{"id":2100,"date":"2023-10-02T09:10:12","date_gmt":"2023-10-02T09:10:12","guid":{"rendered":"http:\/\/localhost\/ecole9ja\/?p=2100"},"modified":"2023-10-02T09:14:57","modified_gmt":"2023-10-02T09:14:57","slug":"week-4-ss1-first-term-general-mathematics-notes","status":"publish","type":"post","link":"https:\/\/ecolebooks.com\/nigeria\/posts\/week-4-ss1-first-term-general-mathematics-notes\/","title":{"rendered":"Week 4 &#8211; SS1 First Term General Mathematics Notes"},"content":{"rendered":"<p>\u00a0WEEK 4\u00a0\u00a0\u00a0\u00a0<br \/>\nMODULAR ARITHMETIC<br \/>\nModular arithmetic is a branch of Mathematics use to predict the outcomes of cyclic events such as days of the week, marketdays, months of the year, time etc.<br \/>\n\u00a0\u00a0\u00a0\u00a0RULES OF MODULAR ARITHMETIC<\/p>\n<ul>\n<li>The modulo value must be greater than the number worked upon.\n<\/li>\n<li>When using cyclic pattern in adding numbers, you must count clock wise direction.\n<\/li>\n<li>In subtraction of numbers , you must count anti -clock wise direction\n<\/li>\n<\/ul>\n<p>             EXAMPLE:<br \/>\nThe shorter hand of a clock points to 5 on a clock face.  What number does it point to after 30 hours?<br \/>\n<img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_0910_Week4SS1Fi1.png\" alt=\"\"\/>        Solution<img decoding=\"async\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_0910_Week4SS1Fi2.png\" alt=\"\"\/><br \/>\n\t30 hours after = 11 o&#8221; clock.<\/p>\n<ol>\n<li>Find the following numbers in their simplest form in modulo 4\n<\/li>\n<li>\n<div>15  b. 102\n<\/div>\n<p>Solution\n<\/li>\n<\/ol>\n<p>15(mod4) = 15\u00f74<br \/>\n3 remainder 3,   therefore 3 the remainder is taken as 3 mod 4<br \/>\n102mod4 = 102 \u00f74   = 25 remainder 2<br \/>\n102 (mod 4) = 2 mod 4<br \/>\nADDITION OF MODULO ARITHMETIC<br \/>\nEXAMPLE<br \/>\n<img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_0910_Week4SS1Fi3.png\" alt=\"\"\/>Find the following modulo addition<br \/>\n<img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_0910_Week4SS1Fi4.png\" alt=\"\"\/>:a.42  28 (mod 8)    b.    54       25 (mod 5)<br \/>\nSolution<\/p>\n<ol>\n<li>\n<div>42 + 28 = 70 mod 8\n<\/div>\n<p>70 mod 8 = 6 mod 8\n<\/li>\n<li>\n<div>54 + 25 = 79 mod 5\n<\/div>\n<p>79 mod 5 = 4 mod 5<br \/>\nSUBTRACTION OF MODULO NUMBERS\n<\/li>\n<\/ol>\n<p>Find the simplest form of the following in their giving moduli.<\/p>\n<ol>\n<li>\n<div>-5 mod 6   b. -17 mod 10   c. -75 mod 7\n<\/div>\n<p>SOLUTION\n<\/li>\n<li>-5 mod 6 = -6&#215;1+1 = 1 mod 6  the value added to the negative number to give the require result becomes your result.\n<\/li>\n<li>-17 mod 10 = -10 x 2 + 3 = 3mod 10.\n<\/li>\n<li>-75 mod 7 = -7 x 11+2 =2 mod 7.\n<\/li>\n<\/ol>\n<p>MULTIPLICATION OF MODULO NUMBERS<br \/>\nEvaluate the following in their moduli.