an open top 0.3 m by 6 m and closed
vertical ends which are equilateral triangles 30 cm on
each side. It is filled with water to half its depth. Find the
volume of the water in cubic meters.
19.) A frustrum of a pyramid has an upper base 100 m
by 10 m and a lower base of 80 m by 8 m. If the
altitude of the frustrum is 5 m, find its volume.
20.) A cylindrical gasoline tank, lying horizontally,
0.90 m in diameter and 3 m long is filled to a
depth of 0.60 m. How many gallons of gasoline
does it contain?
21.) A solid spherical steel ball 20 cm in diameter
is placed into a tall vertical cylinder containing
water, causing the water level to rise by 10 cm.
What is the radius of the cylinder?
22.) An open top cylindrical tank is made of a metal sheet
having an area of 43.82 sq. m. If the diameter is 2/3 the
height, what is the height of the tank?
23.) A cube of edge 25cm is cut by a plane containing two
diagonally opposite edges of the cube. Find the area of the
section thus formed in sq. cm.
24.) The volume of a right circular cone is 36pi. If its
altitude is 3, find its radius.
25.) What is the surface area of a sphere whose
volume is 36 cu. m?
26.) A sphere having a diameter of 30 cm is cut
into 2 segments. The altitude of the first segment is
8 cm. What is the ratio of the volume of the second
segment to that of the first?
27.) The corners of a cubical block touch the closed
spherical shell that encloses it. The volume of the box is 2744
cc. What volume in cc, inside the shell is not occupied by the
block?
28.) The distance between the center of the three circles
which are mutually tangent to each other externally are 10,
12, and 14 units. Find the area of the largest circle.
29.) The base of a right prism is a hexagon with one of each
side equal to 6 cm. The bases are 12 cm apart. What is the
volume of a right prism?
30.) If the lateral area of a cylinder circumscribed about a
sphere “A”, what is the surface area of the sphere?