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 1^{st} and 2^{nd} derivatives of a function to find the maximum or minimum of that function? |
Section 2 (O4) | |

Are you comfortable with using 1^{st} and 2^{nd} 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 problems? e.g. find the work done, distance travelled, or find the centroid of an object | Section 3 (O3) |