<\/p>\n<ol>\n<li>\n<div><img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_0910_Week4SS1Fi5.png\" alt=\"\"\/><img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_0910_Week4SS1Fi6.png\" alt=\"\"\/>16                7  mod 5  b. 21                 65 mod 4\n<\/div>\n<p>SOLUTION\n<\/li>\n<\/ol>\n<p>A 16 X 7 = 117 mod 5, which is  2 mod 5<\/p>\n<ol>\n<li>\n<div>21 x 65  = 1365 mod 4  =  1mod 4\n<\/div>\n<p>EQUATION OF MODULO\n<\/li>\n<\/ol>\n<p> Solve the following equations in their giving moduli<\/p>\n<ol>\n<li>\n<div>3x =5mod 7   b. 2x + 3 =1 mod 6   c.\n<\/div>\n<p>SOLUTION<\/p>\n<ol>\n<li>\n<div>3x =5+7 ,.   3x =12\n<\/div>\n<p>X = 4 mod 7\n<\/li>\n<li>\n<div>2x +3 =1+6 ,      2x +3  =7\n<\/div>\n<p>2x 7 -5, then   2x  = 4<br \/>\nX =2 mod 6<br \/>\nASSESSMENT: Solve the following questions;<\/p>\n<ol>\n<li>\n<div>Use the cycle number in modulo 6 to simplify the following.\n<\/div>\n<ol>\n<li>2 + 10 (ii).  5 + 5  (iii) 15 + 37 (iv) 2 \u2013 9  (v) 0 \u2013 22\n<\/li>\n<\/ol>\n<\/li>\n<li>A toy car starts at a point 0 and runs around a circular track of 2 meters. How far is the car from its starting point along  the track when it has gone :\n<\/li>\n<\/ol>\n<ol>\n<li>\n<div>6m (b) 15m (c) 21m (d) 87m\n<\/div>\n<ol>\n<li>\n<div>Find the following numbers in their simplest form in modulo 4:\n<\/div>\n<p>(i). 62(ii). 102 (iii) -56 (iv) -78 (v) -202\n<\/li>\n<li>\n<div>Solve the following equations in the set of positive integers of each modular arithmetic:\n<\/div>\n<ol>\n<li>\n<div>3X + 4 = 7 mod 8 ii. 4X \u2013 3 = 6 mod 7   iii.    \u2013 2X + 2 = 0 mod 5   IV.  = 2 in (a). Mod 5 (b). Mod 6 (c). mod 9\n<\/div>\n<p>\u00a0<\/li>\n<\/ol>\n<\/li>\n<\/ol>\n<\/li>\n<\/ol>\n<\/li>\n<\/ol>\n<\/li>\n<\/ol>\n<p>\u00a0MORAL OBJECTIVE: EXODUS 15:25and he cried unto the Lord and there he proved them.<\/p>\n<p>\u00a0<br \/>\n\u00a0<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u00a0WEEK 4\u00a0\u00a0\u00a0\u00a0 MODULAR ARITHMETIC Modular arithmetic is a branch of Mathematics use to predict the&#8230;<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1,183],"tags":[],"class_list":["post-2100","post","type-post","status-publish","format-standard","hentry","category-posts","category-first-term-ss1-general-mathematics"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/ecolebooks.com\/nigeria\/wp-json\/wp\/v2\/posts\/2100","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/ecolebooks.com\/nigeria\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/ecolebooks.com\/nigeria\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/ecolebooks.com\/nigeria\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/ecolebooks.com\/nigeria\/wp-json\/wp\/v2\/comments?post=2100"}],"version-history":[{"count":1,"href":"https:\/\/ecolebooks.com\/nigeria\/wp-json\/wp\/v2\/posts\/2100\/revisions"}],"predecessor-version":[{"id":2101,"href":"https:\/\/ecolebooks.com\/nigeria\/wp-json\/wp\/v2\/posts\/2100\/revisions\/2101"}],"wp:attachment":[{"href":"https:\/\/ecolebooks.com\/nigeria\/wp-json\/wp\/v2\/media?parent=2100"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/ecolebooks.com\/nigeria\/wp-json\/wp\/v2\/categories?post=2100"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/ecolebooks.com\/nigeria\/wp-json\/wp\/v2\/tags?post=2100"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}