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Punjab (PTB) · Chapter test · Free

1st Year Mathematics Chapter 13 TestUNIT 13: Differentiation

30 marks · 40 minutes · 21 questions. Covers: UNIT 13: Differentiation.

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1st Year Mathematics Chapter 13 Test

1st Year · Mathematics · Punjab (PTB)

Name: ____________Roll No: ________Class/Section: ________Date: ________Total marks: 30Time: 40 minutes

Q1. Multiple choice questions (Attempt all · 10 × 1 = 10)

  1. The derivative of equals ......:

  2.  is equal to:

    1. f(0)

    2. f'(a)

    3. f'(x)

    4. f'(0)

  3. What is the derivative of  with respect to x:

    2. 2x-1

    3. 1-2x

  4.  is equal to:

    1. n(axn-1+b)

    2. n(ax+b)

    3. naxn-1

    4. na(ax+b)n-1

    1. -xm-1

    2. -mx-m-1

    3. -xm-m+1

    4. -xm-1x

  7. Differentiate (x-1)(x+2)2:

    1. 2x(x+2)

    2. 2(x-1)(x+2)

    3. 2(x-1)

    4. 3x(x+2)

  8. =......

    1. f(a)

    2. f'(a+h)

    3. f'(x)

    4. f'(a)

  9. Derivative of  w.r.t x is.....:

    1. f'(g(x))

    2. f(g'(x))

    3. f[g(x)g'(x)

    4. f'[g(x)]g'(x)

Q2. Short questions (Attempt any 6 of 8 · 6 × 2 = 12)

  1. Find from principle, the derivatives of the following expressions w.r.t their respective independent variables: (3x-2)-2

  2. Find the derivative of the following function by definition: f(x)=c

  3. Find by definition, the derivatives w.r.t 'x' of the following function defined as:

  4. Find derivative of with respect to x.

  5. Find the derivative of  at x=8 from the first principle.

  6. The position of a car after t hours is given by: s(t)=2t3-3r2+t (in kilometres). Find the average velocity over the interval [1,4].

  7. The stress on a beam under a varying load is modeled by S(x)=500x-2x3. where S(x) is the stress in pascals (pa) and x is the distance (in metres) from the beam's fixed end. Find the rate of change of stress at x=5 metres.

  8. Differentiate with respect to x.

Q3. Long questions (Attempt any 2 of 3 · 2 × 4 = 8)

  1. Differentiate w.r.t 'x':

  2. The position of a car traveling along a straight highway is given by x(t)=30t2-4t3, where x(t) is the distance traveled in kilometres and t is the time in hours. Determine the car's acceleration at t=3 hours.

  3. An investment grows according to the function A(t)=1000(1+0.5t)3, where A(t) is the value of the investment and t is the time in years. What is the investment value after 8 years?