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SS1: MATHEMATICS - 1ST TERM

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  1. Number Base System I | Week 1
    6Topics
    |
    2 Quizzes
  2. Number Base System II | Week 2
    3Topics
    |
    1 Quiz
  3. Number Base System III | Week 3
    2Topics
    |
    1 Quiz
  4. Modular Arithmetic I | Week 4
    2Topics
  5. Modular Arithmetic II | Week 5
    2Topics
  6. Modular Arithmetic III | Week 6
    3Topics
    |
    1 Quiz
  7. Indices I | Week 7
    2Topics
  8. Indices II | Week 8
    1Topic
    |
    1 Quiz
  9. Logarithms I | Week 9
    3Topics
  10. Logarithms II
    1Topic
    |
    1 Quiz
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A good example of cyclic event is the 12-hour clock. In the 12-hour clock arithmetic, the hour hand can move in both directions as shown the diagram

Screen Shot 2020 10 03 at 11.27.37 PM

Example 1

If the time is presently 9 o’clock, what would the time be in   (i) 92 hours (ii) 750 hours’ time?

Solution

(i) 92 hours = 92 ÷ 12 = 7 r 8

               = ( 12 x 7) hrs + 8 hrs

               = 9 o’clock + 8hrs

               = 5 o’clock 

(ii)750 hours = 750 ÷ 12 = 62 r 6

                 = (12 x 62)hrs + 6 hrs 

                 = 9 o’clock + 6 hrs

  = 3 o’clock

Example 2

If the time is presently 3 o’clock, what time was it (i) 9 hours ago (ii) 25 hours ago?

Solution:

(i) Counting in the anti-clockwise direction, i.e. we have to count 9 spaces backward i.e. the time was 6 o’clock.

(ii) 25 = (12 x 2)hrs + 1 hr

Hence, counting one step backward (or in an anticlockwise direction), we have (3 – 1) = 2

i.e.  2 o’clock

The clock arithmetic is synonymous with Modular Arithmetic which is by way of wrapping numbers around after they reach a certain value.

Modular Arithmetic system involves integers only. When an integer is divided by 5, the possible remainders are 0, 1, 2, 3, and 4; we thus refer to these numbers as the residues of modulo 5 or mod5.

Similarly, 0, 1, 2, 3, 4, 5 consist of the set of residues for mod 6.

In general, {0, 1, 2, 3, 4, 5, 6, …… n – 1} is called the set of residues for mod n.

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