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NUMERICAL METHODS

Total questions: 65

Worksheet time: 56mins

Name
Class
Date
1.

The value of f(1) can be deduced using Taylor series.

a)

True

b)

False

2.

Let τa(f(x)) denote the Taylor series of the polynomial f(x) centered at a. Which of the following exactly happens after the Taylor series is formed?

a)

τa(f(x)) = f(x)

b)

The Taylor series has the effect of scaling GRAPH OF f(x)

c)

The Taylor series transforms the origin

d)

Scaled up graph obtained by factor of a

3.

A function f(x) which is continuous and differentiable over the real domain exists such that f(n) (x) = [f(n + 1) (x)]2, f(0) = a and f(1)(0) = 1.

a)

True

b)

False

4.

Find the value of √10

a)

3.1633

b)

3.1623

c)

3.1632

d)

3.1645

5.

Expand f(x) = 1⁄x about x = 1.

a)

1 – (x-1) + (x-1)2 – (x-1)3 + ….

b)

1 + (x-1) + (x-1)2 + (x-1)3 + ….

c)

1 + (x-1) – (x-1)2 + (x-1)3 + ….

d)

1 – (x+1) + (x+1)2 – (x+1)3 + ….

6.

An infinite series that can be thought of as a polynomial with an infinite number of terms, such as 1 + x + x2 + x3 +⋯…

a)

Taylor Series

b)

Power Series

c)

Numerical Series

d)

Maclaurin Series

7.

Type of series expansion in which all terms are nonnegative integer powers of the variable.

a)

Taylor Series

b)

Power Series

c)

Numerical Series

d)

Maclaurin Series

8.

A function is an infinite sum of terms that are expressed in terms of the function's derivatives at a single point.

a)

Taylor Series

b)

Power Series

c)

Numerical Series

d)

Maclaurin Series

9.

To find the value of sin(9) the Taylor Series expansion should be expanded with center as

a)

9

b)

8

c)

7

d)

some delta with small interval around 9

10.

f(x)=x3+2x,   [−1,1]

a)

1/√3

b)

±1/√3

c)

-1/√3

d)

The MVT doesn't apply

11.

 

The value of c guaranteed to exist by the MVT for  f\left(x\right)=x^2f(x)=x2  on the interval [0,3] is:

a)

1

b)

3/2

c)

2

d)

1/2

12.

Find all numbers c that satisfies the Mean Value Theorem if it can be applied to f on the closed interval [1,5].

a)

1

b)

3

c)

6

d)

8

13.

A function that fulfills two hypotheses:

f is continuous on the closed interval [a, b].

f is differentiable on the open interval (a, b).

a)

Leibnitz Rule

b)

Rolle's Theorem

c)

Mean Value Theorem

d)

Power Theorem

14.

Ensures that there is at least one point on the curve f(x) , whose abscissa lies in (a, b) at which the tangent is · A.

a)

Rolle's Theorem

b)

Leibnitz Rule

c)

Power Rule

d)

Mean Value Theorem

15.

Numerical techniques more commonly involve

a)

Elimination method

b)

Reduction method

c)

Iterative method

d)

Direct method

16.

Which of the following is an iterative method?

a)

Gauss Seidel

b)

Gauss Jordan

c)

Factorization

d)

Gauss Elimination

17.

Errors may occur in performing numerical computation on the computer due to which of the following reasons

a)

Operator fatigue

b)

Back substitution

c)

Rounding errors

d)

Power fluctuation

18.

Which of the following is also known as the Newton Raphson method?

a)

Chord method

b)

Tangent method

c)

Diameter method

d)

Secant method

19.

If EF exists, then (EF)-1 will be equal to which of the following?

a)

F-1 E-1

b)

E-1 F-1

c)

EF

d)

FE

20.

The Gauss Jordan method reduces a original matrix into a _____________

a)

Skew Hermitian matrix

b)

Non-symmetric matrix

c)

Identity matrix

d)

Null matrix

21.

Which of the following is an assumption of Jacobi’s method?

a)

The coefficient matrix has zeroes on its main diagonal

b)

The coefficient matrix has no zeros on its main diagonal

c)

The rate of convergence is quite slow compared with other methods

d)

Iteration involved in Jacobi’s method converges

22.

when we can't use the Newton Raphson method

a)

f(x)=0

b)

f’(x)=c

c)

f’’(x)=0

d)

f’(x)=0

23.

