Questions
 P varies as the square of R. R. varies as the square of T. When P = 18, R = 3 and T = 5. Express P in terms of T hence find P when T = 10.
 Make r the subject of the formula.
 X varies as the cube of Y and inversely as square root of Z, X = 6 when Y = 3 and Z= 25.
 Find;
 An expression connecting X,Y,Z
 X when Y = 7 and Z = 9
 Y when X = 8 and Z = 16
 If Y is increased by 20% and Z is decreased by 36%, find the percentage increase in X
 Find;
 Make b the subject of the formula;
K = ab
b –a  A quantity Z varies directly as the square of x and inversely as the square root of y. If x increases by 20% and y decreases by 36%, find the percentage change in Z.
 A quantity P varies directly as the square of Q and inversely as quantity R. If P = 2 when Q = 4 and R=6, find P when Q = 8 and R= 4.
 B varies partly as the square of M and partly as the inverse of N. B,M and N are such that when M=2, N= ½ , B=96 while when M= 3 , N=2, B = 46. Write an expression for B in terms of M and N.
 Solve for x and y.
3x = 1
y  1
(2x + 2) : (y – 5) = 1 : 2  Make x the subject of the formula.
 Make d the subject of the formula given that:
 Z varies jointly as the square of x and inversely as the square of y. When x = 10 and
y = 4 then z = 15. Find z in terms of x and y
 Find the value of x when z = 8 and y = 12
 A quantity R partly varies as n and partly as the square root of n. When n = 9 R = 42 and when n = 25 R = 100. Find R when n = 16.
 Make b the subject of the formula.
 P varies party as Q and partly as the square root of Q. When Q = 4, P = 22 and when
Q = 9, P = 42. Find the value of P when Q = 25.  Make C the subject of the formula
b = √(kaC)
hence find the value of C when K= 1, a = 4 and b = 2  The velocity of water flowing through a pipe is inversely proportional to the square of the
radius of the pipe. If the velocity of the water is 30cm/s when the radius of the pipe is 2cm. Find the velocity of water when the radius of the pipe is 4cm.  Make x the subject of the formula.
 Three quantities x, y and z are such that x varies partly as y and partly as the inverse
of the square of Z . When x = 6, y = 3 and z= 2. When x = 8, y = 5 and z= 1. Find the
value of x when y = 10 and z= 8.  The resistance of an electrical conductor is partly constant and partly varies as the temperature. When the temperature is 20^{o}C, the resistance is 55 ohms. When the temperature is 28^{o}C, the resistance is 58 ohms. Find the resistance when the temperature is 60^{o}C
Answers

K ( ba) = ab
Kb – ka = ab
Kb – ab = ka
B(ka) = ka
B = ka
K –a 



 P = KQ + m√Q
22 = K (4) + m(2)……………(1)
42 = K(g) + n(3)……………(2)
22= 4K + 2m
42 = 9K + 3m
3(22) = 3(4K) + 3(2m)
2(42) = 2(9K) + 2(3)
66 = 12k + 6m
84 = 18K + 6m
18= 6k = k=3
22 = 4(3) + 2m
2212 = 2m
20 = 2m
M = 10
= 3(25) + 10(5)
= 75 + 50
= 125  V = 30, r = 2
K = Ur^{2}= 30 x 22 = 120
When r = 4
V = ^{120}/_{42} = 7.5m/s 
 R = m + nI
55 = M + 20n……(i)
58 = m + 28n…….(ii)
3 = 8n
n = ^{3}/_{8} = 0.375
55 = m + 60/8
m =55 7.5 => m = 47.5
R = 47. 5 + 60 X 3/8
R = 70 ohms
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