CUSTOMER_CODE
SMUDE
DIVISION_CODE
SMUDE
EVENT_CODE
OCTOBER15
ASSESSMENT_CODE BCA3010_OCTOBER15
QUESTION_TYPE
DESCRIPTIVE_QUESTION
QUESTION_ID
10676
QUESTION_TEXT
Define algebraic and transcendental equation. List out any three basic
properties of an algebraic equation.
SCHEME OF
EVALUATION
An equation f(x)=0 is called an algebraic equation if it is purely a
polynomial in x (2 Marks)
An equation f(x)=0 is called an transcendental equation if f(x)
contains trigonometric, exponential or logarithmic functions. (2
Marks)
Properties:
1.Every algebraic equation of nth degree, has ne only n roots (2
Marks)
2.Complex roots occur in pairs (2 Marks)
3.(x-a) is a factor of f(x) (2 Marks)
Or
4.Descartes rule of signs (2 Marks)
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
10679
QUESTION_TEXT
Define:
i. Difference equation
ii. Order of difference equation
iii. Degree of difference equation
iv. General solution
v. Particular solution of difference equation
SCHEME OF
EVALUATION
i.Which involves relationship between independent variables,
dependent variables and successive difference of the dependent
variables. (2 Marks)
ii.difference between the largest and the smallest arguments divided by
the unit of increment (2 Marks)
iii.Highest power of Y (2 Marks)
iv.That in which number of arbitrary constants is equal to the order of
the difference equation (2 Marks)
v.That solution which is obtained from the general solution by giving
particular values to the constants (2 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
125706
QUESTION_TEXT
If
where a and b are real constants, calculate
.
Solution: We have
=
=
SCHEME OF
EVALUATION
=
=
QUESTION_TYPE
DESCRIPTIVE_QUESTION
QUESTION_ID
164973
i.
Why Runge Kutta method is better than Taylor’s series
method and Euler’s method of solving differential equations.
QUESTION_TEXT
ii.
What are the merits and demerits of Taylor’s series method of
solving differential equation?
SCHEME OF
EVALUATION
Runge-Kutta method The Taylor’s series method of solving differential
equations is restricted by the labour involved in the determination of
higher order derivatives. Euler’s method is less efficient in practical
problems since it requires h to be small for obtaining reasonable
accuracy. A class of method known as Runge-Kutta method does
not require the calculations of higher order derivatives and they are
designed to give greater accuracy with the advantage of requiring
only the function values at some selected points on the subinterval. (5 marks)
Merits: i. The method of numerical solution by using Taylor series is of
the single-step untruncated type.
ii. The method is very powerful if we can calculate the successive
derivatives of y in an easy manner.
iii. If there is a simple expression for the higher derivatives in terms of
the previous derivatives of y, Taylor’s method will work very well.
Demerits: The differential equation dy/dx= f(x, y), the function f(x, y)
may have a complicated algebraic structure. Then the evaluation of
higher order derivatives may become tedious and so this method has
little application for computer programmes. (5 marks)