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<=KNEC Craft Certificate in ICT module 1 Mathematics past paper: November 2016 with video(s)
given matrices #P=[[3,-1,2],[1,0,3],[3,-2,-5]] # and #Q=[[3,-6,-3],[7,-14,-7],[-1,2,1]]#
Show that;
(i.) PQ is a null matrix;
ii)QP is not a null matrix
Show that;
(i.) PQ is a null matrix;
ii)QP is not a null matrix
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Questions List:
1. Define each of the following terms as used in matrices: (i.) Lower triangular matrix; (ii.)Diagonal matrix.
2. Using binomial theorem, Expand the expression #(2x^2 - y)^3# in descending powers of x.
3. Describe each of the following mathematical functions giving their general form: (i.) Linear function; (ii.) Quadratic function.
4. Given two matrices #A=[[1,0],[-1,2],[2,0]]# and #B=[[3,-1,4],[-1,2,0],[4,0,0]]# , determine #A^T(BA)#
5. Define the following terms as used in statistics; (i)Harmonic mean. ii)Geometric mean
6. Convert the decimal number #75_10# to each of the following equivalents: (i.) Binary; (ii.) Gray code.
7. Explain each of the following terms as used in set theory. (i.) Intersection of sets; (ii.) Complement of a set.
8. Using the substitution method, solve the following set of simultaneous equations; 5x + 3y = 34 4x + 5y = 35
9. Using the binomial expansion, determine the first three terms in the expansion of#(1 − 2y)^7# in ascending powers of y
10. Define the term random experiment as used in probability theory
11. Outline three properties of random experiment.
12. a) The following information relate to the qualifications of employees of AZECT Company. Sam, John, Willy and Ben have diploma certificates with Sam and Ben also having degrees. Sam, Melvin, Willy, Tom, Morris and Ken are members of the ICTAK certifying body, with Tom and Morris having diploma certificates. Assume set ‘A’ to be ‘employees’ with diploma certificates, set ‘B’ employees who are ICTAK
13. Using the elimination method, solve the following simultaneous equations 7x-4y=37 6x+3y=51
14. Differentiate between the terms qualitative data and quantitative data methods.
15. given matrices #P=[[3,-1,2],[1,0,3],[3,-2,-5]] # and #Q=[[3,-6,-3],[7,-14,-7],[-1,2,1]]# Show that; (i.) PQ is a null matrix; ii)QP is not a null matrix
16. Table 1 shows the salary distribution in Kenyan shillings of 370 employees of a certain firm. Use it to answer the questions that follow. Estimate each of the following measures about the salary of the employees; (i.) The mean. (2mks) (ii.) The standard deviation. (3mks)
17. Describe each of the following number systems as used in computer systems. (i.) Hexadecimal number system; (2mks) (ii.) Octal number system. (2mks)
18. A factory keeps the details of ingredients used to produce soaps X and Y as shown in matrix R and quantity produced on each day of the week as shown in matrices Q. Determine the matrix that describes the amount of each ingredients used on each day of the week.
19. State the binomial theorem where n is a positive integer
20. Using the Pascal’s triangle, expand #(x+2y)^6# in descending powers of x
21. Using the matrix method, solve the following simultaneous equations. 3x-y=11 4x+3y=32
22. John intends to prepare a questionnaire to collect statistical data in a work environment survey for the organization he works for. Explain three features of the questionnaire that he should consider.
23. Write the following abbreviations in full as used in computer coding. (i.) ASCII; (ii.) EBCDIC.
24. State two characteristics of binomial distribution.
25. Table 1 shows the age distribution of 30, 100 policy holders in a certain insurance company. Use it to answer the questions that follow. Determine each of the following measures about age distribution; (i.) Median; (ii.) Quartile deviation
26. Given that a matrix A =#[[5,2,1],[0,-1,-1],[10,3,0]]# determine #A^-1# using the cofactor method.
1. Define each of the following terms as used in matrices: (i.) Lower triangular matrix; (ii.)Diagonal matrix.
2. Using binomial theorem, Expand the expression #(2x^2 - y)^3# in descending powers of x.
3. Describe each of the following mathematical functions giving their general form: (i.) Linear function; (ii.) Quadratic function.
4. Given two matrices #A=[[1,0],[-1,2],[2,0]]# and #B=[[3,-1,4],[-1,2,0],[4,0,0]]# , determine #A^T(BA)#
5. Define the following terms as used in statistics; (i)Harmonic mean. ii)Geometric mean
6. Convert the decimal number #75_10# to each of the following equivalents: (i.) Binary; (ii.) Gray code.
7. Explain each of the following terms as used in set theory. (i.) Intersection of sets; (ii.) Complement of a set.
8. Using the substitution method, solve the following set of simultaneous equations; 5x + 3y = 34 4x + 5y = 35
9. Using the binomial expansion, determine the first three terms in the expansion of#(1 − 2y)^7# in ascending powers of y
10. Define the term random experiment as used in probability theory
11. Outline three properties of random experiment.
12. a) The following information relate to the qualifications of employees of AZECT Company. Sam, John, Willy and Ben have diploma certificates with Sam and Ben also having degrees. Sam, Melvin, Willy, Tom, Morris and Ken are members of the ICTAK certifying body, with Tom and Morris having diploma certificates. Assume set ‘A’ to be ‘employees’ with diploma certificates, set ‘B’ employees who are ICTAK
13. Using the elimination method, solve the following simultaneous equations 7x-4y=37 6x+3y=51
14. Differentiate between the terms qualitative data and quantitative data methods.
15. given matrices #P=[[3,-1,2],[1,0,3],[3,-2,-5]] # and #Q=[[3,-6,-3],[7,-14,-7],[-1,2,1]]# Show that; (i.) PQ is a null matrix; ii)QP is not a null matrix
16. Table 1 shows the salary distribution in Kenyan shillings of 370 employees of a certain firm. Use it to answer the questions that follow. Estimate each of the following measures about the salary of the employees; (i.) The mean. (2mks) (ii.) The standard deviation. (3mks)
17. Describe each of the following number systems as used in computer systems. (i.) Hexadecimal number system; (2mks) (ii.) Octal number system. (2mks)
18. A factory keeps the details of ingredients used to produce soaps X and Y as shown in matrix R and quantity produced on each day of the week as shown in matrices Q. Determine the matrix that describes the amount of each ingredients used on each day of the week.
19. State the binomial theorem where n is a positive integer
20. Using the Pascal’s triangle, expand #(x+2y)^6# in descending powers of x
21. Using the matrix method, solve the following simultaneous equations. 3x-y=11 4x+3y=32
22. John intends to prepare a questionnaire to collect statistical data in a work environment survey for the organization he works for. Explain three features of the questionnaire that he should consider.
23. Write the following abbreviations in full as used in computer coding. (i.) ASCII; (ii.) EBCDIC.
24. State two characteristics of binomial distribution.
25. Table 1 shows the age distribution of 30, 100 policy holders in a certain insurance company. Use it to answer the questions that follow. Determine each of the following measures about age distribution; (i.) Median; (ii.) Quartile deviation
26. Given that a matrix A =#[[5,2,1],[0,-1,-1],[10,3,0]]# determine #A^-1# using the cofactor method.
