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.
(b) Find the speed of the water 1 metre above the bottom of the river.
2. 25 men took 60 days to complete a building project.
(a) How long will 12 men take to finish the same project?
(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
(b) What length on the map represents an actual distance of 9.6km?
(c) Calculate the actual area of the park in km2. (km square) 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.
Thanks for helping. I need to get back the hang of my sec two work.
If not my O levels sure fail...
Oh yes for some which I put to the power of 2. Because I cant put the number on top of the algebra.
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