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# Form 3 Revision Questions and Answers on Variation

Form 3 Revision Questions and Answers on Variation.

In this session, several question on variation will be answered with aid of video lessons. Questions on direct, inverse, joint and partial variation are covered.

Lessons (**31**) * SHARE*

- 1.
The force of attraction between two bodies varies inversely as the square of the distance between them. When the distance between them is 2 metres ,the force of attraction is 0.5 Newtons.Find the force when the distance between them is 0.4 metres.

4m 3s - 2.
Two variables p and q are such that p is directly proportional to x and q is inversely proportional to x.When x =2 their sum is 8 and when x =3 their sum is 7.Find the constants of proportionality

4m 42s - 3.
Three quantities P,Q and R are such that P varies directly as the square of Q and inversely as the square root of R.Given that Q increases by 5% and R decreases by 36%,find the percentage change in P.If P=6,when Q=12 and R=25 find the value of P when Q=15 and R=81.

11m 16s - 4.
Given that x varies directly as the square of y and x=2 when y=1,find x when y=4

1m 51s - 5.
The mass of a certain metal rod varies jointly as its length and the square of its radius .A rod 40 cm long and radius 5 cm has a mass of 6kg.Find the mass of a similar rod of length 25 cm and radius 8 cm

3m 52s - 6.
The frequency of vibration of a given string is directly proportional to the square root of the tension T and inversely proportional to the length l and to the diameter d.If T is increased by 50% and l is halved,Calculate the percentage change in the frequency

6m 18s - 7.
The sides of a square are decreased by 5%.By what percentage is the area decreased.

4m 14s - 8.
The electrical resistance ohms of a wire of a given length is inversely proportional to the square of the diameter of the wire,d mm.If R=2.0 ohms when d=3mm,find the value of R when d=4mm.

2m 55s - 9.
Three quantities P,Q and R are such that P varies directly as the square of Q and inversely as the square root to R (a)Given that P=20 when Q=5 and R=9, find P when Q=7 and R=25 (b)If Q is increases by 20% and R decreases by 36%, find the percentage increase in P.

9m 45s - 10.
The density of a solid spherical ball varies directly as its mass and inversely as the cube of its radius.When the mass of the ball is 500g and the radius is 5 cm , its density is 2g per cm3.Calculate the radius of a solid spherical ball of mass 540g and density of 10g per #cm^3#.

4m 44s - 11.
Three quantities t, x and y are such that t varies directly as x and inversely as the square root of y. Find the percentage decrease in t if x decrease by 4% when y increases by 44%.

5m 42s - 12.
Given that y is inversely proportional to #x^n# and k as the constant of proportionality ; a)(i)Write down a formula connecting y,x,n and k. (ii)If x=2 when y=12 and x=4 when y=3,write down two expressions for k in terms of n.Hence,find the value of n and k.
b).Using the values of n and k obtained in (a)(ii) above,find y when #x=5 1/3#.

9m 2s - 13.
Three variables p, q and r are such that p varies directly as q and inversely as the square of r.
(a)When p=9, q=12 and r=2.Find p when q=15 and r=5
(b)Express q in terms of p and r. (c) If p increased by 20% and r decreased by 10%, find: (i) A simplified expression for the change in q in terms of p and r (ii).The percentage change in q.

10m 23s - 14.
The quantities P, Q and R are such that P varies directly as Q and inversely as the square root of R. When P=8, Q=10 and R=16.Determine the equation connecting P,Q and R.

2m 40s - 15.
Three quantities R, S and T are such that R varies directly as S and inversely as the square of T. (a)Given that R= 480 when S=150 and T=5, write an equation connecting R,S and T (b)(i)Find the value of R when S=360 and T=1.5 (ii) Find the percentage change in R if S increases by 5% and T decreases by 20%.

8m 48s - 16.
Three quantities L, M and N are such that L varies directly as M and inversely as the square of N.Given that L=2 when M=12 and N=6,determine the equation connecting the three quantities.

