KNEC Craft Certificate in ICT module 1 Mathematics past paper: July 2019 with video(s) Answers

Watch video solved answers for July 2019 Mathematics paper in CICT

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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Convert each of the decimal numbers to an 8-bit two’s complement binary number. i) #47_10# ii) #-72_10# (6:14)

Differentiate between BCD and EBCDIC computer coding systems (1:09)

Describe each of the following types of statistical data; i) Discrete data ii) Continuous data (1:34)

Use the binomial theorem to expand the expression #(5x + 2b)^3# in the descending powers of x. (7:32)

Given that matrix W = #[[3,-4],[-2,5]]# determine #(2W)^-1# (4:10)

Use the matrix method to solve the following pair of simultaneous equations; X + 2y = -1 3x + 5y = 19 (7:23)

Determine the value of x in each of the following inequalities: i) -2(x+3)<10; ii)-4x(x-3)<16. (4:20)

Outline three methods of collecting statistical data. (0:40)

Describe two ways in which statistical data can be classified. (0:54)

10.

Explain two assumptions in Poisson probability distribution. (1:20)

11.

Describe each of the following types of matrices: i) Column matrix; ii) Scalar matrix. (2:07)

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#. (17:11)

13.

Convert each of the following numbers to their equivalent number systems indicated: i) #63150_8# to binary; ii) #153_8# to hexadecimal. (4:24)

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. (4:04)

15.

Use the substitution method to solve the following pair of simultaneous equations. i) 3x-y=11 ii) 3x-2y=4 (3:14)

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. (3:57)

17.

Outline three properties of binomial probability distribution. (0:58)

18.

Using Pascal’s triangle, expand the expression #(x-3y)^4# in ascending powers of y. (7:05)

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. (6:57)

20.

State the meaning of each of the following set operations. i) A ⊂ B ii) Ø iii) x ∈ T iV) #tilde A# (1:58)

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]]# (12:36)

22.

State the difference between data sets that were used to draw the graphs labeled (i) and (ii) with respect to skewness: (1:05)

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 (6:32)