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<=KNEC Craft Certificate in ICT module 1 Mathematics past paper: July 2019 with video(s)
Given the matrix L = #[[3,-1,2],[-3,1,5],[0,3,7]]# show that
#L^-1 = [[8/63,-13/63,1/9],[-1/3,-1/3,1/3],[1/7,1/7,0]]#
#L^-1 = [[8/63,-13/63,1/9],[-1/3,-1/3,1/3],[1/7,1/7,0]]#
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Questions List:
1. Convert each of the decimal numbers to an 8-bit two’s complement binary number. i) #47_10# ii) #-72_10#
2. Differentiate between BCD and EBCDIC computer coding systems
3. Describe each of the following types of statistical data; i) Discrete data ii) Continuous data
4. Use the binomial theorem to expand the expression #(5x + 2b)^3# in the descending powers of x.
5. Given that matrix W = #[[3,-4],[-2,5]]# determine #(2W)^-1#
6. Use the matrix method to solve the following pair of simultaneous equations; X + 2y = -1 3x + 5y = 19
7. Determine the value of x in each of the following inequalities: i) -2(x+3)<10; ii)-4x(x-3)<16.
8. Outline three methods of collecting statistical data.
9. Describe two ways in which statistical data can be classified.
10. Explain two assumptions in Poisson probability distribution.
11. Describe each of the following types of matrices: i) Column matrix; ii) Scalar matrix.
12. Given the following matrices, X=#[[2,-1],[3,0],[-5,2]]# Y=#[[4,4,-3],[0,-1,-2]]# and Z = #[[1,6],[1,2],[0,-3]]# Determine each of the following matrix operation: i) (XY)Z; ii) #X^TZ#.
13. Convert each of the following numbers to their equivalent number systems indicated: i) #63150_8# to binary; ii) #153_8# to hexadecimal.
14. Table I shows the probability of selling a specified number of cars by a certain car dealer in a certain month. Use it to answer the question that follows. Determine the number of cars the car dealer expects to sell during the period.
15. Use the substitution method to solve the following pair of simultaneous equations. i) 3x-y=11 ii) 3x-2y=4
16. A team comprising of 7 men and 6 women and a committee of 5 persons is to be formed from a group. Determine the number of ways in which a committee of 3 men and 2 women could be formed.
17. Outline three properties of binomial probability distribution.
18. Using Pascal’s triangle, expand the expression #(x-3y)^4# in ascending powers of y.
19. Given the sets U={11,12,13,14,15,16,19}, X={11,12,13,14}and Y={12,14,16}, use Venn diagram to represent each of the following set operations: i) #XuuY# ii) #XnnU# ; iii) X-Y.
20. State the meaning of each of the following set operations. i) A ⊂ B ii) Ø iii) x ∈ T iV) #tilde A#
21. Given the matrix L = #[[3,-1,2],[-3,1,5],[0,3,7]]# show that #L^-1 = [[8/63,-13/63,1/9],[-1/3,-1/3,1/3],[1/7,1/7,0]]#
22. State the difference between data sets that were used to draw the graphs labeled (i) and (ii) with respect to skewness:
23. A box R contains 2 green and 8 white similar balls. A box S contains 4 green and 8 white similar balls. A ball is drawn at random from box R and placed in box S. Then a ball is drawn at random from box S. i) Represent this information using a probability tree. ii) Determine the probability of each of the following events: 1. Drawing a green ball from box R and a white ball from box S. 2. Drawing a
1. Convert each of the decimal numbers to an 8-bit two’s complement binary number. i) #47_10# ii) #-72_10#
2. Differentiate between BCD and EBCDIC computer coding systems
3. Describe each of the following types of statistical data; i) Discrete data ii) Continuous data
4. Use the binomial theorem to expand the expression #(5x + 2b)^3# in the descending powers of x.
5. Given that matrix W = #[[3,-4],[-2,5]]# determine #(2W)^-1#
6. Use the matrix method to solve the following pair of simultaneous equations; X + 2y = -1 3x + 5y = 19
7. Determine the value of x in each of the following inequalities: i) -2(x+3)<10; ii)-4x(x-3)<16.
8. Outline three methods of collecting statistical data.
9. Describe two ways in which statistical data can be classified.
10. Explain two assumptions in Poisson probability distribution.
11. Describe each of the following types of matrices: i) Column matrix; ii) Scalar matrix.
12. Given the following matrices, X=#[[2,-1],[3,0],[-5,2]]# Y=#[[4,4,-3],[0,-1,-2]]# and Z = #[[1,6],[1,2],[0,-3]]# Determine each of the following matrix operation: i) (XY)Z; ii) #X^TZ#.
13. Convert each of the following numbers to their equivalent number systems indicated: i) #63150_8# to binary; ii) #153_8# to hexadecimal.
14. Table I shows the probability of selling a specified number of cars by a certain car dealer in a certain month. Use it to answer the question that follows. Determine the number of cars the car dealer expects to sell during the period.
15. Use the substitution method to solve the following pair of simultaneous equations. i) 3x-y=11 ii) 3x-2y=4
16. A team comprising of 7 men and 6 women and a committee of 5 persons is to be formed from a group. Determine the number of ways in which a committee of 3 men and 2 women could be formed.
17. Outline three properties of binomial probability distribution.
18. Using Pascal’s triangle, expand the expression #(x-3y)^4# in ascending powers of y.
19. Given the sets U={11,12,13,14,15,16,19}, X={11,12,13,14}and Y={12,14,16}, use Venn diagram to represent each of the following set operations: i) #XuuY# ii) #XnnU# ; iii) X-Y.
20. State the meaning of each of the following set operations. i) A ⊂ B ii) Ø iii) x ∈ T iV) #tilde A#
21. Given the matrix L = #[[3,-1,2],[-3,1,5],[0,3,7]]# show that #L^-1 = [[8/63,-13/63,1/9],[-1/3,-1/3,1/3],[1/7,1/7,0]]#
22. State the difference between data sets that were used to draw the graphs labeled (i) and (ii) with respect to skewness:
23. A box R contains 2 green and 8 white similar balls. A box S contains 4 green and 8 white similar balls. A ball is drawn at random from box R and placed in box S. Then a ball is drawn at random from box S. i) Represent this information using a probability tree. ii) Determine the probability of each of the following events: 1. Drawing a green ball from box R and a white ball from box S. 2. Drawing a
