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Form 3 Revision Questions and Answers on Variation
Given that x varies directly as the square of y and x=2 when y=1,find x when y=4
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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.
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
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.
4.
Given that x varies directly as the square of y and x=2 when y=1,find x when y=4
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
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
7.
The sides of a square are decreased by 5%.By what percentage is the area decreased.
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.
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.
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#.
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%.
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#.
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.
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.
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%.
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.
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%
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.
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.
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.
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.
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.
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.
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
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.
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,
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.
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.
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
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.
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.
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