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Punjab (PTB) · Quarter book test · Free

2nd Year Mathematics 1st Quarter Book Paper

28 marks · 1 hour · 24 questions. Covers: UNIT 1: GRAPHICAL REPRESENTATION OF FUNCTIONS, UNIT 2: FURTHER DIFFERENTIATION, UNIT 3: INTEGRATION.

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2nd Year Mathematics 1st Quarter Book Paper

2nd Year · Mathematics · Punjab (PTB)

Name: ____________Roll No: ________Class/Section: ________Date: ________Total marks: 28Time: 1 hour

Q1. Multiple choice questions (Attempt all · 12 × 1 = 12)

  1. The value of a definite integral is always a:

    1. Family of functions

    2. Real number

    3. Variable quantity

    4. Imaginary number

  2. The logarithmic function y=loga x is continuous for:

    1. All x>0

    2. All real numbers

    3. All negative real numbers

    4. Integers only

  3. When finding the global extrema of a function on a closed interval [a,b], at which points should you first evaluate the function?

    1. Only at the point x=0

    2. Only at the midpoint of the interval

    3. At all critical points and endpoints of the interval

    4. At infinity

  4. What is the primary objective of using a trigonometric substitution in integration?

    1. To increase the degree of the polynomial

    2. To convert a definite integral into an indefinite one

    3. To eliminate the radical sign in the integrand

    4. To find the derivative of the function

  5. A sound has an intensity of  and a reference intensity of  Find the sound level in decibels (dB):

    1. 50 dB

    2. 60 dB

    3. 70 dB

    4. 80 dB

  6. Find for the parametric equations x=sin2 t and y= cos 2t:

    1. =-2

    2. =2

    3. = - tan t

    4. =- 4sint cot t

  7. The rule that corresponds to the Product Rule for differentiation is called:

    1. Substitution method

    2. Integration by parts

    3. Partial fractions

    4. Chain rule

  8. Which of the following simplifies to sech2 x?

    1. 1+tanh2x

    2. 1 - tanh2x

    3. coth2x - 1

    4. cosh x + sinh x

  9. Differentiation will be applied to identify which behavior of functions?

    1. ncreasing and decreasing functions

    2. Domain and range

    3. Periodic behavior

    4. Continuity and limits

  10.  What is the process of recovering a function F from its derivative f called?

    1. Differentiation

    2. Linearization

    3. Antidifferentiation

    4. Integration by parts

  11. The modulus or absolute value of any real number is always:

    1. Strictly negative

    2. Zero only

    3. Non-negative

    4. An integer

  12. What is the approximate value of the mathematical constant e used in the natural exponential function?

    1. 3.14159

    2. 2.71828

    3. 1.41421

    4. 1.61803

Q2. Short questions (Attempt any 8 of 12 · 8 × 2 = 16)

  1. Using the second derivative test, find local extreme values of the following function: 

  2. Is the following function is transcendental? 

  3. Evaluate the following integrals: 

  4. Find  if .

  5. Define the term "Shifting of Graphs".

  6. A patient receives an IV bolus dose of a drug. The concentration in the blood is modeled by  where t is the time in hours since that does was taken. the minimum effective concentraction (MEC) is 3 mg/L. The drug is considered effective if total AUC in a 24-hour period is at least 150 mg-h/L. Find the time T (in hours) when the concentration reaches the MEC.

  7. Find  if: 

  8. Solve the equation: 

  9. Evaluate the following: 

  10. Derive the formula for the derivative of the following function w.r.t. x: sec x

  11. Let . Find the function obtained after: a vertical stretch by factor 2.

  12. A patient is given an intravenous dose oof an antibiotic. The concentration in the bloodstream over time is modeled by:  where t is an hours. Find the total drug exposure (AUC) from t=0 to t=6 hours.