{"id":2603,"date":"2023-10-03T10:44:29","date_gmt":"2023-10-03T10:44:29","guid":{"rendered":"http:\/\/localhost\/ecole9ja\/?p=2603"},"modified":"2023-10-03T10:47:41","modified_gmt":"2023-10-03T10:47:41","slug":"week-5-ss1-third-term-further-mathematics-notes","status":"publish","type":"post","link":"https:\/\/ecolebooks.com\/nigeria\/posts\/week-5-ss1-third-term-further-mathematics-notes\/","title":{"rendered":"Week 5 – SS1 Third Term Further Mathematics Notes"},"content":{"rendered":"

\u00a0WEEK 5
\n<\/strong>Topic:<\/em><\/strong> \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0Vectors
\nSub-topic:<\/em>
\n\t\t\t\t<\/strong>\u00a0\u00a0\u00a0\u00a0 Modulus of a vector
\nDuration:<\/em><\/strong> \u00a0\u00a0\u00a0\u00a080 minutes
\nLearning Objectives:<\/em><\/strong> By the end of the lesson, students should be able to perform simple operations on vectors.
\nReference Materials:<\/em><\/strong> New Further Mathematics Project 2 by M. R Tuttuh Adegun
\nPrevious Knowledge<\/em>:<\/strong> Students can perform arithmetic operations on vectors
\nInstructional Materials<\/em>:<\/strong> Mathematical set.
\nContent:\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/em>MAGNITUDE OF A VECTOR
\n<\/strong>The magnitude of a vector a, sometimes called the modulus of the vector is represented by |a|.
\nZero Vector:\u00a0\u00a0\u00a0\u00a0<\/strong>The zero vector is a vector with zero magnitude.
\nUnit Vector:\u00a0\u00a0\u00a0\u00a0<\/strong>The unit vector is the vector represented by a and is such that a = |a| a
\n<\/strong>Negative Vector:\u00a0\u00a0\u00a0\u00a0<\/strong>The negative vector of a is written as \u2013 a
\nEquality of vector:\u00a0\u00a0\u00a0\u00a0<\/strong>Two vectors are equal when they have same magnitude and direction.
\nExample:\u00a0\u00a0\u00a0\u00a0<\/strong>Find the modulus of each of the following vectors<\/p>\n

    \n
  1. 3i + 4j\n<\/li>\n
  2. -2i \u2013 5j\n<\/li>\n
  3. \n
    \n\t\t\t\t<\/div>\n

    Solution
    \n<\/strong><\/li>\n

  4. Let r = 3i + 4j ; then |r| =\n<\/li>\n
  5. Let r = -2i \u2013 5j ; then |r| =\n<\/li>\n
  6. \n
    Let r = ; then |r| =\n<\/div>\n

    \u00a0<\/li>\n<\/ol>\n

    Example:<\/strong>\u00a0\u00a0\u00a0\u00a0If ; find the modulus and direction cosines of:<\/p>\n

      \n
    1. \n\t\t\t<\/li>\n
    2. \n
      \n\t\t\t\t<\/div>\n

      \u00a0Solution
      \n<\/strong><\/li>\n<\/ol>\n

        \n
      1. \n
        \n\t\t\t\t<\/div>\n

        |r1<\/sub> + r2<\/sub>| =\n<\/li>\n<\/ol>\n

        Let cos be the direction cosines of
        \n\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0cos
        \n\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0
        \n<\/strong>
        \n\u00a0<\/p>\n

          \n
        1. \n
          \n\t\t\t\t<\/div>\n

          || =
          \nLet cos be the direction cosines of
          \n\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0cos\n<\/li>\n<\/ol>\n

          \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0
          \n<\/strong>UNIT VECTOR
          \n<\/strong>Example:<\/strong>\u00a0\u00a0\u00a0\u00a0Find the unit vectors in the directions of the following vectors<\/p>\n

            \n
          1. r = 21 + 3j\n<\/li>\n
          2. q = 4i \u2013 5j\n<\/li>\n
          3. p = 7i + 2j \u2013 3k\n<\/li>\n
          4. \n
            t = 3i -5j -3k\n<\/div>\n