Which of these methods is named after the mathematician Carl Friedrich Gauss?

a)

Gauss Jordan method

b)

Runge Kutta method

c)

Secant method

d)

Newton Raphson method

24.

For decreasing the number of iterations in Newton Raphson method:

a)

The value of f’(x) must be increased

b)

The value of f’’(x) must be decreased

c)

The value of f’(x) must be decreased

d)

The value of f’’(x) must be increased

25.

 The order of error s the Simpson's rule for numercal integration with a step size h is

a)

h

b)

h2

c)

h3

d)

h4

26.

In simpson’s 1/3 rule, curve y= f(x) is considered to be a

a)

Hyperbola

b)

Parabola

c)

Circle

d)

Straight line

27.

 Mathematical models provide

a)

estimated results

b)

accurate results

c)

wrong results

d)

approximate results

28.

ANOVA.--------EXPANSION

a)

Analysis of variance

b)

Analysis of variable

c)

Analysis of value

d)

Analysis of optional value

29.

What is an extension of two-way ANOVA?

a)

A two-way ANOVA is an extension of the one-way ANOVA

b)

A two-way ANOVA is an extension of the 2X2 ANOVA

c)

A two-way ANOVA is an extension of the THREE WAY ANOVA

d)

A two-way ANOVA is an extension of the LATIN SQUARE ANOVA

30.

hypothesis and the decision making procedure about the hypothesis is called

a)

hypothesis testing

b)

population

c)

sample

d)

random sampling

31.

statistical investigation the group[ of individual under study is called

a)

universe

b)

population

c)

sampling

d)

parameters

32.

the mean and the standard deviation of population is called

a)

parameter

b)

statistics

c)

sample

d)

population

33.

some basic design of experiment

a)

completely randomized design

b)

randomized block design

c)

Latin square

design

d)

none od the above

34.

various objects of comparison in a comparative experiment are called

a)

treatments

b)

experiment

c)

design

d)

variance

35.

This is an example of a

a)

System of Quadratic Equations

b)

Reduced Row Echelon Form

c)

Augmented Matrix

d)

A Canine Doing a Backflip

36.

What is an appropriate first row command to solve this by Gaussian Elimination?

a)

2R2 + R2 -> R2

b)

-2R1 + R2 -> R2

c)

R3 +R2 --> R3

d)

2R1 + R2 --> R2

37.

Aina is simplifying the matrix using Gaussian Elimination. Did she complete the step correctly?

a)

No, she should have changed the 2 to a zero and multiplied -2 by R2 and added R1

b)

No, she wanted to change the 3 to a zero so she should have multiplied R2 and added it to R3

c)

Yes. When you need a zero you multiply by the number's reciprocal.

d)

No. Just punch in the calculator. Who cares about Carl Gauss

38.

Ammar wrote a matrix to represent his system of equations. What was his mistake

a)

The z's are not aligned correctly

b)

There should be a one in the top row for zero

c)

There should be a zero in the second column of the third representing the y

d)

Nothing. This is correct.

39.

Which of the following is the correct representation for the system of equations?

a)

A

b)

B

c)

C

d)

D

40.

Farah solved the matrix on the left. Ibrahim solved the matrix on the right. Who is correct?

a)

Farah, because she multiplied by the reciprocal.

b)

Ibrahim, because he got the top left number to be a one.

c)

Neither. They needed to take care of the one and make it a zero first.

d)

Both. Each step is legal and takes care of the top left term

41.

Which of the following is a numerical equation ?

a)

aX³+bX²+c=4

b)

3X⁴-8X³+5X²-6X+7=0

c)

cos3x -4x =0

42.

Which of the following is an algebraic equation ?

a)

3X⁴-8X³+5X²-6X+7=0

b)

aX³+bX²+c=4

c)

cos3x -4x =0

43.

Which of the following is a transcendental equation ?

a)

aX³+bX²+c=4

b)

3X⁴-8X³+5X²-6X+7=0

c)

cos3x -4x =0

44.

