Current knowledge checklist and progress chart

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