Calculus Generix Content - Calculus
HOME

EXAMS

JAMB

WAEC

CONTENTS

SIGN IN

JOIN NOW
"Calculus" question number distribution across years
loading...
Search "Calculus" on the following sites online
 
Mathematics index on skoool nigeria
 
JAMB questions for "Mathematics :: Calculus"
Q1

If y = (2x + 1)3, find dy/dx

A

6 (2x + 1)2

B

3 (2x +1)2

C

6 (2x + 1)

D

3 (2x + 1)

E

Answer: A

Calculus
Q2

If y = x sinx, find dy/dx

A

sin x - cos x

B

sin x + cos x

C

sin x - xcos x 

D

sin x + xcos x

E

Answer: D

Calculus
Q3

Find ∫ (sinx + 2)dx

A

-cosx + x2 + k

B

cos + x2 + k

C

-cosx + 2x + k

D

cosx + 2x + k

E

Answer: C

Calculus
Q4

Evaluate ∫sec² θ d θ

A

secθ tanθ + k

B

tan θ + k

C

2sec θ + k

D

sec θ + k

E

Answer: B

Calculus
Q5

The distance travelled by a particular from a fixed point is given as s = (t³ - t² - t + 5)cm. Find the minimum distance that the particle can cover from the fixed point.

A

2.3 cm

B

4.0 cm

C

5.2 cm

D

6.0 cm

E

Answer: B

Calculus
Q6

What value of x will make the function x (4 - x) a maximum?

A

4

B

3

C

2

D

1

E

Answer: C

Calculus
Q7

If s = (2 + 3t)(5t - 4), find ds/dt when t = 4/5 secs

A

0 units per sec

B

15 units per sec

C

22 units per sec

D

26 units per sec

E

Answer: C

Calculus
Q8

Evaluate ∫π/2-π/2 cos xdx

A

0

B

1

C

2

D

3

E

Answer: C

Calculus
Q9

Evaluate ∫21 (6x² - 2x)dx

A

16

B

13

C

12

D

11

E

Answer: D

Calculus
Q10

Find the minimum value of the function y = x(1 + x).

A

-1/4

B

-1/2

C

1/4

D

1/2

E

Answer: A

Calculus
Q11

Differentiate sin x- x cos x

A

x cos x

B

x sin x

C

-x cos x

D

-x sin x

E

Answer: B

Calculus
Q12

Determine the value of ∫π/20 (-2cos x) dx

A

-2

B

-1/2

C

-3

D

-3/2

E

Answer: A

Calculus
Q13

Integrate [(x² - √x)/x] with respect to x

A

x²/2 - 2√x + k

B

[2 (x² - x)/3x] + k

C

x²/2 - √x + k

D

[(x² - √x) / x²] + k

E

Answer: C

Calculus
Q14

Find the value of x for which the function f(x) = 2x³ - x² - 4x + 4 has a maximum value

A

2/3

B

1

C

-2/3

D

-1

E

Answer: B

Calculus
Q15

Differentiate (cos θ - sin θ)2 with respect to θ.

A

-2 sin 2θ

B

-2 cos 2θ

C

1-2 cos 2θ

D

1-2sin 2θ

E

Answer: B

Calculus
Q16

Find the value of x for which the function 3x3 - 9x2 is minimum.

A

3

B

5

C

0

D

2

E

Answer: D

Calculus
Q17

If dy/dx = x + cos x, find y.

A

x2/2 - sin x + c

B

x2 - sin x + c

C

x2/2 + sin x + c

D

x2 + sin x + c

E

Answer: C

Calculus
Q18

If tan θ = 5/4, find sin2θ - cos2θ

A

41/9

B

9/41

C

1

D

5/4

E

Answer: B

Calculus
Q19

If y = (1 - 2x)3, find the value of dy/dx at x = -1.

A

-6

B

57

C

-54

D

27

E

Answer: C

Calculus
Q20

Find the area of the figure bounded by the given pair of curves y = x2 - x + 3 and y = 3.