One root of the equation

X³ +4X²-8X +2 =0 lies between........

a)

0 and 1

b)

-1 and 0

c)

-1 and 1

45.

The roots of the equation

X² - 1 =0 is ................

a)

1,-1

b)

1,1

c)

-1,-1

46.

False Position method is used to solve

a)

quadratic equations

b)

system of linear equations

c)

eigen value problems

d)

nonlinear equations

47.

Solving nonlinear equations means ..

a)

finding the x value for which f(x)=0.

b)

finding the root of the functions.

c)

finding the zero of the functions.

48.

Regula Falsi method is also known as ------

a)

Interval halving method

b)

Bolzano's method

c)

Method of False Position

d)

Newton method

49.

Bisection method is a simple but slowly convergent method.

a)

True

b)

False

50.

The equation f(x) = 0 is called

-------- if f(x) involves logarithmic, trigonometric and exponential functions.

a)

algebraic

b)

transcendental

c)

numerical

51.

In numerical integration the width of the sub intervals is given by

a)

h=xn−x0nh=\frac{x_n-x_0}{n}

b)

h=xn+x0nh=\frac{x_n+x_0}{n}

c)

h=x0−xnnh=\frac{x_0-x_n}{n}

d)

none of thesse

52.

In Trapezoidal rule, for the interval (2,5) if h=0.5 then the value of n is_________

a)

5

b)

2

c)

6

d)

4

53.

Simpson’s 1/3 rule is applicable for five ordinates.

a)

True

b)

False

54.

The iteration formula for Newton-Raphson method is

a)

xn+1=xn+f(xn)f′(xn)x_{n+1}=x_n+\frac{f\left(x_n\right)}{f'\left(x_n\right)}

b)

xn+1=xn−f(xn)f′(xn)x_{n+1}=x_n-\frac{f\left(x_n\right)}{f'\left(x_n\right)}

c)

xn+1=xn−f′(xn)f(xn)x_{n+1}=x_n-\frac{f'\left(x_n\right)}{f\left(x_n\right)}

d)

xn+1=xn+f′(xn)f(xn)x_{n+1}=x_n+\frac{f'\left(x_n\right)}{f\left(x_n\right)}

55.

What line is used to find the next iteration in Newton-Raphson method?

a)

Secant

b)

Normal

c)

Chord

d)

Tangent

56.

In Newton-Raphson method, if we want to give our answer correct to 3 decimal places then we need to use how many decimal places in the calculation of the iterations?

a)

3 decimal places

b)

2 decimal places

c)

4 decimal places

d)

any number of decimal places will do

57.

In Newton-Raphson method, if we want to give our answer correct to 3 decimal places then we need to use how many decimal places in the calculation of the iterations?

a)

3 decimal places

b)

2 decimal places

c)

4 decimal places

d)

any number of decimal places will do

58.

The following are ways to verify whether there is a root in the interval [a, b] for a continuous function f(x) except

a)

f(a) < 0 and f(b) > 0

b)

f(a) x f(b) < 0

c)

f(a) x f(b) > 0

d)

The sign for f(a) and f(b) changes

59.

Bisection method is also known as ----- method.

a)

Newton Raphson

b)

Regula Falsi

c)

Interval Halving

d)

Newton

60.

What is the solution to the 4x5 Matrix ?

a)

( 3, 4, 9, 6 )

b)

( 3, 4, 9, -6 )

c)

( -6, 9, 4, 3 )

d)

( 6, 9, 4, 3 )

61.

Using back-substitution, calculate the solution for the REF matrix.

a)

(3, -6, 3)

b)

(-6, -6, 3)

c)

(6, -6, 3)

d)

(-6, -6, 3)

62.

Iteration method is a self correcting method

a)

True

b)

False

63.

Iteration will converge if the leading diagonal element are greater than the sum of other coefficients of that row.

a)

True

b)

False

64.

This is an example of a

a)

System of Quadratic Equations

b)

Reduced Row Echelon Form

c)

Augmented Matrix

d)

A Canine Doing a Backflip

65.

What is an appropriate first row command to solve this by Gaussian Elimination?

a)

2R2 + R2 -> R2

b)

-2R1 + R2 -> R2

c)

R3 +R2 --> R3

d)

2R1 + R2 --> R2

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