Formulae and variation Questions and Answers - Form 3 Topical Mathematics

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Questions

  1. 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.
  2. Make r the subject of the formula.
    formulae and variation 2q
  3. X varies as the cube of Y and inversely as square root of Z, X = 6 when Y = 3 and Z= 25.
    1. Find;
      1. An expression connecting X,Y,Z
      2. X when Y = 7 and Z = 9
      3. Y when X = 8 and Z = 16
    2. If Y is increased by 20% and Z is decreased by 36%, find the percentage increase in X
  4. Make b the subject of the formula;
    K = ab
         b –a
  5. 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.
  6. 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.
  7. 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.
  8. Solve for x and y.
    3x    = 1
    y - 1
    (2x + 2) : (y – 5) = 1 : 2
  9. Make x the subject of the formula.
    formulae and variation 9q
  10. Make d the subject of the formula given that:-
    formulae and variation 10q
  11. Z varies jointly as the square of x and inversely as the square of y. When x = 10 and
    y = 4 then z = 15.
    1. Find z in terms of x and y
    2. Find the value of x when z = 8 and y = 12
  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.
  13. Make b the subject of the formula.
    formulae and variation 13q
  14. 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.
  15. Make C the subject of the formula
    b = √(k-aC)
    hence find the value of C when K= 1, a = 4 and b = 2
  16. 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.
  17. Make x the subject of the formula.
    formulae and variation 17q
  18. 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.
  19. The resistance of an electrical conductor is partly constant and partly varies as the temperature. When the temperature is 20oC, the resistance is 55 ohms. When the temperature is 28oC, the resistance is 58 ohms. Find the resistance when the temperature is 60oC

Answers


  1. formulae and variation 1a

  2. formulae and variation 2a

  3. formulae and variation 3a
  4. K ( b-a) = ab
    Kb – ka = ab
    Kb – ab = ka
    B(k-a) = ka
    B =    ka 
           K –a


  5. formulae and variation 5a

  6. formulae and variation 6a

  7. formulae and variation 7a
  8.  
    formulae and variation 8a

  9. formulae and variation 9a

  10. formulae and variation 10a
  11.  
    formulae and variation 11a
  12.  
    formulae and variation 12a
  13.  
    formulae and variation 13a
  14. 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
    22-12 = 2m
    20 = 2m
    M = 10
    = 3(25) + 10(5)
    = 75 + 50
    = 125

  15. formulae and variation 15a
  16. V = 30, r = 2
    K = Ur2
    = 30 x 22 = 120
    When r = 4
    V = 120/42 = 7.5m/s

  17. formulae and variation 17a
  18.  
    formulae and variation 18a
  19. 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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