A

7/6 units (sq)

B

1/6 unit (sq)

C

17/6 units (sq)

D

5/6 units (sq)

E

Answer: B

Calculus
Q21

The radius r of a circular disc is increasing at the rate of 0.5cm/sec. At what rate is the area of the disc increasing when its radius is 6cm?

A

3 ∏cm2/sec

B

36 ∏cm2/sec

C

18 ∏cm2/sec

D

6 ∏cm2/sec

E

Answer: D

Calculus
Q22

The maximum value of the function f(x) = 2 + x - xis

A

3/2

B

1/2

C

9/4

D

7/4

E

Answer: C

Calculus
Q23

Find the derivative of y = sin (2x3 + 3x - 4)

A

- cos (2x3 + 3x - 4)

B

-(6x2 + 3) cos (2x3 + 3x - 4)

C

cos (2x3 + 3x - 4)

D

(6x2 + 3) cos (2x3 + 3x - 4)

E

Answer: B

Calculus
Q24

Find the derivative of (2 + 3x)(1-x) with respect to x

A

6x - 1

B

1 -6x

C

6

D

-3

E

Answer: B

Calculus
Q25

Find the derivative of the function y = 2x2(2x-1) at the point x = -1.

A

-6

B

-4

C

16

D

18

E

Answer: C

Calculus
Q26

If y = 3 cos x/3, find dy/dx  when x = 3 π/2.

A

2

B

1

C

-1

D

-3

E

Answer: D

Calculus
Q27

Evaluate ∫31(x2-1) dx 

A

62/3

B

2/3

C

-2/3

D

-62/3

E

Answer: A

Calculus
Q28

Evaluate ∫23 (x2-2x)dx

A

4/3

B

1/3

C

2

D

4

E

Answer: A

Calculus
Q29

If y = s sin (-4x) dy/dx is 

A

-12cos (-4x)

B

12 sin (-4x)

C

12x cos (4x)

D

-12x cos (-4x)

E

Answer: A

Calculus
Q30

Determine the maximum value of y = 3x2 - x3

A

6

B

0

C

2

D

4

E

Answer: D

Calculus
Q31

If nP3 - 6 (nC4) = 0, find the value of n.

A

6

B

5

C

8

D

7

E

Answer: D

Calculus
Q32

If tan θ = 4/3 calculate sin2 θ - cos2 θ

A

7/25

B

9/25

C

16/25

D

24/25

E

Answer: A

Calculus
Q33

If y = x2 - 1/x, find dy/dx

A

2x + x2

B

2x - x

C

2x +1/x2

D

2x - 1/x2

E

Answer: C

Calculus
Q34

Evaluate ∫ sin 3xdx

A

-1/3 cos 3x + c

B

-1/3 cos 3x + c

C

1/3 cos 3x + c

D

2/3 cos 3x + c

E

Answer: B

Calculus
Q35

If dy/dx = 2x - 3 and y = 3 when x = 0, find y in terms of x

A

x2 - 3x

B

x2 - 3x + 3

C

2x2 - 3x - 3

D
E

Answer: B

Calculus
Q36

Find the derivation of y = sin2(5x) with respect to x.

A

2 sin 5x cos 5x 

B

5 sin 5x cos 5x

C

10 sin 5x cos 5x

D

15 sin 5x cos 5x

E

Answer: C

Calculus
Q37

The slope of the tengent to the curve  y = 3x2 - 2x + 5 at the point (1, 6) is

A

1

B

4

C

5

D

6

E

Answer: B

Calculus
Q38

Find the minimum value of the function

f (θ) =        2        for 0 ≤ θ ≤ 2π

            3 - cos θ

A

 

1/2

 

B

2/3

C

1

D

2

E

Answer: A

Calculus
Q39

Find the value of π0  cos 2θ - 1   dθ

   sin2θ

A

π

B

π/2

C

/2

D

E

Answer: D

Calculus
Q40

If y = 2x cos 2x  - sin 2x, find dy/dx when x = π/4

A

π

B

C

/2

D

 

/2

 

E

Answer: B

Calculus
Q41

A function f(x) passes through the origin and its first derivative is 3x + 2, what is f(x)?

