Free Printable full calcalus

1.

a)

cosx

b)

-cosx

c)

-sinx cosx

d)

sinx cosx

2.

Find f(2).

a)

1

b)

-1

c)

5

d)

DNE

3.

FInd the derivative:

f(x) = (-2/3)x³ - (1/2)x² + 9x

a)

-2x² - x + 9

b)

-2x² + x + 9

c)

2x² - x + 9

d)

2x² - x - 9

4.

Find the second derivative of the function:
f (x) = 2x - 5x⁶

a)

f ''(x)= 2 - 30x

b)

f ''(x) = 2-30x⁵

c)

f ''(x) = -30x⁵

d)

f ''(x) = -150x⁴

5.

Differentiate f(x) =(2/ x⁵) - 5.

a)

x⁵-3

b)

-10x⁶

c)

x⁵-5

d)

-10x^-6

6.

Find the derivative of the given equation
f(x) = x⁴ + 4x³- 2x²

a)

x³ + x²- x

b)

4x³ + 12x²+ 4x

c)

4x + 12x - 4x

d)

4x³ + 12x²- 4x

7.

What is the limit of the function as x approaches 1 from the left?

a)

DNE

b)

1

c)

4

d)

-2

8.

What is the limit of the function as x approaches -4 from the left?

a)

2

b)

-4

c)

DNE

d)

-2

9.

a)

b)

c)

d)

10.

a)

b)

c)

d)

11.

a)

b)

c)

d)

12.

a)

b)

c)

d)

13.

a)

b)

c)

d)

14.

a)

b)

c)

d)

15.

Which of the following is TRUE ?

a)

$\int_{ }^{ }\sin\ x\ \ dx\ =\ \cos\ x\ +c$

b)

$\int_{ }^{ }e^x\ \ dx\ =\ \frac{e^{x+1}}{x+1}\ +\ c$

c)

$\int_{ }^{ }\ \frac{1}{x}\ \ dx\ =\ \ln\ \left|x\ \right|\ +c$

d)

$\int_{ }^{ }\ x\ \ dx\ =\ 1\ +\ c$

16.

$\int_{ }^{ }x^3\ -\pi\ dx\ \ =$

a)

$3x^2\ +\ c$

b)

$\frac{x^4}{4}\ +\ c$

c)

$\frac{x^4}{4}\ -\ \pi x$

d)

$\frac{x^4}{4}\ -\ \pi x\ +\ c$

17.

What is $\int_{ }^{ }\ \frac{5}{x^6}\ dx$ ?

a)

$5x^{-6}\ +\ c$

b)

$5x^{-5}\ +\ c$

c)

$-\frac{5}{4x^4}\ +\ c$

d)

$-\frac{1}{x^5}\ +\ c$

18.

Integrate $\int_{ }^{ }\cos\ \left(5x\right)\ dx$ with respect to x.

a)

$\sin\ \left(5x\right)\ +\ c$

b)

$-\frac{1}{5}\sin\ \left(5x\right)\ +\ c$

c)

$\frac{1}{5}\ \sin\ \left(5x\right)\ +\ c$

d)

$\frac{\cos\ \left(5x\right)}{5}\ +\ c$

19.

Which is the integral of $\int_{ }^{ }\ \left(5-3x\right)^3\ dx$ ?

a)

$3\left(5-3x\right)^2\ +c$

b)

$\frac{\left(5-3x\right)^4}{4}+\ c$

c)

$\frac{\left(5-3x\right)^4}{12}+\ c$

d)

$-\frac{\left(5-3x\right)^4}{12}+\ c$

20.

Which of the following is NOT one of techniques of Integration?

a)

Substitution

b)

By Part

c)

Quotient Rule

d)

Partial Fraction

21.

Using integration by part, if given that u = (x + 1) then find v for $\int\left(x\ +1\right)\ e^{2x}\ dx$

a)

$\frac{x^2}{2}+x$

b)

$e^{2x}$

c)

$2e^{2x}$

d)

$\frac{e^{2x}}{2}$

22.

