{"id":2601,"date":"2023-10-03T10:43:52","date_gmt":"2023-10-03T10:43:52","guid":{"rendered":"http:\/\/localhost\/ecole9ja\/?p=2601"},"modified":"2023-10-03T10:47:41","modified_gmt":"2023-10-03T10:47:41","slug":"week-4-ss1-third-term-further-mathematics-notes","status":"publish","type":"post","link":"https:\/\/ecolebooks.com\/nigeria\/posts\/week-4-ss1-third-term-further-mathematics-notes\/","title":{"rendered":"Week 4 – SS1 Third Term Further Mathematics Notes"},"content":{"rendered":"

\u00a0WEEK 4
\n<\/strong>Topic:<\/em><\/strong> \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0Straight line
\nSub-topic:<\/em>
\n\t\t\t\t<\/strong>\u00a0\u00a0\u00a0\u00a0 Angle of slope and angle between lines
\nDuration:<\/em><\/strong> \u00a0\u00a0\u00a0\u00a080 minutes
\nLearning Objectives:<\/em><\/strong> By the end of the lesson, students should be able to calculate the angle of slope and angle between two lines.
\nReference Materials:<\/em><\/strong> New Further Mathematics Project 2 by M. R Tuttuh Adegun
\nPrevious Knowledge<\/em>:<\/strong> Students can draw the graph of a linear equation (straight-line graph).
\nInstructional Materials<\/em>:<\/strong> Graph board and graph book.
\nContent:\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/em>ANGLE OF SLOPE
\n<\/strong>Example:\u00a0\u00a0\u00a0\u00a0<\/strong>Find the gradient of the line joining (3, 2) and (7, 10) and the angle of slope of the line.
\nSolution
\n<\/strong>Let m be the gradient of the line, then
\n\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0m =
\nLet be the angle of slope of the line; then:
\n\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0
\n\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0
\n\t\t\t<\/strong>
\n\u00a0ANGLE BETWEEN TWO LINES
\n<\/strong>Condition for Parallelism
\n<\/em><\/strong>If two lines are parallel, the angle between them is zero, hence
\nExample:<\/strong>\u00a0\u00a0\u00a0\u00a0Determine if AB is parallel to PQ in each of the following.<\/p>\n

    \n
  1. A(3, 1); B(4, 3) and P(4,6); Q(5, 8)\n<\/li>\n
  2. A(-1, -2); B(2, -3) and P(5, 4) ; Q(6, 7)\n<\/li>\n<\/ol>\n

    Solution
    \n<\/strong><\/p>\n

      \n
    1. \n
      Let be the gradient joining A and B and be the gradient joining P and Q.\n<\/div>\n

      \u00a0<\/p>\n

      \u00a0Since ; AB||PQ
      \n<\/strong><\/li>\n<\/ol>\n

      \u00a0<\/p>\n

        \n
      1. \n
        Let be the gradient joining A and B and be the gradient joining P and Q.\n<\/div>\n

        \u00a0<\/p>\n

        \u00a0Since ; AB is not parallel to PQ<\/strong>
        \n\t\t\t\t\t
        \n\t\t\t\t\t<\/strong><\/li>\n<\/ol>\n

        CONDITION FOR PERPENDICULARITY
        \n<\/strong>\u00a0\u00a0\u00a0\u00a0<\/strong>If the lines are perpendicular, and ; therefore:
        \n\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a01 +
        \n\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0
        \n\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0
        \nExample:<\/strong>\u00a0\u00a0\u00a0\u00a0Determine if AB is parallel to PQ in each of the following.<\/p>\n

          \n
        1. A(5, -1); B(3, 2) and P(2, 4); Q(5, 6)\n<\/li>\n
        2. A(-1, -2); B(2, -3) and P(5, 4) ; Q(6, 7)\n<\/li>\n<\/ol>\n

          Solution
          \n<\/strong><\/p>\n

            \n
          1. \n
            Let be the gradient joining A and B and be the gradient joining P and Q.\n<\/div>\n

            \u00a0<\/p>\n

            \u00a0Since ; AB is perpendicular to PQ
            \n<\/strong><\/li>\n<\/ol>\n

            \u00a0<\/p>\n

              \n
            1. \n
              Let be the gradient joining A and B and be the gradient joining P and Q.\n<\/div>\n

              \u00a0<\/p>\n

              \u00a0Since ; AB is perpendicular to PQ<\/strong>
              \n\t\t\t\t\t
              \n\t\t\t\t\t<\/strong><\/li>\n<\/ol>\n

              EQUATION OF A LINE
              \n<\/strong>The equation of a straight line is given by:\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0y =mx + c
              \n<\/em><\/strong>Example:<\/strong>\u00a0\u00a0\u00a0\u00a0Find the gradient and intercept on the y-axis of the following lines:<\/p>\n

                \n
              1. y = 3x \u2013 4\n<\/li>\n
              2. y = – \u00bdx \u2013 3\n<\/li>\n<\/ol>\n

                Solution:
                \n<\/strong><\/p>\n

                  \n
                1. Compare y = 3x \u2013 4 with y = mx + c ; Hence the gradient is 3, intercept on y-axis is -4\n<\/li>\n
                2. Gradient is \u2013 \u00bd , intercept on y-axis\n<\/li>\n<\/ol>\n

                  GRADIENT AND ONE POINT FORM
                  \n<\/strong>Example:<\/strong>\u00a0\u00a0\u00a0\u00a0Find the equation of a straight line of slope 2, if it passes through the point (3, -2)
                  \n\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0y –
                  \n\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0m = 2;
                  \n\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0Hence the equation of the straight line is:
                  \n\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0y \u2013 (-2) = 2(x \u2013 3)
                  \n\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0y + 2 = 2x \u2013 6
                  \n\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0y = 2x -6 -2 = 2x \u2013 8
                  \n\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0y = 2x \u2013 8
                  \n<\/strong><\/p>\n","protected":false},"excerpt":{"rendered":"

                  \u00a0WEEK 4 Topic: \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0Straight line Sub-topic: \u00a0\u00a0\u00a0\u00a0 Angle of slope and angle between lines Duration:…<\/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-2601","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\/2601","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=2601"}],"version-history":[{"count":1,"href":"https:\/\/ecolebooks.com\/nigeria\/wp-json\/wp\/v2\/posts\/2601\/revisions"}],"predecessor-version":[{"id":2602,"href":"https:\/\/ecolebooks.com\/nigeria\/wp-json\/wp\/v2\/posts\/2601\/revisions\/2602"}],"wp:attachment":[{"href":"https:\/\/ecolebooks.com\/nigeria\/wp-json\/wp\/v2\/media?parent=2601"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/ecolebooks.com\/nigeria\/wp-json\/wp\/v2\/categories?post=2601"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/ecolebooks.com\/nigeria\/wp-json\/wp\/v2\/tags?post=2601"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}