{"id":3287,"date":"2023-10-04T13:57:25","date_gmt":"2023-10-04T13:57:25","guid":{"rendered":"http:\/\/localhost\/ecole9ja\/?p=3287"},"modified":"2023-10-04T14:01:39","modified_gmt":"2023-10-04T14:01:39","slug":"week-1-ss2-second-term-mathematics-notes","status":"publish","type":"post","link":"https:\/\/ecolebooks.com\/nigeria\/posts\/week-1-ss2-second-term-mathematics-notes\/","title":{"rendered":"Week 1 – SS2 Second Term Mathematics Notes"},"content":{"rendered":"

SCHEME OF WORK MATHEMATICS
\n<\/strong>SS 2 MATHEMATICS
\n<\/strong><\/p>\n

    \n
  1. Revision
    \n\t\t\t\t<\/strong><\/li>\n
  2. Straight line \u2013 Gradient of straight line, Gradient of a curve., drawing of tangents to a curve
    \n\t\t\t\t<\/strong><\/li>\n
  3. \n
    Inequalities
    \n\t\t\t\t\t<\/strong><\/div>\n

    (a)\u00a0\u00a0\u00a0\u00a0Revision of linear inequalities in one variable
    \n(b)\u00a0\u00a0\u00a0\u00a0Solutions of inequalities in 2 variables
    \n(c)\u00a0\u00a0\u00a0\u00a0Range of values combined inequalities\n<\/li>\n

  4. \n
    Graphs of linear inequalities in two variables
    \n\t\t\t\t\t<\/strong><\/div>\n

    Max and minimum values of simultaneous linear inequalities\n<\/li>\n

  5. \n
    App of linear inequalities in real life\n<\/div>\n

    Introduction to linear programming\n<\/li>\n

  6. \n
    Algebraic fractions\n<\/div>\n
      \n
    1. Simplification of fractions\n<\/li>\n
    2. Operations in algebraic fractions\n<\/li>\n
    3. Equation involving fractions\n<\/li>\n
    4. Undefined fraction: if Then y is undefined when ax + c = 0\n<\/li>\n<\/ol>\n

      7.\u00a0\u00a0\u00a0\u00a0Review of the first half term’s work and periodic test\n<\/li>\n<\/ol>\n

      8.\u00a0\u00a0\u00a0\u00a0 Fractions (continued)<\/p>\n

        \n
      1. Substitution in fraction\n<\/li>\n
      2. Simultaneous equation involving fractions\n<\/li>\n<\/ol>\n

        9.\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0Logic<\/p>\n

          \n
        1. Simple and compound statement\n<\/li>\n
        2. Logical operation and the truth tables\n<\/li>\n
        3. Conditional statements and indirect proofs\n<\/li>\n<\/ol>\n

          10.\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0Chord properties of circles
          \n\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0Perpendicular bisector of chord
          \n\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0Distance of equal chords from the centre of the circle
          \n\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0Angles subtended by 2 equal chords.
          \n11.\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0Circle Theorems: angle properties of circle
          \nAngle subtended by an arc at the centre is twice the one subtended at the circumference.
          \n\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0Angles in the same segment
          \n\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0Angles in a semi circle
          \n\u00a0\u00a0\u00a0\u00a0Opposite angles of cyclic quadrilateral
          \n12&13\u00a0\u00a0\u00a0\u00a0Revision and Second term Examinations
          \n WEEK 1
          \n<\/strong>
          \n\u00a0REVISION\/STRAIGHT LINE
          \n<\/strong>GRADIENTS OF A STRAIGHT LINE AND GRADIENT OF A CURVE
          \n<\/strong>In coordinate geometry, we make use of points in a plane. A point consists of the x-coordinate called abscissa and the y-coordinate known as ordinate. In locating a point on the x \u2013 y plane x \u2013 coordinate is first written and then the y-coordinate. For example, in a given point (a, b), the value of x is a and that of y is b. Similarly, in a point (3, 5), the value of x is 3 and that of y is 5. A linear graph gives a straight line graph from any given straight line equation which is in the general form y = mx + c or ax + by + c = 0
          \nExample<\/strong>: Draw the graph of equation 4x + 2y = 5<\/p>\n

