Computational Mathematics July 2017 Past Examination Question Paper – KNEC
This Past Paper examination was examined by the Kenya National Examination Council (KNEC) and it applies to the following courses
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Diploma in Information Communication Technology – Module I
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THE KENYA NATIONAL EXAMINATIONS COUNCIL
DIPLOMA IN INFORMATION COMMUNICATION TECHNOLOGY
MODULE I
COMPUTATIONAL MATHEMATICS
3 hours
Explain each of the following measurement scales«as used in the classification of statistical data:
(i) nominal scale;
(ii) ordinal scale;
(iii) interval scale;
(iv) ratio scale. (8 marks)
Given two polynomial functions: y — 16x — x — 13, and y = 2x + 11:
(i) Determine by calculation the coordinates of their points of intersection;
(6 marks)
(ii) Determine the surface area enclosed by the two lines. (6 marks)
Distinguish between interpolation and extrapolation as used in mathematics. (2 marks)
When data is grouped into classes, any measure calculated is merely an estimate no matter how accurate the calculation is. Justify this statement. (2 marks)
The data in Table 1 shows the distribution of heights in cm of 500 male students of a certain secondary school. Use it to answer the questions that follow.
Height in cm 140- 150 150- 160 160-170 170-180 180-190 190-200 200-210
No. of students 15 50 100 160 120 45 10
Table 1
Six family couples run a business as partners. A delegation of four people is to be chosen to represent the business in a conference. Determine the number of ways in which the delegation can be selected under each of the following conditions:
(i) if a man and his wife cannot both be selected; (4 marks)
(ii) if each sex must be at least one quarter of the total delegation. (4 marks)
Explain the term parity bit as used in computer data representation. (2 marks)
(i) Using the binomial theorem, expand the binomial expression (3x + y)6 in
ascending powers of x. (5 marks)
(ii) Using the expansion in (i), evaluate the expression (15.1)6 (3 marks)
A cubic polynomial function is given by f(x) = x3 — 5×2 + 3x + 8 . Using the Newton-Raphson iterative method, determine the root of the equation rounded off to 4 decimal places. Take the initial root x0 = 2.0. (10 marks)
Define each of the following terms as used in numerical analysis:
(i) absolute error;
(ii) relative error. (4 marks)
Explain three properties of the standard deviation as a measure of dispersion. (6 marks) Given two matrices A and B such that:
Show that:
(i) AB^ BA
(ii) det (A) X det (B) = det (AB)
(iii) A_1B_1 =£ (AB)-1 (10 marks)
Some of the measures of central tendency are viewed as points of equilibrium. Explain the context in which each of the following statistical measures is considered as a point of equilibrium in a distribution:
(i) the arithmetic mean;
(ii) the median. (4 marks)
Differentiate between a diagonal matrix and a non-singular matrix as used in mathematics. (4 marks)
Solve the following set of simultaneous equations using the matrix method.
3x + 4y = 52
5x + 8y = 96 (4 marks)
Turn over
A manufacturing company produces ballpoint pens in two colours as follows: blue 75%, and red 25%. The machine is set to produce these colours randomly but maintaining the proportions. A quality assurance officer picks three pens at random one at a time from the production line for inspection.
(i) present this information using a probability tree diagram; (3 marks)
(ii) determine the probability of picking three pens with alternating colours;
(3 marks)
(iii) determine the probability of picking three pens of the same colour. (2 marks)
(i) Define the term model as used in statistics, stating two examples. (2 marks)
(ii) Distinguish between an independent variable and a dependent variable.
(4 marks)
A binary arithmetic subtraction operation is given as: 110012 – 10102
Perform this operation using each of the following methods:
(i) one’s complement;
(ii) two’s complement. (5 marks)
(i) Outline four disadvantages of the arithmetic mean as a measure of central
tendency. (4 marks)
(ii) One of the properties of the arithmetic mean is that it is dependent on origin.
Explain this property using a suitable illustration. (3 marks)
8- (a)
A curve is defined by the quadratic function y = 12x — x2 — 20.
(i) Determine the roots of the equation using the factorisation method; (3 marks)
(ii) By using calculus techniques, determine the coordinates of the turning point of
the curve. (3 marks)
General observation on a certain road indicates that there are 3 potholes for every 240- metre distance along the road. A random length of 900 metres was selected from a section of the road.
(i) Model this problem as a Poisson probability distribution; (2 marks)
(ii) Determine the probability of getting exactly 10 potholes on the selected length.
(2 marks)
(iii) Determine the probability of getting between 4 and 6 potholes inclusive on the
selected length of the road. (3 marks)
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