| Reciprocal trigonometric functions |
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| Do you know what the functions cosec, sec and cot are? |
Section 1 (O1) |
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| Are you comfortable evaluating and re-arranging formulae containing cosec, sec and cot? |
Section 1 (O1) |
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| Compound angle formulae |
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| Have you seen the addition formulae for sine and cosine before? e.g. \(\sin(A+B)=\ldots\) |
Section 1 (O2) |
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| Do you know how to solve for \(k\) and \(B\) in \[\sin(x) + 3 \cos(x) = k \sin(x+B)\] |
Section 1 (O2) |
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| Trigonometric identities |
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| Do you know the standard trigonometric identities? e.g \(\sin^2 (\alpha) + \cos^2(\alpha) =1\) or \(\cos(2\alpha)=2\cos^2(\alpha)+1\) |
Section 1 (O2) |
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| Are you comfortable using (these identities) to solve problems? |
Section 1 (O2) |
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| Hyperbolic functions |
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| Do you know what the functions \(\sinh\), \(\cosh\) and \(\tanh\) are? |
Section 1 (O3) |
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| Are you comfortable evaluating things like \(\sinh(0.2)\) or \(\tanh(0.3)\)? |
Section 1 (O3) |
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| Hyperbolic identities |
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| Do you know the standard hyperbolic identities? e.g. \(\cosh^2(y) - \sinh^2(y) = 1\) |
Section 1 (O3) |
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| Are you comfortable using (these identities) to solve problems? |
Section 1 (O3) |
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| Differentiation: first principles |
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| Have you ever learned about differentiation, to find the derivative of a function? |
Section 2 (O1) |
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| Are you comfortable explaining differentiation as a measure of instant gradient of a function via small triangles approximations? |
Section 2 (O1) |
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| Differentiation of standard functions |
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| Do you know the derivatives of standard functions? e.g. \(ax^n\), \((ax+b)^n\), \(\sin(x)\), \(\cos(x)\), \(\ln(ax+b)\) |
Section 2 (O2) |
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| Are you comfortable using derivatives of standard functions to answer questions? |
Section 2 (O2) |
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| The Chain Rule for differentiation |
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| Do you know what the chain rule is, for differentiating functions of functions? e.g. \(\sin(2x+3)\) or \(\cos(x^2+1)\) |
Section 2 (O3) |
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| Are you comfortable using the chain rule to differentiate functions of functions (often called a composition of functions)? |
Section 2 (O3) |
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| Second derivatives |
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| Have you ever calculated 1st and 2nd derivatives of a function to find the maximum or minimum of that function? |
Section 2 (O4) |
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| Are you comfortable with using 1st and 2nd derivatives to find the max and min of functions? |
Section 2 (O4) |
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| Rates of change |
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| Have you ever used differentiation to calculate rates of change, like velocity or acceleration? |
Section 2 (O4) |
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| Are you comfortable finding rates of change in real described problems using differentiation? |
Section 2 (O4) |
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| Optimisation using differentiation (minima and maxima) |
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| Have you ever used differentiation with respect to a parameter variable in a problem to find the best value of that parameter? |
Section 2 (O5) |
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| Do you feel comfortable using differentiation to find best parameter values in real problems described in words? |
Section 2 (O5) |
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| Integration basics: indefinite and definite integrals |
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| Have you ever studied integration? i.e. seen things like \(\int_{0}^{1} x^2 \textrm{d}x\) |
Section 3 (O1) |
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| Are you comfortable applying the rules for addition and multiplication for integrals? |
Section 3 (O1) |
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| Integration: definite integrals interpretation |
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| Do you know what \(\int_{1}^{4} x^2 \textrm{d}x\) represents for the graph of \(y = x^2\)? |
Section 3 (O1) |
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| Can you write down the integral formula to describe the area between two curves? |
Section 3 (O1) |
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| Integration of standard functions |
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| Do you know the standard integrals of expressions like \(x^n\), \(\sin(x)\), and \(x^2+2x+3\)? |
Section 3 (O2) |
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| Do you know how to calculate \(\int_{1}^{2} \left( x^2 + 2x \right) \textrm{d}x\) and \(\int 2 \sin(x) \textrm{d}x\)? |
Section 3 (O2) |
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| Applications of integration |
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| Have you ever used integration to answer a real world problem described in words? e.g. find a distance travelled using a velocity graph? |
Section 3 (O3) |
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| Do you feel comfortable using integration of appropriately chosen functions to calculate real-world quantities to solve problems? e.g. find the work done, distance travelled, or find the centroid of an object |
Section 3 (O3) |
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