Integrate the partial fraction with respect to x
$\int_{ }^{ }\ \frac{1}{\left(x\right)}\ +\ \frac{4}{\left(2x\ -1\ \right)}\ dx$

a)

$\ln\ \left|x\right|\ +\ 8\ \ln\left|2x-1\right|+c$

b)

$\ln\ \left|x\right|\ +\ 4\ \ln\ \left|x-1\right|+c$

c)

$\ln\ \left|x\right|\ +\ 4\ \ln\left|2x-1\right|+c$

d)

$\ln\ \left|x\right|\ +\ 2\ \ln\left|2x-1\right|+c$

23.

Evaluate $\int_1^2\ \ 3x^2\ \ dx$

a)

$7$

b)

$8$

c)

$12$

d)

$x^3$

24.

Evaluate the integral $\int_0^2\ \frac{x^3\ +\ x^2}{x^2}\ dx$

a)

$2$

b)

$4$

c)

$6$

d)

$8$

25.

_{Evaluate the integral}

a)

30/3

b)

31/3

c)

29/3

d)

32/3

26.

a)

12/3

b)

6.5

c)

5.5

d)

11/3

27.

Find the area under a curve defined by the equation 5x⁴+3x+7 between the x values 0 and 4.

a)

1200

b)

1/12

c)

1134

d)

1076

28.

a)

40

b)

32

c)

64

d)

Not possible

29.

a)

-1

b)

-2

c)

1/2

d)

-1/2

30.

Calculator Question

a)

(A)

b)

(B)

c)

(D)

d)

(E)

31.

a)

(A)

b)

(B)

c)

(C)

d)

(D)

32.

a)

(A)

b)

(C)

c)

(D)

d)

(E)

33.

Evaluate the Definite Integral

a)

8π

b)

16π

c)

4π

d)

2π

34.

a)

1 ⁄ (1+x³)

b)

(3x²) ⁄ (1+x³)

c)

x³ ⁄ (1+x³)

d)

HELP

35.

a)

A

b)

B

c)

C

d)

D

36.

Evaluate in terms of area

∫₀² f(x) dx

a)

4

b)

-4

c)

4 + 2π

d)

-4 - 2π

37.

a)

12/3

b)

6.5

c)

5.5

d)

11/3

38.

a)

A

b)

B

c)

C

d)

D

39.

a)

A

b)

B

c)

C

d)

D

40.

The polynomial expression $2x^3y+8xyz^4-3x^2y^3$ has a degree of _____.

a)

6

b)

3

c)

4

d)

5

41.

The equation $xy=0$ implies that _____.

a)

$x=0\ and\ y=0$

b)

$x=0\ or\ y=0$

c)

$x=0\ and\ y\ne0$

d)

$x=0\ or\ y\ne0$

42.

If $\log_A10=0.25$ , then find the value of $\log_{10}A$ .

a)

3

b)

4

c)

5

d)

6

43.

How many arithmetic means must be inserted between 1 and 36 so that the sum of the resulting arithmetic progression will be 148?

a)

5

b)

6

c)

7

d)

8

44.

The 3rd term of a harmonic progression is 15 and the 9th term is 6. Find the 11th term.

a)

4

b)

8

c)

5

d)

7

45.

Which of the following is not a first quadrant angle?

a)

$60^{\circ}$

b)

$-330^{\circ}$

c)

$-120^{\circ}$

d)

$440^{\circ}$

46.

What is the period of the equation below?

$y=3\sin\left(\frac{x}{2}\right)$

a)

$2\pi$

b)

$3\pi$

c)

$4\pi$

d)

$6\pi$

47.

Simplify the trigonometric expression shown below:

$\cos^4\left(x\right)-\sin^4\left(x\right)$

a)

$\cos\left(4x\right)$

b)

$\sin\left(4x\right)$

c)

$\sin\left(2x\right)$

d)

$\cos\left(2x\right)$

48.

If $\sin\left(A\right)=3.5x$ and $\cos\left(A\right)=5.5x$ , find the value of the angle $A$ .

a)

32.47 degrees

b)

33.47 degrees

c)

34.47 degrees

d)

35.47 degrees

49.

The altitude of an equilateral triangle is 4. Find the length of each side.

a)

3.62

b)

4.62

c)

5.62

d)

6.62

50.

The diagonals of a rhombus are 6 cm and 8 cm long. Find the perimeter of the rhombus.

a)

20 cm

b)

24 cm

c)

22 cm

d)

26 cm

51.