            Solution
            \n<\/strong><\/li>\n

          5. \n
            Let be the unit vector in the direction of r; then\n<\/div>\n<\/li>\n
          6. \n
            Let be the unit vector in the direction of q; then\n<\/div>\n<\/li>\n
          7. \n
            Let be the unit vector in the direction of p; then\n<\/div>\n<\/li>\n
          8. \n
            Let be the unit vector in the direction of t; then\n<\/div>\n<\/li>\n<\/ol>\n

            ARITHMETIC OPERATIONS ON VECTORS
            \n<\/strong>Example:<\/strong>\u00a0\u00a0\u00a0\u00a0If p = 2i – 3j; q = 3i + 5j and r = i + j; Find the values of<\/p>\n

              \n
            1. 2p + q + 3r\n<\/li>\n
            2. \n
              3p \u2013 2q\n<\/div>\n

              Solution
              \n<\/strong><\/li>\n

            3. \n
              2p = 2(2i \u2013 3j ) = 4i \u2013 6j\n<\/div>\n

              3r = 3( i + j ) = 3i + 3j
              \nTherefore; 2p + q + 3r = (4i \u2013 6j) + (3i + 5j) + (3i + 3j)
              \n\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0= 10i + 2j<\/strong>\n\t\t\t\t<\/li>\n

            4. \n
              3p = 3(3i \u2013 3j) = 9i \u2013 9j\n<\/div>\n

              2q = 2(3i + 5j) = 6i + 10j
              \nTherefore 3p \u2013 2q = (9i \u2013 9j) \u2013 (6i + 10j) =3i \u2013 19j
              \n<\/strong>
              \n\u00a0Example:<\/strong>\u00a0\u00a0\u00a0\u00a0Given that = a \u2013 b and = 2a + 3b, where a = 2i + 3j <\/strong>and b = 3i \u2013 2j<\/strong>, find \u00a0\u00a0\u00a0\u00a0<\/p>\n

              \t\t\t\t\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0= (2a + 3b) \u2013 (a \u2013 b)
              \n\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0= 2a + 3b \u2013 a + b = a + 4b<\/strong>
              \n\t\t\t\t\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0= (2i + 3j) + 4(3i \u2013 2j) = 14i \u2013 5j\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\n<\/li>\n<\/ol>\n

              Evaluation:
              \n\t\t\t\t<\/em><\/strong>New Further Mathematics Project 2, by M.R Tuttuh Adegun et al. Page 262, Exercise 14, no 5
              \n\t\t\t\t<\/strong>Conclusion:<\/em><\/strong> Teacher summarizes the topic, marks the students’ notes, does correction and allows the students to copy.
              \n\t\t\t\t<\/strong>Assignment:<\/em><\/strong>
              \n\t\tNew Further Mathematics Project 2, by M.R Tuttuh Adegun et al. Page 262, Exercise 14, no 6
              \n\t\t\t\t<\/strong>
              \n\t\t\u00a0<\/p>\n","protected":false},"excerpt":{"rendered":"

              \u00a0WEEK 5 Topic: \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0Vectors Sub-topic: \u00a0\u00a0\u00a0\u00a0 Modulus of a vector Duration: \u00a0\u00a0\u00a0\u00a080 minutes Learning Objectives:…<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1,216],"tags":[],"class_list":["post-2603","post","type-post","status-publish","format-standard","hentry","category-posts","category-third-term-ss1-further-mathematics"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/ecolebooks.com\/nigeria\/wp-json\/wp\/v2\/posts\/2603","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=2603"}],"version-history":[{"count":1,"href":"https:\/\/ecolebooks.com\/nigeria\/wp-json\/wp\/v2\/posts\/2603\/revisions"}],"predecessor-version":[{"id":2604,"href":"https:\/\/ecolebooks.com\/nigeria\/wp-json\/wp\/v2\/posts\/2603\/revisions\/2604"}],"wp:attachment":[{"href":"https:\/\/ecolebooks.com\/nigeria\/wp-json\/wp\/v2\/media?parent=2603"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/ecolebooks.com\/nigeria\/wp-json\/wp\/v2\/categories?post=2603"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/ecolebooks.com\/nigeria\/wp-json\/wp\/v2\/tags?post=2603"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}