{"id":1174,"date":"2024-03-03T13:09:23","date_gmt":"2024-03-03T13:09:23","guid":{"rendered":"https:\/\/blogs.glowscotland.org.uk\/an\/brechinhighschool\/?page_id=1174"},"modified":"2025-09-07T12:10:11","modified_gmt":"2025-09-07T11:10:11","slug":"mathematics-advanced-higher","status":"publish","type":"page","link":"https:\/\/blogs.glowscotland.org.uk\/an\/brechinhighschool\/curriculum\/maths-and-numeracy\/mathematics-s5-s6\/mathematics-advanced-higher\/","title":{"rendered":"Mathematics: Advanced Higher"},"content":{"rendered":"\r\n
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Mathematics: Advanced Higher<\/h1>\r\n

Recommended Entry Requirements:<\/strong><\/p>\r\n\r\n\r\n\r\n

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  • Ideally, Higher Maths A\/B pass<\/li>\r\n<\/ul>\r\n\r\n\r\n\r\n

    Course Content:<\/strong><\/p>\r\n\r\n\r\n\r\n

    Calculus<\/u><\/strong><\/p>\r\n\r\n\r\n\r\n

    Differentiating exponential and natural logarithmic functions<\/p>\r\n\r\n\r\n\r\n

    Differentiating functions using the chain rule<\/p>\r\n\r\n\r\n\r\n

    Differentiating functions given in the form of a product and in the form of a quotient<\/p>\r\n\r\n\r\n\r\n

    Differentiating inverse trigonometric functions<\/p>\r\n\r\n\r\n\r\n

    Finding the derivative where relationships are defined implicitly<\/p>\r\n\r\n\r\n\r\n

    Finding the derivative where relationships are defined parametrically<\/p>\r\n\r\n\r\n\r\n

    Applying differentiation to problems in context<\/p>\r\n\r\n\r\n\r\n

    Integrating expressions using standard results<\/p>\r\n\r\n\r\n\r\n

    Integrating by substitution<\/p>\r\n\r\n\r\n\r\n

    Integrating by parts<\/p>\r\n\r\n\r\n\r\n

    Applying integration to problems in context<\/p>\r\n\r\n\r\n\r\n

    Solving first-order differential equations with variables separable<\/p>\r\n\r\n\r\n\r\n

    Solving first-order linear differential equations using an integrating factor<\/p>\r\n\r\n\r\n\r\n

    Solving second-order differential equations<\/p>\r\n\r\n\r\n\r\n

    Algebra, proof and number theory<\/u><\/strong><\/p>\r\n\r\n\r\n\r\n

    Decomposing a rational function into a sum of partial fractions (denominator of degree at most three)<\/p>\r\n\r\n\r\n\r\n

    Finding the asymptotes to the graphs of rational functions<\/p>\r\n\r\n\r\n\r\n

    Investigating features of graphs and sketching graphs of functions<\/p>\r\n\r\n\r\n\r\n

    Expanding expressions using the binomial theorem<\/p>\r\n\r\n\r\n\r\n

    Finding the general term and summing arithmetic and geometric progressions<\/p>\r\n\r\n\r\n\r\n

    Applying summation formulae<\/p>\r\n\r\n\r\n\r\n

    Using the Maclaurin expansion to find specified terms of the power series for simple functions<\/p>\r\n\r\n\r\n\r\n

    Disproving a conjecture by providing a counterexample<\/p>\r\n\r\n\r\n\r\n

    Using indirect or direct proof in straightforward examples<\/p>\r\n\r\n\r\n\r\n

    Using proof by induction<\/p>\r\n\r\n\r\n\r\n

    Using Euclid\u2019s algorithm to find the greatest common divisor of two positive integers<\/p>\r\n\r\n\r\n\r\n

    Matrices, vectors and complex numbers<\/u><\/strong><\/p>\r\n\r\n\r\n\r\n

    Using Gaussian elimination to solve a 3 3 system of linear equations<\/p>\r\n\r\n\r\n\r\n

    Understanding and using matrix algebra<\/p>\r\n\r\n\r\n\r\n

    Calculating the determinant of a matrix<\/p>\r\n\r\n\r\n\r\n

    Finding the inverse of a matrix<\/p>\r\n\r\n\r\n\r\n

    Using transformation matrices<\/p>\r\n\r\n\r\n\r\n

    Calculating a vector product<\/p>\r\n\r\n\r\n\r\n

    Working with lines in three dimensions<\/p>\r\n\r\n\r\n\r\n

    Working with planes<\/p>\r\n\r\n\r\n\r\n

    Performing algebraic operations on complex numbers<\/p>\r\n\r\n\r\n\r\n

    Performing geometric operations on complex numbers<\/p>\r\n\r\n\r\n\r\n

    Assessment:<\/strong><\/p>\r\n\r\n\r\n\r\n

      \r\n
    • The Advanced Higher course is 100% externally assessed by formal exam.<\/li>\r\n<\/ul>\r\n\r\n\r\n\r\n

      Candidates must complete two external examinations set by the SQA.<\/p>\r\n\r\n\r\n\r\n

      Paper 1 – Non calculator<\/p>\r\n\r\n\r\n\r\n

      Paper 2 – Calculator<\/p>\r\n<\/div>\r\n<\/div>\r\n","protected":false},"excerpt":{"rendered":"","protected":false},"author":7553,"featured_media":0,"parent":1160,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-1174","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/blogs.glowscotland.org.uk\/an\/brechinhighschool\/wp-json\/wp\/v2\/pages\/1174","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/blogs.glowscotland.org.uk\/an\/brechinhighschool\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/blogs.glowscotland.org.uk\/an\/brechinhighschool\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/blogs.glowscotland.org.uk\/an\/brechinhighschool\/wp-json\/wp\/v2\/users\/7553"}],"replies":[{"embeddable":true,"href":"https:\/\/blogs.glowscotland.org.uk\/an\/brechinhighschool\/wp-json\/wp\/v2\/comments?post=1174"}],"version-history":[{"count":4,"href":"https:\/\/blogs.glowscotland.org.uk\/an\/brechinhighschool\/wp-json\/wp\/v2\/pages\/1174\/revisions"}],"predecessor-version":[{"id":1732,"href":"https:\/\/blogs.glowscotland.org.uk\/an\/brechinhighschool\/wp-json\/wp\/v2\/pages\/1174\/revisions\/1732"}],"up":[{"embeddable":true,"href":"https:\/\/blogs.glowscotland.org.uk\/an\/brechinhighschool\/wp-json\/wp\/v2\/pages\/1160"}],"wp:attachment":[{"href":"https:\/\/blogs.glowscotland.org.uk\/an\/brechinhighschool\/wp-json\/wp\/v2\/media?parent=1174"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}