1m 58s - 17.
Three quantities X,Y and Z are such that X varies directly as the square root of Y and inversely as the fourth root of Z .When X=64,Y=16 and Z=625. (a)Determine the equation connecting X, Y and Z (b)Find the value of Z when Y=36 and X=160. (c) Find the percentage change in X when Y is increased by 44%

1m 51s - 18.
A variable p varies directly as #t^3# and inversely as the square root of s .When t=2 and s=9,p=16.Determine the equation connecting p, t and s, hence find p when s=36 and t=3.

2m 59s - 19.
A quantity p varies inversely as the square of another quantity L. When P=0.625, L=4. Determine P when L=0.2.

2m 19s - 20.
For a lifting machine the effort E required to lift a load L is partly constant and partly varies as L. When L=2, E=#5 1/2# and when L=6,E=#6 1/2# .Determine the equation connecting E and L.

4m 54s - 21.
Two variables P and L are such that P varies partly as L and partly as the square root of L.Determine the relationship between P and L given that when L=16,P=500 and when L=25,P=800.

0m 0s - 22.
The volume V #cm^3# of a solid depends partly on #r^2# and partly on #r^3# where r cm is one of the dimensions of the solid. When r=1, the volume is #54.6cm^3# and when r=2,the volume is #226.8cm^3#. (a)Find an expression for V in terms of r. (b)Calculate the volume of the solid when r=4
(c) Find the value of r for which the two parts of the volume are equal.

9m 44s - 23.
A quantity T is partly constant and partly varies as the square root of S. (a)Using constants a and b , write down an equation connecting T and S. (b)If S=16 when T=24 and S=36 when T=32, find the values of the constants a and b.

4m 11s - 24.
The charge,C shillings per person for a certain seminar is partly fixed and partly inversely proportional to the total number N of people. (a)Write down an expression for C in terms of N. (b) When 100 people attend the charge is sh.8,700 per person while for 35 people the charge is sh 10,000 per person.Calculate the fixed charge.
(c)If a person had paid the full amount and does not attend ,the

10m 36s - 25.
Two variables A and B are such that A varies partly as B and partly as the square root of B. Given that A=30, when B=9 and A=16 when B=14,find A when B=36.

8m 32s - 26.
A quantity p is partly constant and partly varies inversely as a quantity q.Given that p=10 when q=1.5 and p=20 when q=1.25,find the value of p when q=0.5M,

5m 43s - 27.
The distance s metre of an object varies partly with time t second and partly with the square root of the time.Given that s=14 when t=4 and s=27 when t=9,write an equation connecting s and t.

4m 15s - 28.
The mass of wire m grams (g) is partly a constant and partly varies as the square of its thickness t mm.When t=2mm,m=40g and when t=3mm,m=65g.Determine the value of m when t=4mm.

4m 16s - 29.
In a uniformly accelerated motion the distance ,s metre, travelled in time t seconds varies partly as the time and partly as the square of the time. When the time 2 seconds ,the distance travelled is 80 metres and when the time is 3 seconds ,the distance travelled is 135 metres . (a)Express s in terms of t. (b)Find:
(i)The distance travelled in 5 second. (ii)The time taken to travel a distance of

10m 6s - 30.
The cost C, of producing n items varies partly as n and partly as the inverse of n. To produce two items it cost ksh 135 and to produce three items it costs ksh 140.Find: (a) The constant of proportionality and hence write the equation connecting C and n. (b) The cost of producing 10 items.
(c)the number of items produced at a cost of ksh 756.

9m 31s - 31.
A quantity p varies partly as the square of m and partly as n. When p=3.8,m=2 and n=-3.When p=-0.2,m=3 and n=2. (a) Find: (i)the equation that connect p, m and n (ii)the value of p when m=10 and n=4. (b)Express m in terms of p and n.
(c) If p and n are each increased by 10%,find the percentage increase in m correct to 2 decimal places.

13m 58s