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Punjab (PTB) · Quarter book test · Free

1st Year Mathematics 3rd Quarter Book Paper

40 marks · 1 hour · 28 questions. Covers: 4 chapters (UNIT 9: Division of Polynomials to UNIT 12: Limit and Continuity).

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1st Year Mathematics 3rd Quarter Book Paper

1st Year · Mathematics · Punjab (PTB)

Name: ____________Roll No: ________Class/Section: ________Date: ________Total marks: 40Time: 1 hour

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

  1. Period of 2 cos 3x is equal to:

    3. 2

    4. None of these

  2. Sin 196o =......:

    1. Sin 16o

    2. Cos 33o

    3. Cos 16o

    4. -Sin 16o

    1. e-1

    2. e-1/2

    3. e2

    4. e3

  4. If x-a is factor of f(x) then f(x)=0, x=a is called:

    1. Root

    2. Factor

    3. Polynomial

    4. Degree

  5. Period of  its:

    2. 4

    3. 2

    4. 8

  6. =?

    1. Tan 

    2. - tan 

    3. - tan 

    4. Cot 

  7. ......:

  8. Synthetic division is a process of ......:

    1. Addition

    2. Multiplication

    3. Subtraction

    4. Division

  9. The trigonometric function are periodic so their curves repeat after a ......:

    1. Fixed interval

    2. Not fixed interval

    3. Both a and b

    4. None of these

  10. :

    1. Sin 

    2. Cot 

    3. - Cot 

    4. Tan 

    1. 40

    2. 60

    3. 80

    4. 120

  12. x3-3x2+2x-6 has factor:

    1. x-4

    2. x-3

    3. x+3

    4. x+2

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

  1. Find the maximum and minimum values of the following function:

  2. Without using the table, find the value of: cos (-240o).

  3. The value of an investment grows according to the formula for continuous compounding A(t) = Poert, where Po is the initial principal, r is the annual interest rate, and t is the time rate in years. What happens to the value of the investment as . 

  4. When the polynomial 4x4+2x3+kx2+13 is divided by x+1, the remainder is 16. Find the value of k.

  5. Find the maximum and minimum values of the following function:

  6. If are the angles of a triangle ABC, then prove that:

  7. The apparent brightness B(d) of a star decreases as the distance from Earth increases following the inverse square law , where L is the star's luminosity. Find the limit of the brightness as .

  8. Use factor theorem to find the values of a and b if -2 and 2 are the roots of the polynomial 2x3+4x2+ax+b.

  9. Determine whether the following functions are even, odd or neither odd nor even:

  10. Find distance between the following point: P(cos x, cos y), Q (sin x , sin y)

  11. A company weekly sales (in thousands) follow the function . What is the limit of S(t) as  and what does it represent?

  12. Find the remainder without performing division when f(x)=x4+x3+x2+1 is divided by x+1.

Q3. Long questions (Attempt any 3 of 4 · 3 × 4 = 12)

  1. A retailer company has developed a polynomial regression model to predict weekly product demand: D(w)=w3-2w2+5w-4, where D(w) represent predicted demand (in units) and w is the week number. Use the demand is 22 units, calculated the prediction error.

  2. Evaluate the following limit:

  3. Prove that:

  4. A signal process system has a transfer function . Find the zero(s) of the transfer function by using factor theorem.