1. At a height h metres above the bottom of a river, the water
flows at a speed of v m/s , where v is directly proportional to h
to the power of 2. On the surface of the river, h = 2 and v =
0.24
(a) Form the equation that expresses v in terms of h.
v is proprotional to h^2, v=kH^2 where k is a sclar
constant.
when v=0.24, h^2 = 4, k = 0.06, therefore, v = 0.06
h^2
(b) Find the speed of the water 1 metre above the bottom of the
river.
since v=0.06h^2, v under 1 meter = 0.06 (3)^2 =
0.54
Note: Since h=2 on surface, under 1 m = h=3, please
write your answer clearly , you are not to follow my style of
writing as it will be presentation error to have more than 1 (=) on
a line
2. 25 men took 60 days to complete a building
project.
(a) How long will 12 men take to finish the same project?
Equation is men=k/days where k is a scalar constant,
others use qns 1 method.
(b) Given that the project
must be completed in 50days, how many more men will be
needed?
3. Given that F is inversely proportional to r to the power of 2
and that F = 2 when r = 4. Find
(a) The equation connecting F and r.
(b) The value of F when r = 12
(c) The value(s) of r when F = 1/2
4. The scale on a map is 2cm to 3km. The area of a park on the
map is 4.5cm to the power of 2.
(a) Express the scale of the map in the form 1 : n
Remember when it is 1:n. always both LHS RHS units must
be the same that is cm, for area scale, otherwise you have to
derive by squaring both side of factor scale (1:n) also called RF.
Or can square both side of scale.
RF= 1 : 150 000 (3km= 300000 cm, 2cm rep 300000cm, 1 cm
rep 150000cm
Area scale: 4cm^2 rep 9 km^2
(b) What length on the map represents an actual distance of
9.6km?
USE conversion: 1 cm rep 1.5 km to do
(c) Calculate the actual area of the park in km2. (km
square)
Area of park is 4.5/4 X 9 km^2 =10.125 Km^2
Cant put the 2 on top.
(d) Calculate the area, in cm2, of the park on another map which
has a scale of 1 : 50,000.
Find area scale in term of cm2 for new map, convert back
to km2, then divide 10.125 by new area scale in km2, can
find
Thanks for helping. I need to get back the hang of my sec two
work.
If not my O levels sure fail...
Nevermind, one day you understand easy liao. Like me Sec
2 EM 51/100. Prelim 1 85.9/100 for EM, 65/100 for AM
Oh yes for some which I put to the power of 2. Because I cant put
the number on top of the algebra.
Please use x^2 as far as possible