{"id":1550,"date":"2023-09-29T10:20:35","date_gmt":"2023-09-29T10:20:35","guid":{"rendered":"http:\/\/localhost\/ecole9ja\/?p=1550"},"modified":"2023-09-29T10:22:50","modified_gmt":"2023-09-29T10:22:50","slug":"week-5-and-6-jss-3-second-term-mathematics-notes","status":"publish","type":"post","link":"https:\/\/ecolebooks.com\/nigeria\/posts\/week-5-and-6-jss-3-second-term-mathematics-notes\/","title":{"rendered":"Week 5 and 6 – Jss 3 Second Term Mathematics Notes"},"content":{"rendered":"

WEEK 5
\n<\/strong><\/p>\n

VARIATION
\n<\/h2>\n

Variation may be described as the relationship that exist between two or more quantities in which a change in one quantity leads to a change in the other(s)
\nVariation can be classified into;<\/p>\n

    \n
  1. \n
    Direct\n<\/div>\n<\/li>\n
  2. \n
    Inverse\n<\/div>\n<\/li>\n
  3. \n
    Joint\n<\/div>\n<\/li>\n
  4. \n
    Partial variation\n<\/div>\n<\/li>\n<\/ol>\n

    DIRECT VARIATION
    \n<\/h3>\n

    Direct Variation occurs when two variables x and y are related directly, here an increase or decrease in x results into a proportional increase or decrease in the other.
    \nFor example.
    \nIf y varies directly as x, then y x
    \nThe symbol ” means “is proportion to” or “varies directly with”. This symbol can be change to an “= “sign by introducing a constant.
    \n y x
    \nY = kx; where k is a constant
    \nExample 1
    \nThe relationship between M and L
    \nThe value of L when M = 15
    \nSolution
    \nM L\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0K = = 3
    \nM = KL\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0M = 3L
    \n6 = K2\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0M = 3L is the relationship
    \nii.\u00a0\u00a0\u00a0\u00a0M = 3L, M = 15
    \n =
    \nL = 5<\/p>\n

    INVERSE VARIATION
    \n<\/h3>\n

    Two variables are said to be inverse proportion when their product is a constant.
    \nIf the value of y varies as a result of the variation of Z such that y x Z is always a constant, then y is said to vary inversely with Z. Inverse variation is written as y , y = where K is the constant.
    \nExample 2.
    \nIf P varies inversely with A where P = 4 and A = 8, find the constant and write down the equation.
    \nSolution
    \nP \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0P =
    \nP =
    \nPA = K
    \n4 x 8 = k
    \nK = 32<\/p>\n

    \u00a0 WEEK 6
    \n<\/strong><\/p>\n

    JOINT VARIATION
    \n<\/h2>\n

    In joint variation, we usually have at least three variables.
    \nIf P qx, that means p is proportional to qx. This is called joint variation. The equation for such a variation is p = Kqx where k is a constant. For example, the mass of a sheet of metal is proportional to both the area and the thickness of the metal, i.e M At (where M, A and t are the mass, area and thickness). The mass varies jointly with the area and thickness.
    \nAgain, at mid-day, the temperature To<\/sup>C inside a house is proportional to the outside temperature thickness of the house wall tcm.
    \nHere T
    \nT = <\/p>\n

    \u00a0<\/p>\n

    PARTIAL VARIATION
    \n<\/h3>\n

    When the variation of y depends partly on p and partly on V such that y = k, P + K2<\/sub>v, the variation is called a partial variation. The cost is partly constant and it partly varies with the amount of time taken. Hence, c = a + bt where c is the cost, t is time taken and a and b are constant.<\/p>\n

    \t\t\u00a0<\/p>\n","protected":false},"excerpt":{"rendered":"

    WEEK 5 VARIATION Variation may be described as the relationship that exist between two or…<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1,142],"tags":[],"class_list":["post-1550","post","type-post","status-publish","format-standard","hentry","category-posts","category-second-term-jss3-mathematics"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/ecolebooks.com\/nigeria\/wp-json\/wp\/v2\/posts\/1550","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=1550"}],"version-history":[{"count":1,"href":"https:\/\/ecolebooks.com\/nigeria\/wp-json\/wp\/v2\/posts\/1550\/revisions"}],"predecessor-version":[{"id":1551,"href":"https:\/\/ecolebooks.com\/nigeria\/wp-json\/wp\/v2\/posts\/1550\/revisions\/1551"}],"wp:attachment":[{"href":"https:\/\/ecolebooks.com\/nigeria\/wp-json\/wp\/v2\/media?parent=1550"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/ecolebooks.com\/nigeria\/wp-json\/wp\/v2\/categories?post=1550"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/ecolebooks.com\/nigeria\/wp-json\/wp\/v2\/tags?post=1550"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}