What is the angle at the center of a circle if the subtending chord is equal to two-thirds of the radius?

a)

39.95 degrees

b)

38.94 degrees

c)

37.93 degrees

d)

36.92 degrees

52.

It is a polyhedron whose faces are all squares.

a)

tetrahedron

b)

hexahedron

c)

octahedron

d)

dodecahedron

53.

Find the length of the diagonal of a rectangular box whose edges are 6, 8, and 10.

a)

$7\sqrt{2}$

b)

$8\sqrt{2}$

c)

$9\sqrt{2}$

d)

$10\sqrt{2}$

54.

If $b^2-4ac<0$ , then the graph of the equation

$y=ax^2+bx+c$ will ______.

a)

crosses the x-axis once

b)

crosses the x-axis twice

c)

do not cross the x-axis

d)

touches the x-axis once

55.

If the eccentricity of the conic is $\frac{3}{5}$ , then it is a/an _____.

a)

ellipse

b)

circle

c)

parabola

d)

hyperbola

56.

The parabola $y=3x^2-6x+5$ has its vertex at ______.

a)

(0, 5)

b)

(1, 2)

c)

(-1, 14)

d)

(2, 5)

57.

The graph of the equation $y=x^5-x$ will cross the x-axis _____.

a)

twice

b)

3 times

c)

4 times

d)

5 times

58.

Evaluate the following:

$\lim_{x\rightarrow\infty}\left(\frac{4x^3+3x^2-6}{2x^3+5x+3}\right)$

a)

$\infty$

b)

$0$

c)

$\frac{1}{2}$

d)

$2$

59.

Find the slope of the tangent line to the curve $y=1-x^3$ at a point where $y=9$ .

a)

-11

b)

-12

c)

-10

d)

-13

60.

It is the foundation of knowledge in Calculus?

a)

Basic Operations

b)

Integers

c)

Function

d)

Limit

61.

f(x) is the representation of? (WRITE YOUR ANSWER IN small letter)

(a)

62.

How do you represent limit?

(a)

63.

How will you interpret this expression?

\lim_{x\rightarrow2}5

(WRITE YOUR ANSWER IN small letter)

(a)

64.

What is the answer in the given expression?

\lim_{x\rightarrow50}25

a)

50

b)

25

c)

2

d)

125

65.

What is the answer in the given expression?

\lim_{x\rightarrow121}3\pi

a)

121

b)

11

c)

3 $\pi$

d)

3.14

66.

What is the answer in the given expression?

\lim_{x\rightarrow143}x

a)

x

b)

1143

c)

143

d)

234

67.

What is the answer in the given expression?

\lim_{\frac{x\rightarrow35}{2}}x

a)

$\frac{35}{2}$

b)

18

c)

17.5

d)

All of athe above

68.

What is the answer in the given expression?

\lim_{x\rightarrow2}-4x

a)

-4

b)

2

c)

-8

d)

-6

69.

What is the answer in the given expression?

\lim_{x\rightarrow\frac{1}{25}}100x

a)

4

b)

10

c)

$\frac{1}{25}$

d)

100

70.

What is the answer in the given expression?

\lim_{x\rightarrow15}x+15

a)

15

b)

30

c)

1

d)

x

71.

What is the answer in the given expression?

\lim_{x\rightarrow\frac{2}{\text{5}}}10x-7

a)

20/5

b)

10

c)

2/5

d)

-3

72.

What is the answer in the given expression?

\lim_{x\rightarrow13}\left(x+5\right)\left(x-2\right)

a)

10

b)

198

c)

13

d)

20

73.

What is the answer in the given expression?

\lim_{x\rightarrow\frac{1}{\text{2}}}\left(x-10\right)\left(2x-5\right)

a)

50

b)

9.5

c)

34

d)

38

74.

What is the answer in the given expression?

undefined

a)

2

b)

-2

c)

16

d)

4

75.

$\lim_{x\rightarrow2}\frac{x+\sqrt{2}}{2}$

What is the answer in the given expression?

a)

2

b)

1.70

c)

1

d)

1.71

76.

$\lim_{x\rightarrow-1}^{ }x^2-1$

What is the answer in the given expression?

a)

-1

b)

1

c)

0

d)

undetermined

77.

$\lim_{x\rightarrow\frac{1}{\text{4}}}2x^3+4$

What is the answer in the given expression?

a)

4.12

b)

8

c)

1/4

d)

4.13

78.

