2nd Year Math Notes Chapter 2

Handwritten notes of 2nd Year Math Notes Chapter 2 written by Professor Asad Khalid Suib. These notes are very helpful in the preparation of 2nd Year Math Notes Chapter 2 for the students of Mathematics of the Intermediate and these are according to the paper patterns of all Punjab boards.

Summary and Contents:
Topics which are discussed in the notes are given below:
  • Important 2nd year math chapter 2 mcqs for Intermediate part-II students.
  • 1. The function f(x)=(x^2-1)/(x-1) is discontinuous at 
  • (a) 1 (b) 2                       (c) 3              (d) 4
  • 2. L.H.L of f(x)=|x-5|  at x=5 is
  • (a) 5 (b) 0                       (c) 2 (d) 4
  • 3. The change in variable x is called increment of x.It is denoted by δx which is
  • (a) +iv only (b) –iv only            (c) +iv or –iv   (d) none of these
  • 4. The notation dy/dx or df/dx is used by
  • (a) Leibnitz (b) Newton             (c)   Lagrange   (d)  Cauchy
  • 5. The notation f ̇(x) is used by
  • (a) Leibnitz (b) Newton                      (c) Lagrange                (d) Cauchy
  • Important 2nd year math ch 2 mcqs for Intermediate part-II students.
  • 6. The notation f^' (x) or y^' is used by
  • (a) Leibnitz (b) Newton              (c) Lagrange       (d)  Cauchy
  • 7. The notation Df(x) or Dy is used by
  • (a) Leibnitz (b) Newton              (c) Lagrange    (d) Cauchy 
  • 8. (lim)┬(x→a)⁡〖(f(x)-f(a))/(x-a)=〗
  • (a) f^' (x)  (b)  f^' (a)               (c)   f(0)     (d)  f(x-a)
  • 9. d/dx (x^n )=nx^(n-1) is called 
  • (a) Power rule            (b) Product rule (c)  Quotient rule     (d) Constant
  • Important 2nd year maths chapter 2 mcqs solved for Intermediate part-II students.
  • 10. The derivative of a constant function is
  • (a) one            (b)   zero               (c) undefined      (d)  None of these
  • 11. The process of finding derivatives is called 
  • (a) Differentiation   (b) differential   (c) Increment      (d) Integration
  • 12. If f(x)=1/x  ,then f^'' (a)=
  • (a) -2/(a)^3 (b)   -1/a^2 (c)    1/a^2       (d)   2/a^3   
  • 13. (fog)^' (x)=
  • (a) f'g'             (b)   f^' g(x)             (c)  f^' (g(x))g^' (x)   (d) cannot be calculated
  • Important 2nd year maths chapter 2 mcqs for Intermediate part-II students.
  • 14. d/dx (g(x))^n=
  • (a) n[g(x)]^(n-1) (b)  n[(g(x)]^(n-1) g(x)         (c) n[(g(x)]^(n-1) g^' (x)     (d)   [g(x)]^(n-1) g^' (x)
  • 15. d/dx (3x^(4/3) )=
  • (a) 4x^(2/3) (b)   4x^(1/3)              (c)   2x^(1/3) (d)   3x^(1/3)
  • 16. If x=at^2 and y=2at then dy/dx=
  • (a) 2/ya (b)    y/2a           (c)  2a/y              (d)    2/y
  • 17. d/dx (tan^(-1) x-cot^(-1) x)=
  • (a) 2/√(1+x^2 )   (b)   2/(1+x^2 )           (c) 0      (d)      (-2)/(1+x^2 )
  • 18. If Sin √x, then dy/dx is equal to
  • (a) (cos√x)/(2√x)    (b)     (cos√x)/√x (c)  cos√x      (d)     cosx/√x
  • Important 2nd year maths chapter 2 mcqs with answers for Intermediate part-II students.
  • 19. d/dx sec^(-1) x=
  • (a) 1/(|x|√(x^2-1))    (b)    (-1)/(|x|√(x^2-1)) (c)   1/(|x|√(1+x^2 )) (d)   (-1)/(|x|√(1+x^2 ))
  • 20. d/dx cosec^(-1) x=
  • (a) 1/(|x|√(x^2-1)) (b)   (-1)/(|x|√(x^2-1))  (c)    1/(|x|√(1+x^2 )) (d)   (-1)/(|x|√(1+x^2 ))
  • Important 2nd year math chapter 2 important questions for Intermediate part-II students.
  • The Derivative: In every day life we come across problems of the type:
  • How fast is the train many after 10 seconds?
  • At what rate is the population increasing?
  • What is the rate of change of profit when sales reach Rs 10,000?
  • What is the rate of change of profit when sales reach Rs 5000?
  • Important 2nd year math chapter 2 examples for Intermediate part-II students.
  • To answer such problems we need derivative.
  • Use of derivative in Daily Life: 
  • (1) Rate of flow of water?
  • (2) Rate of Increase of height of plant?
  • (3) Rate of change of Price in share market?
  • (4) Slope of Mountain?
  • (5) Cricket math run rate?
  • Important 2nd year math chapter 2 important long questions for Intermediate part-II students.
  • History: The ancient Greeks knew the concepts of area, volume and centroids etc. Which are related of area, volume and centroids etc. Which are related to Integral Calculus. Later on, in the Seventeeth centory "Sir Isaac Newton" an English Mathematician (1642 - 1727) and "Mathematician (1646 - 1716) considered the problem of Instantaneous rates of change.
  • Important 2nd year math exercise 2.1 solution pdf for Intermediate part-II students.
  • Some other definition of Derivative: In Mathematics, derivative is a way to show rate of change that is the amount by which a function is changing at one given point. OR (A function which tells us the slope of the line tangent to curve at any point.)
  • Important 2nd year math chapter 2 for Intermediate part-II students.
  • Geometrical Interpretation of Derivative: When we use the word slope means ( Rise over Run) or Vertical change over the horizental change), if we have a straight line we can find slope because we have two points anywhere on the line.
  • Important 2nd year math exercise 2.1 solved for Intermediate part-II students.
  • When we have to find the slope of curved graph. Let see we see that there is only one point but for finding slope we require two points.
  • Important 2nd year maths chapter 2 exercise 2.1 for Intermediate part-II students.
  • Important 2nd year maths chapter 2 exercise 2.2 for Intermediate part-II students.
  • Important 2nd year maths chapter 2 exercise 2.3 for Intermediate part-II students.
  • Important 2nd year maths chapter 2 exercise 2.4 for Intermediate part-II students.
  • Important 2nd year maths chapter 2 exercise 2.5 for Intermediate part-II students.
  • Important 2nd year maths chapter 2 exercise 2.6 for Intermediate part-II students.

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