Calculus Generix Content - Calculus
"Calculus" question number distribution across years
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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

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

Calculus
Q3

Find ∫ (sinx + 2)dx

A

-cosx + x2 + k

B

cos + x2 + k

C

-cosx + 2x + k

D

cosx + 2x + k

E

Calculus
Q4

Evaluate ∫sec² θ d θ

A

secθ tanθ + k

B

tan θ + k

C

2sec θ + k

D

sec θ + k

E

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

Calculus
Q6

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

A

4

B

3

C

2

D

1

E

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

Calculus
Q8

Evaluate ∫π/2-π/2 cos xdx

A

0

B

1

C

2

D

3

E

Calculus
Q9

Evaluate ∫21 (6x² - 2x)dx

A

16

B

13

C

12

D

11

E

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

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

Calculus
Q12

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

A

-2

B

-1/2

C

-3

D

-3/2

E

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

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

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

Calculus
Q16

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

A

3

B

5

C

0

D

2

E

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

Calculus
Q18

If tan θ = 5/4, find sin2θ - cos2θ

A

41/9

B

9/41

C

1

D

5/4

E

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

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

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

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

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

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

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

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

Calculus
Q27

Evaluate ∫31(x2-1) dx

A

62/3

B

2/3

C

-2/3

D

-62/3

E

Calculus
Q28

Evaluate ∫23 (x2-2x)dx

A

4/3

B

1/3

C

2

D

4

E

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

Calculus
Q30

Determine the maximum value of y = 3x2 - x3

A

6

B

0

C

2

D

4

E

Calculus
Q31

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

A

6

B

5

C

8

D

7

E

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

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

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

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

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

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

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

Calculus
Q39

Find the value of π0  cos 2θ - 1   dθ

sin2θ

A

π

B

π/2

C

/2

D

E

Calculus
Q40

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

A

π

B

C

/2

D

/2

E

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

Calculus
Q42

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

A

13

B

12

C

11

D

10

E

Calculus
Q43

Evaluate ∫1-2 (x - 1)2 dx

A

-31/3

B

7

C

9

D

11

E

Calculus
Q44

Evaluate ∫oπ/4 (sin x - cos x) dx

A

√2 + 1

B

√2 - 1

C

-√2 - 1

D

1 - √2

E

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

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

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

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

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

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

Calculus
Q51

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

A

-5

B

-2

C

2

D

27

E

Calculus
Q52

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

A

1

B

-1

C

-4

D

4

E

Calculus
Q53

Simplify cos²x(sec²x + sec²tan²x)

A

Tan x

B

Tan x sec x

C

Sec²x

D

Cosec²x

E

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

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

Calculus
Q56

If cosθ = 12/13, find 1 + cot²θ

A

169/25

B

25/169

C

169/144

D

144/169

E

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

Calculus
Q58

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

A

30°

B

45°

C

60°

D

90°

E

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

Calculus
Q60

If cos²θ + 1/8 = sin²θ, find tan θ

A

3

B

3 √7/7

C

3 √7

D

√7

E