$\lim_{x\rightarrow5}3x\sqrt{x}$

What is the answer in the given expression?

a)

34

b)

33.6

c)

$\sqrt{5}$

d)

5

79.

$\lim_{x\rightarrow20}\sqrt{x}\left(2x\right)$

What is the answer in the given expression?

a)

178.8

b)

2 $\sqrt{5}$

c)

179

d)

All of the above

80.

Find the gradient of the curve with equation

2x² − 4xy + 3y² = 3, at the point (2, 1).

a)

2

b)

3

c)

4

d)

5

81.

The equation of a curve is x²y + y² = 6x

the equation of the tangent to the curve at the point with coordinates (1, 2)

a)

3x – 5y + 8 = 0

b)

2x – 5y + 8 = 0

c)

2x – 5y - 8 = 0

d)

3x – 5y - 8 = 0

82.

A solid rectangular block has a square base of side x cm. The height of the block is h cm and the total surface area of the block is 96 cm^2.Find the stationary value of V

a)

V = 84

b)

V = 74

c)

V = 64

d)

V = 54

83.

The diagram shows the curve y = (x − 2)² and the line y + 2x = 7, which intersect at points A and B. Find the area of the shaded region.

a)

$10\ \frac{5}{7}$

b)

$10\ \frac{3}{4\ }$

c)

$10\ \frac{1}{3\ }$

d)

$10\ \frac{2}{3}$

84.

$\int_{ }^{ }\left(x^{3\ }+\frac{1}{x^3}\right)\ dx$

a)

$\frac{x^{4\ }}{4}-\frac{x^{-2}}{2\ }+c$

b)

$\frac{x^{4\ }}{4}+\frac{x^{-2}}{2}+c$

c)

$\frac{x^4}{4}-\frac{x^2}{2\ }+c$

d)

$\frac{-x^4}{4}+\frac{x^{2\ }}{2\ }+c$

85.

the equation of the curve $y=\frac{4}{3x-4}$
and P(2, 2) is a point on the curve. The equation of the tangent to the curve at P and the angle that this tangent makes with the x-axis respectively

a)

y − 2 = −3(x − 2) and $108.4^o$

b)

y − 2 = 3(x − 2) and $128.8^o$

c)

y − 2 = −3(x + 2) and $78.3^o$

d)

y + 2 = −3(x − 2) and $45^o$

86.

The diagram shows part of the curve $y=4\sqrt{x}-x$
The curve has a maximum point at M and meets the x-axis at O and A. Find the volume obtained when the shaded region is rotated through 360o about the x-axis, givingyour answer in terms of π

a)

138.5π

b)

137.5π

c)

136.5π

d)

135.5π

87.

The equation of a curve is $y=4\sqrt{x}+\frac{2}{\sqrt{x}}$
A point is moving along the curve in such a way that the x-coordinate is increasing at a constant rate of 0.12 units per second. Find the rate of change of the y-coordinate when x = 4

a)

0.105

b)

0.125

c)

0.345

d)

0.546

88.

The diagram shows part of the curve y = −x² + 8x − 10 which passes through the points A and B. The curve has a maximum point at A and the gradient of the line BA is 2. evaluate the area of the shaded region.

a)

$9\ \frac{1}{3}$

b)

$10\ \frac{1}{3}$

c)

$11\ \frac{1}{3}$

d)

$12\ \frac{1}{3}$

89.

A curve is such that $\frac{dy}{dx}=\frac{6}{x^2}$ and (􏰎2, 9)􏰏 is a point on the curve. Find the equation of the curve

a)

$y=-6x^{-1}+12$

b)

$y=6x^{-1}-12$

c)

$y=-6x^{-2}+12$

d)

$y=6x^{-2}+12$

90.

The straight line y = mx + 14 is a tangent to the curve $y=\frac{12}{x}+2$
at the point P. Find the value of the constant m and the coordinates of P

a)

m = 3 and y = - 8

b)

m = −3 and y = 8

c)

m = 8 and y = - 3

d)

m = −8 and y = 3

91.

