CUSTOMER_CODE
SMUDE
DIVISION_CODE
SMUDE
EVENT_CODE
OCTOBER15
ASSESSMENT_CODE BCA3010_OCTOBER15
QUESTION_TYPE
DESCRIPTIVE_QUESTION
QUESTION_ID
10677
QUESTION_TEXT
Define curve fitting. What are the methods of curve fitting.
SCHEME OF
EVALUATION
The process of finding the equation of the curve of best fit which may
be suitable for predicting the unknown values in known is curve
fitting. (2 Marks)
Methods:
i.Graphic method (1 Mark)
ii.Method of group average (1 Mark)
iii.Method of moments (1 Mark)
iv.Method of least squares (1 Mark)
Graphical method explanation (4 Marks)
QUESTION_TYPE
DESCRIPTIVE_QUESTION
QUESTION_ID
10680
QUESTION_TEXT
Define significant digits. State the rules and describe the notion of
significant digits
SCHEME OF
EVALUATION
The digits that are used to express a number (1 Mark)
Rule 1: (Numbers without decimal point) (2 Marks)
Rule 2: (Numbers with decimal point) (2 Marks)
Note:
1.All non zero digits are significant (1 Mark)
2.All zeros occurring between non zero digits are significant digits
(1 Mark)
3.Trailing zeros following a decimal point (1 Mark)
4.Zeros between decimal point and preceding a non zero digit are
not significant (1 Mark)
5.When the decimal point is not written trailing zeros are not
considered to be significant. (1 Mark)
QUESTION_TYPE
DESCRIPTIVE_QUESTION
QUESTION_ID
73415
QUESTION_TEXT
Explain Blunders and Data uncertainty.
SCHEME OF
EVALUATION
Blunders: These errors can be either due to human imperfection or
computer malfunctioning. It can occur at any stage of the mathematical
modeling process and can contribute to all the other components of
error.
Blunders are usually not considered when we discuss about the
different types of error this is just because mistakes are to some extent
unavoidable no matter how efficiently we are going to work.
(5 marks)
Data uncertainty: This type of error is also known as noise. Uncertainty
error is due to uncertainty in physical data upon which a model is
based. This error shows both inaccuracy and imprecision. If the given
data has n significant digits of accuracy then the result obtained from it
will contain n significant digits of accuracy. For example if a = 2.467 and
b = 0.03241 both have 4 significant digits of accuracy then a-b = 2.43459
. Although a-b have 6 significant digits the correct answer will have four
significant digits only that is 2.434 so the answer will be 2.434. (5
marks)
QUESTION_TYPE
DESCRIPTIVE_QUESTION
QUESTION_ID
73416
QUESTION_TEXT
Explain six steps to apply Cramer’s Rule
SCHEME OF
EVALUATION
Step i. Write the given equations in order so
that
constant terms all on the right side (1.5
Marks)
Step ii. Take = the determinant formed by
the
coefficients of x, y, z (1.5 Marks)
Step iii. Replace the first column of  by constant
terms of
the equations and denote as x
(1.5 Marks)
Step iv. Replace the second column of by
constant
terms of the equations and denote
as y (1.5 Marks)
Step v. Replace the third column of by
constant
terms of the equations and denote
as z (1.5 Marks)
Step vi. Write the solution
(3 marks)
QUESTION_TYPE DESCRIPTIVE_QUESTION
QUESTION_ID
73417
Using the given figure explain Regula–Falsi method.
QUESTION_TEXT
Choose two points xo and x1 such that f(x1) and f(x2) are of opposite
signs. Since the graph of y=f(x) crosses the X–axis between these two
points.
This indicates that a root lies between these two points x1 and x2.
SCHEME OF
EVALUATION
Equation of the chord joining the points A(x1, f(x1)) and B(x2, f(x2)) is
y–f(x1) = f(x2)–f(x1) divided by x2–x1 Whole multiplied by (x–x1)-------(i) (3.5 marks)
Where f(x2)–f(x1) divided by x2–x1 is the slope of the line AB.
The method consists in replacing the curve AB by means of the Chord
AB and taking the point of intersection of the chord with the X–axis as
an approximation to the root. The point of intersection in the present
case is given by putting y=0 in (i).
Thus we obtain
0–f(x1)=f(x2)–f(x1) divided by x2–x1 whole multiplied by (x–x1). Solve
for x,
We get x=x1–f(x1)(x2–x1) divided by f(x2)–f(x1)-------(ii) (3.5 marks)
Hence the second approximation to the root of f(x)=0 is given by
x3=x=x1–f(x1)(x2–x1) divided by f(x2)–f(x1)------(iii)
If f(x3) and f(x1) are of opposite signs, then the root lies between x1
and x3, and we replace x2 by x3 in (iii), and obtain the next
approximation. Otherwise, f(x3) and f(x1) are of same sign; we replace
x1 by x3 and generate the next approximation. The procedure is
replaced till the root is obtained to the desired accuracy. (3 marks)
QUESTION_TYPE
DESCRIPTIVE_QUESTION
QUESTION_ID
125706
QUESTION_TEXT
SCHEME OF
EVALUATION
If
where a and b are real constants, calculate
.
Solution: We have
=
=
=
=