A

y = 3/2 x2 + 2x

B

y = 3/2 x2 + x

C

y = 3x2 + x/2

D

y = 3x2 + 2x

E

Answer: A

Calculus
Q42

If the maximum value of y = 1 + hx - 3x2 is 13, find h

A

13

B

12

C

11

D

10

E

Answer: B

Calculus
Q43

Evaluate ∫1-2 (x - 1)2 dx

A

-31/3

B

7

C

9

D

11

E

Answer: D

Calculus
Q44

Evaluate ∫oπ/4 (sin x - cos x) dx

A

√2 + 1

B

 

√2 - 1

 

C

 

-√2 - 1

 

D

1 - √2

E

Answer: D

Calculus
Q45

If y = 3x2 (x3 + 1)1/2 find dy/dx

A

6x(x3 + 1) + 3x2 / 2(x3 + 1)1/2

B

 

12x(x3 + 1) + 3x2 / 2(x3 + 1)1/2

 

C

 

15x4 + 6x / 2(x3 + 1)1/2

 

D

 

12x(x3 + 1) + 9x4 / 2(x3 + 1)1/2

 

E

Answer: D

Calculus
Q46

What is the derivative if t2 Sin (3t - 5) with respect to the variable t?

A

6t cos (3t - 5)

B

2t sin (3t - 5) - 3t2 cos (3t - 5)

C

 

2t sin (3t - 5) + 3t2 cos (3t - 5)

 

D

 

2t sin (3t - 5) - t2 cos 3t

 

E

Answer: C

Calculus
Q47

Find the value of x for, which the function y = x3 - x has a minimum value.

A

-√3

B

-√3/3

C

 

√3/3

 

D

 

√3

 

E

Answer: C

Calculus
Q48

If the function f is defined by f(x + 2) = 2x2 + 7x - 5, find f(-1)

A

-10

B

-8

C

4

D

10

E

Answer: B

Calculus
Q49

Given that θ is an acute angle and sinθ = m/n, find cotθ.

A

√[(N2 - M2)/M]

B

√[(N + M) (N -M)/M]

C

M/√(N2 - M2)

D

√[N/(N2 -M2)]

E

Answer: B

Calculus
Q50

If y = x sin x, find d2y/dx2

A

2 cos x - x sin x

B

sin x + x cos x

C

sin x - x cos x

D

x sin x - 2 cos x

E

Answer: A

Calculus
Q51

Obtain a maximum value of the function f(x) = x3 - 12x + 11.

A

-5

B

-2

C

2

D

27

E

Answer: D

Calculus
Q52

At what value of x is the function y = x² - 2x - 3 minimum

A

1

B

-1

C

-4

D

4

E

Answer: A

Calculus
Q53

Simplify cos²x(sec²x + sec²tan²x)

A

Tan x

B

Tan x sec x

C

Sec²x

D

Cosec²x

E

Answer: C

Calculus
Q54

If cos x =√(a/b), find cosec x

A

b/ √b - a

B

√b/a

C

√b/b-a

D

√b - a/b

E

Answer: C

Calculus
Q55

At what value of x is the function x2 + x + 1 minimum ?

A

-1

B

-1/2

C

1/2

D

1

E

Answer: B

Calculus
Q56

If cosθ = 12/13, find 1 + cot²θ

A

169/25

B

25/169

C

169/144

D

144/169

E

Answer: A

Calculus
Q57

If f(x) = 2x² - 5x + 3, find f(x + 1)

A

2x² - x

B

2x² - x + 10

C

4x² + 3x + 2

D

 

4x² + 3x + 12

 

E

Answer: A

Calculus
Q58

4 sin²x - 3 = 0, find x if 0 ≤ x ≤ 90°

A

30°

B

45°

C

60°

D

90°

E

Answer: C

Calculus
Q59

If cos²θ = x/y, find cosec θ

A

1/y(x² + y²)

 

B

√(x/y)

C

1/y√x² + y²

D

y/x

E

Answer: D

Calculus
Q60

If cos²θ + 1/8 = sin²θ, find tan θ

A

3

B

3 √7/7

C

3 √7

D

√7

E

Answer: B

Calculus