            \n
          1. \n
            Point of intersection of two linear equations
            \n\t\t\t\t\t<\/strong><\/div>\n

            Two lines y = ax +b and y2<\/sub> = cx + d
            \nIntercept when ax + b = cx + d
            \nThat is you solve the two equations simultaneously\n<\/li>\n

          2. \n
            Intersection of a line with the x or y axis
            \n<\/strong><\/div>\n

            The point of intersection of a line with the x \u2013axis can be obtained by putting y = o to find the corresponding value of x = a, say the required point of intersection gives (a, o). Similarly, for the point of intersection of a line with the y-axis, put x = o to find the corresponding value of y. If the corresponding value of y is b, the required point of intersection is (o, b)\n<\/li>\n<\/ol>\n

            Example<\/strong>: Find the point of intersection of the line 2x + 3y + 2 = 0 with the
            \ni.\u00a0\u00a0\u00a0\u00a0x \u2013 axis\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0(ii)\u00a0\u00a0\u00a0\u00a0y \u2013 axis
            \nExample 3<\/strong>: Find the point of intersection of the lines y = 3x + 2 and y = 2x + 5
            \nSolution
            \ny = 3x + 2 \u00a0\u00a0\u00a0\u00a0(1)
            \ny = 2x + 5\u00a0\u00a0\u00a0\u00a0(2)
            \nAt the point of intersection
            \n3x + 2 = 2x + 5
            \n3x \u2013 2x = 5 -2
            \nX = 3
            \nSubstitute 3 for x in equation (1), we obtain y = 3(3) + 2 = 11.
            \nHence, the point of intersection is (3, 11)
            \nGRADIENT OF A STRAIGHT LINE
            \n<\/strong>The Gradient of a straight line is defined as the ratio
            \nChange in y in moving from one
            \n\"\"\/Change in x point to another on the line. The Gradient of a straight line is always constant.
            \n\"\"\/\"\"\/
            \n\t\t\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0Gradient from A to B =
            \n\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0Gradient of a line that passes through points (x1<\/sub>, y1<\/sub>)
            \n\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0And (x2<\/sub>, y2<\/sub>) is given as gradient m =
            \n\"\"\/\"\"\/\"\"\/\"\"\/\"\"\/\"\"\/\"\"\/\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/p>\n

            \u00a0
            \n\u00a0
            \n\u00a0
            \n\u00a0Meaning that the gradient of the line is the ratio of increase in y to increase in x
            \nTANGENT OF ANGLE OF SLOPE
            \n<\/strong>In the above diagram, tan = .
            \nSince = y2<\/sub> \u2013 y1<\/sub> \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 tan = = m
            \nAnd = x2<\/sub> \u2013 x1<\/sub>
            \n\t\t tan = m. it then follows that the gradient of a line can be defined as tangent of angle of slope.
            \nExample:
            \n<\/strong>Calculate the gradient and the angle of slope of the line passing through (1, 3) and (-4, 2)<\/p>\n

            \u00a0EQUATION OF A STRAIGHT LINE AND TANGENT TO A CURVE
            \n<\/strong>EQUATION OF A STRAIGHT LINE
            \n<\/strong>Equation of a line with gradients in m and y intercept c. Equation of a line with gradient m and y intercept c is given as y = mx + c.
            \nii.\u00a0\u00a0\u00a0\u00a0Equation of a line passing through the point (x1<\/sub>, y1<\/sub>) with gradient.
            \nThe general equation of a line with known gradient m and which passes through the point (x1<\/sub>,y1<\/sub>) is given as m = –
            \nExample 2
            \nThe equation of the line with gradient 2 and which pass\u00e9 through the point (-3, 2).
            \nThe solution (equation) of a line with known gradient and passing through the point (x1<\/sub>, y1<\/sub>) is given by –
            \nHere, m = 2, (x1<\/sub>, y1<\/sub>) = (-3, 2)
            \nThe required equation of the line is <\/p>\n

