Free Printable Yellow Book

1.

When f”(x) is negative the curve of y=f(x) is concave _____.

a)

Downward

b)

To the right

c)

Upward

d)

To the left

2.

If the second derivative of the equation of a curve is equal to the negative of the equation of a curve is equal to the negative of the equation of the same curve, the curve is:

a)

A paraboloid

b)

A sinusoid

c)

A cissoids

d)

An exponential

3.

A function F(x) is called ______ of f(x) if F’(x)=f(x)

a)

Explicit function

b)

Derivative

c)

Implicit function

d)

Antiderivative

4.

Points of derivatives which do not exists (and so equals zero) are called ______.

a)

Stationary points

b)

Minimum points

c)

Maximum points

d)

Minimun and maximum

5.

At the point of inflection where x=a,

a)

f“(a) ≠ 0

b)

f“(a) = 0

c)

f“(a) > 0

d)

f“(a) < 0

6.

At the minimum point, the slope of the tangent line is:

a)

Negative

b)

Infinity

c)

Positive

d)

Zero

7.

What is the point where the second derivative is zero?

a)

Maxima

b)

Minima

c)

Point of inflection

d)

Point of intersection

8.

The point on the curve where the second derivative of a function is equal to zero is called:

a)

Maxima

b)

Minima

c)

Point of inflection

d)

Critical point

9.

The point of the curve where the first derivative of a function is zero and the second derivative is positive is called:

a)

Maxima

b)

Minima

c)

Point of inflection

d)

Critical point

10.

Evaluate the integral of tanh u du.

a)

ln sinh u + c

b)

ln cosh u + c

c)

cosh u + c

d)

coth u + c

11.

The derivative of $a^u$ with respect to x is:

a)

$a^u\ \ln a\ \frac{du}{dx}$

b)

$a^u\ \ln u\ \frac{du}{dx}$

c)

$u^a\ \ln a\ \frac{du}{dx}$

d)

$u^a\ \ln u\ \frac{du}{dx}$

12.

If y = tanh x, find dy/dx

a)

$\operatorname{sech}^2x$

b)

$-\operatorname{sech}^2x$

c)

$\operatorname{sech}\ x\ \tanh\ x$

d)

$-\operatorname{sech}\ x\ \tanh\ x$

13.

The field of mathematics which rest upon the fundamental concept of limits and was created by Newton and Leibniz.

a)

Physics

b)

Calculus

c)

Boolean Algebra

d)

Quantum Mechanics

14.

The _______ of a relation is the set of second elements of the pair in the relation.

a)

Domain

b)

Range

c)

Graph

d)

Function

15.

A relation in which there is exactly one range element associated with each domain element.

a)

Graph

b)

Set

c)

Formula

d)

Function

16.

The _____ of a relation is the set of first elements of pairs in the relation.

a)

Domain

b)

Range

c)

Graph

d)

Function

17.

Any set of ordered pair is called a:

a)

Relation

b)

Range

c)

Domain

d)

Graph

18.

Any pair of elements (x,y) having a first element x and a second derivative y is called:

a)

Range

b)

Domain

c)

Coordinates

d)

Ordered pair

19.

The operation of finding the derivative of a function.

a)

Differentiating

b)

Differentiation

c)

Differential

d)

Integrating

20.

The derivative of a function is identical to the _____ of the graph of the function.

a)

Tangent

b)

Secant

c)

Slope

d)

Normal

21.

The ______ derivative of the function is the rate of change of the slope of the graph.

a)

First

b)

Second

c)

Third

d)

Fourth

22.

A point on the graph where the tangent line is either horizontal or vertical is known as:

a)

Point of inflection

b)

Critical point

c)

Stationary point

d)

All of the above

23.

The critical points of a graph occur when the derivative of a function is:

a)

Zero

b)

Approaches infinity

c)

Zero or approaches infinity

d)

Either 1 or -1

24.

A point of inflection:

a)

y‘=0

b)

y“=0

c)

y“ is negative

d)

y“ is positive

25.

At a point where y’=0 changes from positive to negative as x increases.

a)

Y is minimum

b)

X is minimum

c)

Y is maximum

d)

X is maximum

26.

The point where the second derivative of a function is zero.

a)

Maximum point

b)

Minimum point

c)

Point of intersection

d)

Point of inflection

27.

The point where the first derivative of a function is zero and the second derivative is positive.

a)

Maximum point

b)

Minimum point

c)

Point of inflection

d)

Critical point

28.

A point at which the curve changes from concave upward to concave downward and vice versa is known as:

a)

Maximum point

b)

Minimum point

c)

Point of inflection

d)

Yield point

29.

At a point where y’=0, if y changes from positive to negative as x increases

a)

Y is maximum

b)

Y is minimum

c)

X is maximum

d)

Y is minimum

30.

At maximum point

a)

The curve is concave downward

b)

y“ is negative

c)

y’=0

d)

All of the above

31.

________ is also known as the composite function rule.

a)

L’Hospital Rule

b)

Trapezoidal rule

c)

Simpson’s rule

d)

Chain rule

32.

