Free Printable ECP115-Competency Appraisal 1 - Midterm Exam (Multiple Choice)

1.

Compute the following limit: lim (x→∞) ((x−4)/ (x+4)).

a)

0

b)

1

c)

2

d)

Infinite

2.

Evaluate $\lim(x→4)\left((x^2−16)/(x−4)\right)$ .

a)

0

b)

1

c)

8

d)

16

3.

Occurs when the curve has a “hole” in it from a missing point because the function has a value at that point that is “off the curve”.

a)

Jump Continuity

b)

Point Continuity

c)

Essential Continuity

d)

Removable Continuity

4.

Occurs when there is a rational expression with common factors in the numerator and denominator.

a)

Jump Continuity

b)

Point Continuity

c)

Essential Continuity

d)

Removable Continuity

5.

Occurs when the curve “breaks” at a particular place and starts somewhere else.

a)

Jump Continuity

b)

Point Continuity

c)

Essential Continuity

d)

Removable Continuity

6.

Occurs when the curve has a vertical asymptote.

a)

Jump Continuity

b)

Point Continuity

c)

Essential Continuity

d)

Removable Continuity

7.

Differentiate y = $e^x cos x^2$ .

a)

$-e^x \sin x^2$

b)

$e^x(cos x^2 − 2x sin x^2)$

c)

$e^x \cos x^2 - 2x \sin x^2$

d)

−2x $e^x \sin x$

8.

Differentiate y = $sec(x^2 + 2)$ .

a)

2x $cos(x^2 + 2)$

b)

$-cos(x^2 + 2) cot(x^2 + 2)$

c)

$2x \sec(x^2 + 2) \tan(x^2 + 2)$

d)

$cos(x^2 + 2)$

9.

The derivative of tan x is

a)

sec x dx

b)

$sec^2 x dx$

c)

sec x tan x dx

d)

$-csc^2 x dx$

10.

The derivative of cot x is

a)

$sec^2 x dx$

b)

sec x tan x dx

c)

sec x dx

d)

$-csc^2 x dx$

11.

Differentiate y = $e^{2x}$ .

a)

$2e^{2x}$

b)

$-2e^{2x}$

c)

$e^{2x}$

d)

$e^{2x}/2$

12.

Find y if y = arc sin cos x.

a)

−1

b)

−2

c)

1

d)

2

13.

Find the second derivative of $x^3 - 5x^2 + x$ = 0.

a)

10x − 5

b)

6x − 10

c)

$3x^2 - 5x$

d)

3x + 10

14.

Given f(x) = $x^3 - 6x + 2$ . Find the first derivative at x=2.

a)

6

b)

7

c)

$3x^2 - 6$

d)

8

15.

If y = 4cos x + sin 2x, what is the slope of the curve when x = 2 radians?

a)

−2.21

b)

−4.94

c)

−3.25

d)

2.21

16.

Find the slope of $x^2 y = 8$ , at the point (2,2).

a)

2

b)

−1

c)

−1/2

d)

-2

17.

Find the partial derivatives with respect to x of the function $x y^2 - 5y + 6$ .

a)

$y^2 - 5$

b)

$y^2$

c)

x y − 5y

d)

2x y

18.

Locate the points of inflection of the curve y = $x^2 e^x$ .

a)

−2 ± √3

b)

2 ± √2

c)

−2 ± √2

d)

2 ± √3

19.

Differentiate y = $3^x$ .

a)

$3^x ln 3$

b)

$3^x$

c)

ln x

d)

$3^x ln x$

20.

Find the minimum distance from the point (4,2) to the parabola $y^2 = 8x$ .

a)

4√3

b)

2√2

c)

√3

d)

2√3

21.

Find the derivative of 1/x.

a)

1/x

b)

ln x

c)

ln 1/x

d)

1/ln x

22.

An integral that is defined by the limit values a and b of the independent variable.

a)

Integral Calculus

b)

Definite Integral

c)

Differential Calculus

d)

Indefinite Integral

23.

An integral with no restrictions imposed on its independent variables.

a)

Integral Calculus

b)

Definite Integral

c)

Differential Calculus

d)

Indefinite Integral

24.

If an arc is rotated about an axis, it will generate a surface area equal to the product of the length of the arc and circumference described by its centroid.

a)

The First Proposition of Pappus

b)

The 2nd Proposition of Pappus

c)

Hooke’s Law

d)

Area by Integration

25.

What is the integral of $(3t - 1)^3$ dt?

a)

$\frac{1}{12} (3t - 1)^4 + C$

b)

$\frac{1}{12} (3t - 4)^4 + C$

c)

$\frac{1}{4} (3t - 1)^{4} + C$

d)

$\frac{1}{4} (3t - 1)^{3} + C$

26.

Evaluate the integral of dx/(x+2) from -6 to -10.

a)

$2^{1/2}$

b)

1/2

c)

ln 3

d)

ln 2

27.

Integrate x cos(2x^2 + 7) dx.

a)

$\frac{1}{4} \sin(2x^2 + 7) + C$

b)

$\frac{1}{8} \cos(2x^2 + 7) + C$

c)

$sin x/(4(2x^2 + 7)) + C$

d)

$sin(2x^2 + 7) + C$

28.