            \t\ty \u2013 2 = 2(x + 3)
            \ny = 2x + 6 + 2
            \ny = 2x + 8
            \ny = 2x + 8
            \nEquation of a line passing through two given points
            \n<\/strong>The equation of a line passing through two given points (x1<\/sub>, y1<\/sub>) and (x2<\/sub>, y2<\/sub>)
            \nIs =
            \niv.\u00a0\u00a0\u00a0\u00a0Double Intercept form of the equation of a line. The equation of a line which has an intercept “a” on the x \u2013 axis and intercept “b” on the y-axis is given by + = 1
            \nDouble intercept form of the equation of a line
            \n<\/strong>The Equation of a line which has an intercept ‘a’ on the axis and intercept ‘b’ on the y-axis is given by + = 1
            \nv.\u00a0\u00a0\u00a0\u00a0Equation of a line passing through a point and making an angle with the horizontal axis.
            \nThe equation of a line passing through the point (x1<\/sub>, y1<\/sub>) and making an angle with the horizontal axis is = tan or y \u2013 y1<\/sub> = (x \u2013 x1<\/sub>) tan .
            \nDrawing Tangents to a cure
            \n<\/strong>The gradient at any particular point on a curve is defined as being the gradient of the tangent to the curve at that point the gradient of the curve at point A is the gradient of the tangent BA, that is, tan . The tangent is drawn by placing a ruler against the curve at A and drawing a line considering that the angels between the line and the curve are equal. (Note: Gradient to the horizontal line of a curve is zero because the tangent is horizontal known as a turning points (maximum\/minimum)<\/p>\n

            \u00a0WRAP UP AND ASSESSMENT
            \n<\/strong>The gradients of a straight line is given as gradient = change in y \/ change in x.
            \nThe gradient of a curve at a point is given by the gradient of the tangent at that point.
            \nThe gradient at a turning point of any quadratic equation equals zero.
            \nExercise 14.5 no 1; the figure below (the text recommended) represents the graph of the function y = x2<\/sup> + 4x \u2013 5, (a)\u00a0\u00a0\u00a0\u00a0use the given tangents to find the gradient of the curve at (i) A (ii) B.
            \n(b)\u00a0\u00a0\u00a0\u00a0Use the Graph to find the roots of the function.
            \n(c)\u00a0\u00a0\u00a0\u00a0State the equation of the line of symmetry of the curve.
            \nTICKET OUT:
            \n<\/strong>Ex 14.5 Pg 194, No 2. And 4 copy and complete the table below for the function y = use a scale of 2cm for 1 unit on both axes, draw the graph of the function.<\/p>\n","protected":false},"excerpt":{"rendered":"

            SCHEME OF WORK MATHEMATICS SS 2 MATHEMATICS Revision Straight line \u2013 Gradient of straight line,…<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1,264],"tags":[],"class_list":["post-3287","post","type-post","status-publish","format-standard","hentry","category-posts","category-second-term-ss2-mathematics"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/ecolebooks.com\/nigeria\/wp-json\/wp\/v2\/posts\/3287","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=3287"}],"version-history":[{"count":1,"href":"https:\/\/ecolebooks.com\/nigeria\/wp-json\/wp\/v2\/posts\/3287\/revisions"}],"predecessor-version":[{"id":3288,"href":"https:\/\/ecolebooks.com\/nigeria\/wp-json\/wp\/v2\/posts\/3287\/revisions\/3288"}],"wp:attachment":[{"href":"https:\/\/ecolebooks.com\/nigeria\/wp-json\/wp\/v2\/media?parent=3287"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/ecolebooks.com\/nigeria\/wp-json\/wp\/v2\/categories?post=3287"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/ecolebooks.com\/nigeria\/wp-json\/wp\/v2\/tags?post=3287"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}