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SS1: MATHEMATICS - 1ST TERM

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  1. Number Base System I | Week 1
    6 Topics
    |
    2 Quizzes
  2. Number Base System II | Week 2
    3 Topics
  3. Number Base System III | Week 3
    2 Topics
    |
    1 Quiz
  4. Modular Arithmetic I | Week 4
    2 Topics
  5. Modular Arithmetic II | Week 5
    3 Topics
  6. Modular Arithmetic III | Week 6
    4 Topics
    |
    1 Quiz
  7. Indices I | Week 7
    3 Topics
    |
    1 Quiz
  8. Indices II | Week 8
    1 Topic
    |
    1 Quiz
  9. Logarithms I | Week 9
    3 Topics
  10. Logarithms II | Week 10
    4 Topics
    |
    1 Quiz



Lesson Progress
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Topic Content:

  • Questions & Solutions – Modular Arithmetic

Example 6.3.1:

From the multiplication table for arithmetic (mod 6) find the following:  

(i) \(\scriptsize 2 \bigotimes x = 3 \)
(ii) \(\scriptsize 5 \bigotimes x = 1 \)
(iii) \(\scriptsize 0 ⨸ 3 \)
(iv) \(\scriptsize 2 ⨸ 5 \)

Solution

(i) \(\scriptsize 2 \bigotimes x = 3 \)

Screenshot 2023 09 14 at 08.44.16

For \( \scriptsize 2 \: \bigotimes \: x = 3\)

From the table, x does not exist.

(ii) \( \scriptsize 5 \: \bigotimes \: x = 1 \)

Screenshot 2023 09 16 at 17.44.57

For \( \scriptsize 5 \: \bigotimes \: x = 1 \)

From the table, x = 5

(iii) \(\scriptsize 0 ⨸ 3 \)

Let 0 ⨸ 3 = p

i.e. 3p = 0 (mod 6)

From the table, p = 0, 2 and 4

Screenshot 2023 09 14 at 08.49.51

(iv) \(\scriptsize 2 ⨸ 5 \)

Let 2 ⨸ 5 = p

i.e.   5p = 2 (mod 6)

Screenshot 2023 09 14 at 08.52.51

From the table p = 4

Example 6.3.2:

Find the value(s) of the following:

(i) \( \scriptsize 7 \: \bigotimes \: 9^{-1} \: (mod \:17) \)
(ii) \( \scriptsize 20 \: ⨸ \: 8 \: (mod \:12) \)
(iii)  \( \scriptsize 1 \: ⨸ \: 2 \: (mod \:4) \)
(iv) \( \scriptsize 98 \: ⨸ \: 10 \: (mod \:6) \)

Solution

 

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