The L’Hospital rule was formulated by:

a)

Marquis de L’Hospital

b)

Marrione de L’Hospital

c)

J. Beroulli

d)

I. Newton

33.

A collective term for maxima or minima, whether absolute of relative is called:

a)

Infintium

b)

Extrema

c)

Domain

d)

None of the above

34.

Which of the following is not determinate form?

a)

$\infty\cdot\infty$

b)

$\infty+\infty$

c)

$-\infty-\infty$

d)

$\frac{\infty}{\infty}$

35.

The derivative of csc θ is

a)

$\sec\theta\tan\theta$

b)

$-\csc^2\theta$

c)

$-\csc\theta\cot\theta$

d)

$-\csc\theta\tan\theta$

36.

Catenary is the shape assumed by perfectly flexible uniform cable hanging between supports. It is a graph of:

a)

Parabola

b)

$y=\sinh x$

c)

$y-\cosh x$

d)

$x=\cosh y$

37.

Which of the following is determinate?

a)

$\frac{0}{0}$

b)

$0\cdot\infty$

c)

$\infty\cdot\infty$

d)

$\infty^0$

38.

The quantity $\frac{2}{\left(e^x-e^{-x}\right)}$ is equal to:

a)

$\cosh x$

b)

$\tanh x$

c)

$\operatorname{csch}x$

d)

$\operatorname{sech}x$

39.

What is $1-\tanh^2x$ equal to?

a)

$\operatorname{sech}^2x$

b)

$\cosh^2x$

c)

$\coth^2x$

d)

$\operatorname{csch}^2x$

40.

In calculus, all functions are classified as either algebraic or transcendental. Which of the following is NOT an algebraic functions?

a)

Rational integral function

b)

Irrational function

c)

Rational fractional function

d)

Exponential logarithmic function

41.

The integral of $\sin^m\theta\cos^n\theta\ d\theta$ can easily be determined by using Wallis formula provided the limits are form:

a)

$0\ to\ \pi$

b)

$0\ to\ \frac{\pi}{2}$

c)

$0\ to\ \frac{\pi}{4}$

d)

$0\ to\ 2\pi$

42.

The integral of any quotient whose numerator is the difference of the denominator is the _____ of the denominator.

a)

Reciprocal

b)

Product

c)

Logarithm

d)

Derivative

43.

Many integrals may be evaluated by introducing a new variable of integration in place of the original variable, the two variables being connected by some suitable formulas. This process is called:

a)

Integration by parts

b)

Integration by substitution

c)

Partial derivatives

d)

The chain rule

44.

The variable inside the integral is called variable of integration or integration. It is sometimes referred to as:

a)

Calculus variable

b)

Dummy variable

c)

Limits variable

d)

Limits range

45.

The value of x in trigonometric substitution with an integrand involving $\left(a^2-x^2\right)$ is

a)

$a\sec\theta$

b)

$a\tan\theta$

c)

$a\cos\theta$

d)

$a\sin\theta$

46.

The area of the surface generated by rotating any plane curve about a certain axis in its plane is equal to the product of the length of the arc and the distance travelled by its centroid

a)

Varignon’s theorem

b)

First proposition of Pappus

c)

Method of section

d)

Second proposition of Pappus

47.

The volume of a any solid revolution is equal to the generating are times the circumference of the circle described by the centroid of the area. This is known as:

a)

First proposition of Pappus

b)

Cavalieri’s theorem

c)

Second proposition of Pappus

d)

Simpson’s Rule

48.

Newton was inspired by an apple. Pappus proposition inspired by what fruits?

a)

Apple and pear

b)

Lemon and orange

c)

Apple and Lemon

d)

Apple and banana

49.

When the ellipse is rotated about is shorter axis, the ellipsoid is:

a)

Paraboloid

b)

Prolate

c)

Spheroid

d)

Oblate

50.

When the ellipse is rotated about is longer axis, the ellipsoid is:

a)

Paraboloid

b)

Prolate

c)

Spheroid

d)

Oblate

51.

When a catenary (y = cosh x) is rotated about its axis of symmetry, it generates a solid called:

a)

Paraboloid

b)

Conoid

c)

Catenoid

d)

Hyperboloid

52.

A solid of revolution of a parabola is known as:

a)

Paraboloid

b)

Hyperboloid

c)

Catenoid

d)

Conoid

53.

A _______ section of a surface of revolution is the section containing.

a)

Right

b)

Central

c)

Median

d)

Meridian

54.

An infinite sees in which successive terms are of constant times successive integral power of the variable. It takes the form of:

a_0+a_zx+a_2x^2+a_3x^3+\ ...

a)

Fourier Series

b)

Taylor’s Series

c)

McClaurin Series

d)

Power Series

55.

Who invented the symbol “∝” for infinity?

a)

John Stockton

b)

John Venn

c)

John Wallis

d)

John Napier

56.

Calculus was invented by:

a)

Newton

b)

Leibneiz

c)

Gauss

d)

Newton and Leibnizz

57.

Varignon’s theorem is used to determine ____.

a)

Location of centroid

b)

Moment of inertia

c)

Mass moment of inertia

d)

Moment of area

Yellow Book - Calculus

Total questions: 57

Worksheet time: 29mins

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