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<=KNEC Craft Certificate in ICT module 1 Mathematics past paper: November 2021 with video(s)
Outline two types of skewness in statistics.
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Questions List:
1. Convert the decimal number 742310 to its equivalent for each of the following number systems: a)Octal b)BCD
2. Convert the octal number 3258 to its equivalent for each of the following number systems: a)Excess-3 b)Hexadecimal.
3. Use graphical method to solve the following set of equations: 4y + 3x = 100 4y − 193 = 12
4. Given that set U={a, b, c, d, b, e, f, g, h}, B={a, c, d, e} and A={a, b, c}; Determine each of the following operations: a)AnB; b)AcnB
5. Use the binomial theorem to expand the following expression (4x+3)4
6. Describe each of the following matrices: a)Diagonal matrix: b)Triangular matrix.
7. Given the matrices x=[[1,5,-1],[-1,2,2],[0,-3,3]] and Y=[[-1,-4,3],[1,-2,-2],[-3,3,-5]] determine X+3Y
8. Solve 5x ≤ −4y − 12 and represent the solution on a graph.
9. Determine the fourth term of the expression (3x + y)^7
10. Explain each of the following terms as used in statistics. a)discrete variable; b)continuous variable.
11. Given Matrix S=[[1,7],[9,2]] and R=[[2,4],[4,3]] show that i)SR != RS ii)(SR)^T=S^TR^T
12. A quadratic equation has Z and -3 as its roots. Determine its equation.
13. Differentiate between floating point and fixed point methods of data representation.
14. Outline five advantages of arithmetic mean as a measure of central tendency in statistics.
15. Use the binomial theorem to expand the binomial expression (x − 2y)^5 .
16. Given three sets A, B and C, draw a Venn diagram and shade the area representing each of the following: i)AUBUC; ii)AU(BnC)
17. Outline two types of skewness in statistics.
18. Table 1 shows the frequency distribution of weight of patients who attended a hospital. Use it to answer the questions that follow. Determine each of the following measures about patient’s weight: I. Mean II. Standard deviation
19. Use the substitution method to solve the following set of equations: y − 4x = 3 y + 3x = 17
20. Table 2 shows lunch preferences for 195 students when taken out for three different trips. Use it to answer the question that follows. Represent this information in a clustered column chart.
21. With the aid of a sketch, describe the three types of Kurtosis in statistics.
22. Use the Pascal’s triangle to expand the binomial expression (2x − 5)^4.
23. Use the inverse matrix method to solve the following systems of equation: 3x + 2y = 33 5x − 7y = −7
24. Define each of the following terms as used in probability: i)Event; ii)Outcome: iii)Sample space.
25. Given that the universal set is the set of all even numbers less than 30 and sets A= {4, 8, 12, 16, 20, 24, 28} B= {6, 12, 18, 24, 28}. i)Use a Venn diagram to represent this information. ii)Determine AᴒBc.
26. A swimming coach intends to choose 3 swimmers from group of 5. Determine the number of ways the coach can use to choose the swimmers.
1. Convert the decimal number 742310 to its equivalent for each of the following number systems: a)Octal b)BCD
2. Convert the octal number 3258 to its equivalent for each of the following number systems: a)Excess-3 b)Hexadecimal.
3. Use graphical method to solve the following set of equations: 4y + 3x = 100 4y − 193 = 12
4. Given that set U={a, b, c, d, b, e, f, g, h}, B={a, c, d, e} and A={a, b, c}; Determine each of the following operations: a)AnB; b)AcnB
5. Use the binomial theorem to expand the following expression (4x+3)4
6. Describe each of the following matrices: a)Diagonal matrix: b)Triangular matrix.
7. Given the matrices x=[[1,5,-1],[-1,2,2],[0,-3,3]] and Y=[[-1,-4,3],[1,-2,-2],[-3,3,-5]] determine X+3Y
8. Solve 5x ≤ −4y − 12 and represent the solution on a graph.
9. Determine the fourth term of the expression (3x + y)^7
10. Explain each of the following terms as used in statistics. a)discrete variable; b)continuous variable.
11. Given Matrix S=[[1,7],[9,2]] and R=[[2,4],[4,3]] show that i)SR != RS ii)(SR)^T=S^TR^T
12. A quadratic equation has Z and -3 as its roots. Determine its equation.
13. Differentiate between floating point and fixed point methods of data representation.
14. Outline five advantages of arithmetic mean as a measure of central tendency in statistics.
15. Use the binomial theorem to expand the binomial expression (x − 2y)^5 .
16. Given three sets A, B and C, draw a Venn diagram and shade the area representing each of the following: i)AUBUC; ii)AU(BnC)
17. Outline two types of skewness in statistics.
18. Table 1 shows the frequency distribution of weight of patients who attended a hospital. Use it to answer the questions that follow. Determine each of the following measures about patient’s weight: I. Mean II. Standard deviation
19. Use the substitution method to solve the following set of equations: y − 4x = 3 y + 3x = 17
20. Table 2 shows lunch preferences for 195 students when taken out for three different trips. Use it to answer the question that follows. Represent this information in a clustered column chart.
21. With the aid of a sketch, describe the three types of Kurtosis in statistics.
22. Use the Pascal’s triangle to expand the binomial expression (2x − 5)^4.
23. Use the inverse matrix method to solve the following systems of equation: 3x + 2y = 33 5x − 7y = −7
24. Define each of the following terms as used in probability: i)Event; ii)Outcome: iii)Sample space.
25. Given that the universal set is the set of all even numbers less than 30 and sets A= {4, 8, 12, 16, 20, 24, 28} B= {6, 12, 18, 24, 28}. i)Use a Venn diagram to represent this information. ii)Determine AᴒBc.
26. A swimming coach intends to choose 3 swimmers from group of 5. Determine the number of ways the coach can use to choose the swimmers.
