{"id":60,"date":"2025-09-19T21:44:20","date_gmt":"2025-09-19T21:44:20","guid":{"rendered":"https:\/\/wp.engelwebdev.tech\/?page_id=60"},"modified":"2025-09-19T22:32:12","modified_gmt":"2025-09-19T22:32:12","slug":"cambridge","status":"publish","type":"page","link":"https:\/\/wp.engelwebdev.tech\/index.php\/cambridge\/","title":{"rendered":"Cambridge"},"content":{"rendered":"\n
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Cambridge IGCSE, AS & A Levels: Mathematics Overview<\/h1>\n

A structured guide to key topics, equations, and examples for students studying Cambridge International Mathematics.<\/p>\n <\/header>\n\n

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IGCSE Mathematics (0580)<\/h2>\n

IGCSE Mathematics provides a strong foundation in core mathematical concepts, including number, algebra, geometry, and statistics.<\/p>\n\n

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1. Algebra & Functions<\/h4>\n
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Summary Equation:<\/strong> Quadratic Formula<\/p>\n

\n $$ x = \\frac{-b \\pm \\sqrt{b^2 – 4ac}}{2a} $$\n <\/div>\n <\/div>\n
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Example:<\/strong> Solve the equation $$x^2 + 5x + 6 = 0$$.<\/p>\n

Here, $$a=1, b=5, c=6$$.<\/p>\n

\n $$ x = \\frac{-5 \\pm \\sqrt{5^2 – 4(1)(6)}}{2(1)} = \\frac{-5 \\pm \\sqrt{25 – 24}}{2} = \\frac{-5 \\pm 1}{2} $$\n <\/div>\n

The solutions are $$x = -2$$ and $$x = -3$$.<\/p>\n <\/div>\n <\/div>\n\n

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2. Geometry & Trigonometry<\/h4>\n
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Summary Equation:<\/strong> Pythagorean Theorem<\/p>\n

\n $$ a^2 + b^2 = c^2 $$\n <\/div>\n <\/div>\n
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Example:<\/strong> A right-angled triangle has sides of length 3 cm and 4 cm. Find the length of the hypotenuse.<\/p>\n

\n $$ c^2 = 3^2 + 4^2 = 9 + 16 = 25 $$\n $$ c = \\sqrt{25} = 5 \\text{ cm} $$\n <\/div>\n <\/div>\n <\/div>\n\n
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3. Statistics<\/h4>\n
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Summary Equation:<\/strong> Mean<\/p>\n

\n $$ \\text{Mean} = \\frac{\\sum x}{n} $$\n <\/div>\n <\/div>\n
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Example:<\/strong> Find the mean of the numbers 2, 4, 6, 8.<\/p>\n

\n $$ \\text{Mean} = \\frac{2 + 4 + 6 + 8}{4} = \\frac{20}{4} = 5 $$\n <\/div>\n <\/div>\n <\/div>\n <\/section>\n\n
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AS & A Level Mathematics (9709)<\/h2>\n

AS & A Level Mathematics delves into more complex areas like pure mathematics, mechanics, and probability & statistics.<\/p>\n\n

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1. Pure Mathematics<\/h4>\n
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Summary Equation:<\/strong> Differentiation (Power Rule)<\/p>\n

\n $$ \\frac{d}{dx} x^n = nx^{n-1} $$\n <\/div>\n <\/div>\n
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Example:<\/strong> Differentiate $$y = 3x^4$$.<\/p>\n

\n $$ \\frac{dy}{dx} = 3(4)x^{4-1} = 12x^3 $$\n <\/div>\n <\/div>\n <\/div>\n\n
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2. Mechanics<\/h4>\n
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Summary Equation:<\/strong> Constant Acceleration (SUVAT) Equations<\/p>\n

\n $$ v^2 = u^2 + 2as $$\n <\/div>\n <\/div>\n
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Example:<\/strong> A car accelerates from rest at $$2 \\text{ m\/s}^2$$. How far has it traveled when its velocity is $$10 \\text{ m\/s}$$?<\/p>\n

Here, $$u=0, a=2, v=10$$. We need to find $$s$$.<\/p>\n

\n $$ 10^2 = 0^2 + 2(2)s $$\n $$ 100 = 4s $$\n $$ s = 25 \\text{ m} $$\n <\/div>\n <\/div>\n <\/div>\n\n
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3. Probability & Statistics<\/h4>\n
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Summary Equation:<\/strong> Binomial Probability Formula<\/p>\n

\n $$ P(X=r) = {n \\choose r}p^r(1-p)^{n-r} $$\n <\/div>\n <\/div>\n
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Example:<\/strong> A coin is tossed 5 times. What is the probability of getting exactly 3 heads?<\/p>\n

Here, $$n=5, r=3, p=0.5$$.<\/p>\n

\n $$ P(X=3) = {5 \\choose 3}(0.5)^3(0.5)^{5-3} = 10 \\times 0.125 \\times 0.25 = 0.3125 $$\n <\/div>\n <\/div>\n <\/div>\n <\/section>\n <\/div>\n","protected":false},"excerpt":{"rendered":"

Cambridge IGCSE, AS & A Levels: Mathematics Overview A structured guide to key topics, equations, and examples for students studying Cambridge International Mathematics. IGCSE Mathematics (0580) IGCSE Mathematics provides a strong foundation in core mathematical concepts, including number, algebra, geometry, and statistics. 1. Algebra & Functions Summary Equation: Quadratic Formula $$ x = \\frac{-b \\pm […]<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_gspb_post_css":"","footnotes":""},"class_list":["post-60","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/wp.engelwebdev.tech\/index.php\/wp-json\/wp\/v2\/pages\/60","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/wp.engelwebdev.tech\/index.php\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/wp.engelwebdev.tech\/index.php\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/wp.engelwebdev.tech\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/wp.engelwebdev.tech\/index.php\/wp-json\/wp\/v2\/comments?post=60"}],"version-history":[{"count":6,"href":"https:\/\/wp.engelwebdev.tech\/index.php\/wp-json\/wp\/v2\/pages\/60\/revisions"}],"predecessor-version":[{"id":80,"href":"https:\/\/wp.engelwebdev.tech\/index.php\/wp-json\/wp\/v2\/pages\/60\/revisions\/80"}],"wp:attachment":[{"href":"https:\/\/wp.engelwebdev.tech\/index.php\/wp-json\/wp\/v2\/media?parent=60"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}