KNEC Craft Certificate in ICT module 1 Mathematics past paper: November 2021 with video(s) Answers

Watch video answers for Mathematics exam November 2021

Course Name:  Information and Communication Technology
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Course Level:  Craft Certificate
Sub Level:       Module I
Course Unit:   Mathematics
Exam body:    KNEC
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1. Convert the decimal number #7423_10# to its equivalent for each of the following number systems: a)Octal b)BCD (4:37)
2. Convert the octal number #325_8# to its equivalent for each of the following number systems: a)Excess-3 b)Hexadecimal. (7:17)
3. Use graphical method to solve the following set of equations: 4y + 3x = 100 4y − 193 = 12 (5:57)
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)#A^c#nB (3:09)
5. Use the binomial theorem to expand the following expression #(4x + 3)^4# (9:49)
6. Describe each of the following matrices: a)Diagonal matrix: b)Triangular matrix. (2:20)
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 (3:19)
8. Solve 5x ≤ −4y − 12 and represent the solution on a graph. (6:14)
9. Determine the fourth term of the expression #(3x + y)^7# (4:10)
10. Explain each of the following terms as used in statistics. a)discrete variable; b)continuous variable. (1:57)
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# (10:21)
12. A quadratic equation has Z and -3 as its roots. Determine its equation. (4:06)
13. Differentiate between floating point and fixed point methods of data representation. (0:48)
14. Outline five advantages of arithmetic mean as a measure of central tendency in statistics. (1:19)
15. Use the binomial theorem to expand the binomial expression #(x − 2y)^5# . (12:21)
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) (4:27)
17. Outline two types of skewness in statistics. (0:18)
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 (12:55)
19. Use the substitution method to solve the following set of equations: y − 4x = 3 y + 3x = 17 (4:52)
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. (8:34)
21. With the aid of a sketch, describe the three types of Kurtosis in statistics. (2:20)
22. Use the Pascal’s triangle to expand the binomial expression #(2x − 5)^4#. (6:36)
23. Use the inverse matrix method to solve the following systems of equation: 3x + 2y = 33 5x − 7y = −7 (8:31)
24. Define each of the following terms as used in probability: i)Event; ii)Outcome: iii)Sample space. (1:30)
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. (5:57)
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. (5:10)
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