The diagram shows the curve $y=\sqrt{1+4x}$
which intersects the x-axis at A and the y-axis at B. The normal to the curve at B meets the x-axis at C. the area of the shaded region

a)

$\frac{6}{5}$

b)

$\frac{5}{6}$

c)

$\frac{6}{7}$

d)

$\frac{7}{6}$

92.

$\int-\frac{dx}{1+x^2}=$

a)

$\left(1+x^2\right)^{-1}+C$

b)

$-\tan x+C$

c)

$-\ln\left(1+x^2\right)+C$

d)

$\ln\left(1+x^2\right)+C$

93.

$\int dx=$

a)

$0$

b)

$x+C$

c)

$1$

d)

$undefined$

94.

$\frac{\text{d}}{\text{d}x}\left(c\right)=$

a)

$1$

b)

$c$

c)

$0$

d)

$cx$

95.

$\int\frac{1}{x^2+1}dx=$

a)

$\sec^{-1}x+C$

b)

$\tan^{-1}x+C$

c)

$\ln\left|x^2+1\right|+C$

d)

$\cos^{-1}x+C$

96.

$\int\sin xdx$

a)

$\cos x+C$

b)

$\sin^2x+C$

c)

$-\cos x+C$

d)

$\frac{1}{2}\sin^2x+C$

97.

$\int\frac{dx}{\sqrt{1-x^2}}=$

a)

$\sec^{-1}x+C$

b)

$\tan^{-1}x+C$

c)

$\cos^{-1}x+C$

d)

$\sin^{-1}x+C$

98.

$\frac{\text{d}}{\text{d}x}\left(\tan^{-1}x\right)=$

a)

$\frac{1}{1+x^2}$

b)

$\frac{1}{1-x^2}$

c)

$\frac{1}{\sqrt{1-x^2}}$

d)

$\frac{1}{\sqrt{x^2-1}}$

99.

$\int-\csc^2xdx$

a)

$\frac{1}{3}\csc^3x+C$

b)

$\cot x+C$

c)

$-\cot x+C$

d)

$\csc x\cot x+C$

100.

$\int\sec u\tan udu=$

a)

$\tan u+C$

b)

$\tan^2u+C$

c)

$\sec u+C$

d)

$\sec^2u+C$

101.

$\int\frac{dx}{\left|x\right|\sqrt{x^2-1}}=$

a)

$\sec^{-1}x\ +\ C$

b)

$\csc^{-1}x+C$

c)

$\sec x+C$

d)

$\csc x+C$

102.

$\frac{\text{d}}{\text{d}x}\left(\sec x\right)=$

a)

$\sec x\tan x$

b)

$\sec^2x$

c)

$\tan^2x$

d)

$\frac{1}{2}\sec^2x$

103.

$\frac{\text{d}}{\text{d}x}\left(xy\right)=$

a)

$x\frac{\text{d}y}{\text{d}x}$

b)

$\frac{\text{d}y}{\text{d}x}$

c)

$x\frac{\text{d}y}{\text{d}x}+y$

d)

$y\frac{\text{d}y}{\text{d}x}+x$

104.

$\int u^ndu=$

a)

$\ln u+C$

b)

$u^{n+1}+C$

c)

$\frac{u^{n+1}}{n+1}+C$

d)

$u^{n-1}+C$

105.

$\int\sec^2xdx=$

a)

$\sec^3x+C$

b)

$\frac{1}{3}\sec^3x+C$

c)

$\tan x+C$

d)

$2\sec x\ +\ C$

106.

$\int\cos udu$

a)

$\sin u+C$

b)

$-\sin u+C$

c)

$\frac{1}{2}\cos^2u\ +\ C$

d)

$\cos\left(2u\right)+C$

107.

$\frac{\text{d}}{\text{d}x}\left(\ln\left|x\right|\right)=$

a)

$e^x$

b)

$-x^{-1}$

c)

$-x^{-2}$

d)

$\frac{1}{\left|x\right|}$

108.

$\int\frac{du}{u}=$

a)

$\ln\left|u\right|\ +C$

b)

$u^o+C$

c)

$e^u+C$

d)

$\frac{1}{2}u^2+C$

109.

$\int e^xdx=$

a)

$e^{x+1}+C$

b)

$\ln x\ +\ C$

c)

$e^x+C$

d)

$\frac{e^{x+1}}{x+1}+C$

full calcalus

Total questions: 109

Worksheet time: 3hrs 20mins

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