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# Mathematics: Analysis & Approaches | Resources

5 topics, FE2021

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## [Plan](https://0e5b113685.clvaw-cdnwnd.com/41af4b1467c93b79b2d59d3f8552dcc1/200000607-1bd4b1bd4e/MAA%20HL%20teaching%20order.pdf?ph=0e5b113685)

<table><thead><tr><th width="40"></th><th>Topics</th><th data-hidden></th></tr></thead><tbody><tr><td>1</td><td>Number &#x26; Algebra</td><td>1</td></tr><tr><td>2</td><td>Functions</td><td>2</td></tr><tr><td>3</td><td>Geometry &#x26; Trigonometry</td><td>3</td></tr><tr><td>4</td><td>Statistics &#x26; Probability</td><td>4</td></tr><tr><td>5</td><td>Calculus</td><td>5</td></tr></tbody></table>
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<details>

<summary>Year 1</summary>

<table><thead><tr><th width="52"></th><th>Topic 1: Number and Algebra (part of the topic)</th></tr></thead><tbody><tr><td>1.1</td><td>Numbers – rounding – scientific form</td></tr><tr><td>1.2</td><td>Sequences in general – Series</td></tr><tr><td>1.3</td><td>Arithmetic sequences</td></tr><tr><td>1.4</td><td>Geometric sequences</td></tr><tr><td>1.5</td><td>Applications of G.S. – Percentage growth</td></tr><tr><td>1.6</td><td>The Binomial theorem – (a+b)ⁿ</td></tr><tr><td>1.7</td><td>Deductive proof</td></tr><tr><td>1.8</td><td>Methods of proof</td></tr><tr><td>1.9</td><td>Mathematical induction</td></tr></tbody></table>

<table><thead><tr><th width="55"></th><th>Topic 2: Functions</th></tr></thead><tbody><tr><td>2.1</td><td>Lines (or Linear functions)</td></tr><tr><td>2.2</td><td>Quadratics (or Quadratic functions)</td></tr><tr><td>2.3</td><td>Functions, domain, range, graph</td></tr><tr><td>2.4</td><td>Composition of functions: fogfogfog</td></tr><tr><td>2.5</td><td>The inverse function: f−1f<sup>−1</sup>f−1</td></tr><tr><td>2.6</td><td>Transformations of functions</td></tr><tr><td>2.7</td><td>Asymptotes</td></tr><tr><td>2.8</td><td>Exponents – the exponential function axa<sup>x</sup>ax</td></tr><tr><td>2.9</td><td>Logarithms – the logarithmic function logaxlog<sub>a</sub>xloga​x</td></tr><tr><td>2.10</td><td>Exponential equations</td></tr><tr><td></td><td>At this point a quick introduction to complex numbers (only the Cartesian part) as well as a reference to the fundamental theorem of algebra is needed. See paragraphs 1.10-1.11 from Topic 1. A full treatment of complex numbers will take place in year 2.</td></tr><tr><td>2.11</td><td>Polynomial functions</td></tr><tr><td>2.12</td><td>Sum and product of roots</td></tr><tr><td>2.13</td><td>Rational functions – Partial fractions</td></tr><tr><td>2.14</td><td>Polynomial and rational inequalities</td></tr><tr><td>2.15</td><td>Symmetries of f(x)f(x)f(x) – More transformations</td></tr><tr><td>2.16</td><td>Modulus equations and inequalities</td></tr></tbody></table>

<table><thead><tr><th width="50"></th><th>Topic 3: Trigonometry (part of the topic)</th></tr></thead><tbody><tr><td>3.1</td><td>3D Geometry</td></tr><tr><td>3.2</td><td>Triangles – Sine and Cosine rules</td></tr><tr><td>3.3</td><td>Applications in 3D Geometry – Navigation</td></tr><tr><td>3.4</td><td>The trigonometric circle – Arcs and Sectors</td></tr><tr><td>3.5</td><td>sinθ, cosθ, tanθ on the unit circle</td></tr><tr><td>3.6</td><td>Trigonometric identities and equations</td></tr><tr><td>3.7</td><td>Trigonometric functions</td></tr><tr><td>3.8</td><td>More trigonometric equations – identities</td></tr><tr><td>3.9</td><td>Inverse trigonometric functions</td></tr></tbody></table>