Integrate (7x^3 + 4x^2) dx.

a)

$7x^4/4 + 4x^2/2 + C$

b)

$7x^4/4 + 4x^3/3 + C$

c)

3cos 2x − 2sin 6x

d)

$7x^4 - \frac{4x^2}{2} + C$

29.

Evaluate the integral of $sin^6 x$ dx from 0 to $\frac{\pi}{2}$ .

a)

pi/32

b)

2pi/17

c)

3pi/32

d)

5pi/32

30.

The integral of cos x with respect to x is

a)

sin x + C

b)

sec x + C

c)

−sin x + C

d)

csc x + C

31.

The integral of sin A with respect to A is

a)

−cos A + C

b)

cos A + C

c)

−sin A + C

d)

sin A + C

32.

The integral of tan u with respect to u is

a)

ln|sin u| + C

b)

ln|sec u| + C

c)

ln|sec u + tan u| + C

d)

ln|csc u − cot u| + C

33.

The integral of secu with respect to u is

a)

ln|sin u| + C

b)

ln|sec u| + C

c)

ln|sec u + tan u| + C

d)

ln|csc u − cot u| + C

34.

Evaluate the integral of ln x dx, the limits are 1 and e.

a)

0

b)

1

c)

2

d)

3

35.

Find the area of the region bounded by the curve $x^2 = -9y$ and the line $y + 1 = 0$ .

a)

3 sq. units

b)

4 sq. units

c)

5 sq. units

d)

6 sq. units

36.

An equation containing only one independent variable, thus having only ordinary derivatives in the equation.

a)

Ordinary DE

b)

Partial DE

c)

Differential Calculus

d)

Order

37.

Determine the order and degree of the differential equation $2x \frac{d^2y}{dx^2} + 5x^2 \left(\frac{d^3y}{dx^3}\right) - xy = 0$ .

a)

Fourth order, first degree

b)

Third order, first degree

c)

First order, fourth degree

d)

First order, third degree

38.

Which of the following equations is an exact DE.

a)

$(x^2 + 1)dx - xydy = 0$

b)

xdy + (3x − 2y)dx = 0

c)

$2xy dx + (2 + x^2) dy = 0$

d)

$x^2 y dy - y dx = 0$

39.

Radium decomposes at a rate proportional to the amount at any instant. In 100 years, 100 mg of radium decomposes to 96 mg. How many mg will be left after 100 years?

a)

88.60

b)

95.32

c)

92.16

d)

90.72

40.

The population of a country doubles in 50 years. How many years will it be five times as much? Assume that the rate of increase is proportional to the number of inhabitants.

a)

100 years

b)

116 years

c)

120 years

d)

98 years

41.

If the nominal interest rate is 3%, how much is 5000 worth in 10 years in continuously compounded account?

a)

5750

b)

6750

c)

7500

d)

6350

42.

Simplify $2^{i 9}$ = $i^{21 + i}$ .

a)

1

b)

−1i

c)

1+i

d)

2i

43.

Write the polar form of the vector 3+ j4.

a)

6.25∠31°

b)

10.2∠53.1°

c)

5.25∠1°

d)

5∠53.1°

44.

The expression 3+4i is a complex number. Compute its absolute values.

a)

4

b)

5

c)

6

d)

7

45.

The inverse laplace transform of $\frac{s}{s^2 + w^2}$ .

a)

sin wt

b)

w

c)

$e^{wt}$

d)

cos wt

46.

The inverse laplace transform of $\frac{w}{s^2 + w^2}$ .

a)

sin wt

b)

w

c)

$e^{wt}$

d)

cos wt

47.

Determine the inverse laplace transform of $\frac{2s - 18}{s^2 + 9}$ as a function of x.

a)

2cos x − sin 3x

b)

2cos 3x − 6sin 3x

c)

3cos 2x − 2sin 6x

d)

6cos x − 3sin 2x

48.

Determine the inverse laplace transform of $\frac{1}{4s^2 - 8s}$ .

a)

$\frac{1}{4} e^{t} sinh t$

b)

$\frac{1}{2}$ e^{t} $sinh t$

c)

$\frac{1}{4} e^{t} \cosh t$

d)

$\frac{1}{2}$ e^{t} $cosh t$

49.

One term of a fourier series in cosine form is 10 cos 40πt. Write it in exponential form.

a)

$5e^{j40\pi t} + 5e^{−j40\pi t}$

b)

$5e^{j40\pi t} - 5e^{-j40\pi t}$

c)

$10e^{j40\pi t}$

d)

$10e^{j40\pi t}$

50.

Find the laplace transform of $2e^{−t} − 4$ .

a)

$2e^{−t} − 4e^{−3t}$

b)

$e^{−2t} + e^{−3t}$

c)

$e^{−2t} − e^{−3t}$

d)

$(2e^{−t})(1 − 2e^{−3t})$

ECP115-Competency Appraisal 1 - Midterm Exam (Multiple Choice)

Total questions: 50

Worksheet time: 2hrs 37mins

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