<table><thead><tr><th width="58"></th><th>Topic 5: Calculus (part of the topic)</th></tr></thead><tbody><tr><td>5.1</td><td>The limit f(x)f(x)f(x) – The derivative f′(x)f'(x)f′(x): A rough idea</td></tr><tr><td>5.2</td><td>Derivatives of known functions – Rules</td></tr><tr><td>5.3</td><td>Tangent line – Normal line at some point x0x<sub>0</sub>x0​</td></tr><tr><td>5.4</td><td>The chain rule</td></tr><tr><td>5.5</td><td>Monotony – max, min</td></tr><tr><td>5.6</td><td>Concavity – points of inflection</td></tr><tr><td>5.7</td><td>Optimization</td></tr><tr><td>5.14</td><td>Implicit differentiation (without kinematics)</td></tr><tr><td>5.15</td><td>Rate of change problems</td></tr><tr><td>5.8</td><td>The indefinite integral</td></tr><tr><td>5.9</td><td>Integration by substitution</td></tr><tr><td>5.16</td><td>Further integration by substitution</td></tr><tr><td>5.17</td><td>The definite integral – Areas between curves</td></tr><tr><td>5.18</td><td>Further areas between curves – Volumes</td></tr></tbody></table>

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<details>

<summary>Year 2</summary>

<table><thead><tr><th width="59"></th><th>Topic 5: Calculus (part of the topic)</th></tr></thead><tbody><tr><td>5.12</td><td>Continuity and differentiability</td></tr><tr><td>5.13</td><td>L'Hôpital's rule</td></tr><tr><td>5.11</td><td>Kinematics (+last paragraph of 5.14)</td></tr><tr><td>5.19</td><td>Differential equations</td></tr><tr><td>5.20</td><td>Maclaurin series – Extension of Binomial Theorem</td></tr></tbody></table>

<table><thead><tr><th width="56"></th><th>Topic 4: Statistics and Probability</th></tr></thead><tbody><tr><td>4.1</td><td>Basic concepts of Statistics</td></tr><tr><td>4.2</td><td>Measures of central tendency – Measures of spread</td></tr><tr><td>4.3</td><td>Frequency tables – Grouped Data</td></tr><tr><td>4.4</td><td>Regression</td></tr><tr><td>4.5</td><td>Elementary Set Theory</td></tr><tr><td>4.6</td><td>Probability</td></tr><tr><td>4.7</td><td>Conditional probability – Independent events</td></tr><tr><td>4.8</td><td>Tree diagrams</td></tr><tr><td>4.9</td><td>Distributions – Discrete random variables</td></tr><tr><td>4.10</td><td>Binomial distribution – B(n,p)B(n, p)B(n,p)</td></tr><tr><td>4.11</td><td>Normal distribution – N(μ,σ)N(μ, σ)N(μ,σ)</td></tr><tr><td>4.12</td><td>Continuous random variables</td></tr><tr><td>4.13</td><td>Counting – Permutations – Combinations</td></tr></tbody></table>

<table><thead><tr><th width="54"></th><th>Topic 1: Number and Algebra (part of the topic)</th></tr></thead><tbody><tr><td>1.10</td><td>Systems of linear equations</td></tr><tr><td>1.11</td><td>Complex numbers – basic operations</td></tr><tr><td>1.12</td><td>Polynomials over the Complex field</td></tr><tr><td>1.13</td><td>The complex plane</td></tr><tr><td>1.14</td><td>De Moivre's theorem</td></tr><tr><td>1.15</td><td>Roots of zn=az<sup>n</sup>=azn=a</td></tr></tbody></table>

<table><thead><tr><th width="58"></th><th>Topic 3: Vectors (part of the topic)</th></tr></thead><tbody><tr><td>3.10</td><td>Vectors: Geometric representation</td></tr><tr><td>3.11</td><td>Vectors: Algebraic representation</td></tr><tr><td>3.12</td><td>Scalar (or Dot) product – angle between vectors</td></tr><tr><td>3.13</td><td>Vector equation of a line in 2D</td></tr><tr><td>3.14</td><td>Vector equation of a line in 3D</td></tr><tr><td>3.15</td><td>Vector (or Cross) project</td></tr><tr><td>3.16</td><td>Planes</td></tr><tr><td>3.17</td><td>Intersection among lines and planes</td></tr><tr><td>3.18</td><td>Distances</td></tr></tbody></table>

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