| 1 | Study Plan | Study plan – Topic 7 – Differential Calculus |
| Objective: On completion of the course formative assessment a tailored study plan is created identifying the lessons requiring revision. |
| 2 | Calculus | Limits |
| Objective: On completion of the lesson the student will be able to solve problems using limiting sum rule. |
| 3 | Calculus=1st prin | Differentiation from first principles. |
| Objective: On completion of the lesson the student will be able apply the first principles (calculus) formula to find the gradient of a tangent at any point on a continuous curve. |
| 4 | Calculus=1st prin | Differentiation of y = x to the power of n. |
| Objective: On completion of the Calculus lesson the student will be able to differentiate a number of expressions involving x raised to the power of n. |
| 5 | Calculus-differential, integ | Meaning of dy over dx – equations of tangents and normals. |
| Objective: On completion of the Calculus lesson the student will be able to apply differentiation and algebra skills to find the equation of the tangent and the normal to a point on a curve. |
| 6 | Calculus-differential, integ | Function of a function rule, product rule, quotient rule. |
| Objective: On completion of the Calculus lesson the student will understand how to use the chain rule, the product rule and the quotient rule. |
| 7 | Calculus-differential, integ | Increasing, decreasing and stationary functions. |
| Objective: On completion of the lesson the student will understand how to find the first derivative of various functions, and use it in various situations to identify increasing, decreasing and stationary functions. |
| 8 | Calculus | First Derivative – turning points and curve sketching |
| Objective: On completion of the Calculus lesson the student will be able to use the first derivative to find and identify the nature of stationary points on a curve. |
| 9 | Calculus-2nd derivative | The second derivative – concavity. |
| Objective: On completion of the Calculus lesson the student will be able to find a second derivative, and use it to find the domain over which a curve is concave up or concave down, as well as any points of inflexion. |
| 10 | Calculus – Curve sketching | Curve sketching |
| Objective: On completion of the Calculus lesson the student will be able to use the first and second derivatives to find turning points of a curve, identify maxima and minima, and concavity, then use this information to sketch a curve. |
| 11 | Calculus – Maxima minima | Practical applications of maxima and minima |
| Objective: On completion of the lesson the student will be able to apply calculus to a suite of simple maxima or minima problems. |
| 12 | Calculus – Integration | Integration – anti-differentiation, primitive function |
| Objective: On completion of the Calculus lesson the student will be able to use rules of integration to find primitives of some simple functions. |
| 13 | Calculus – Computation area | Computation of an area |
| Objective: On completion of the Calculus lesson the student will be able to select an appropriate formula to calculate an area, re-arrange an expression to suit the formula, and use correct limits in the formula to evaluate an area. |
| 14 | Calculus – Computation volumes | Computation of volumes of revolution |
| Objective: On completion of the Calculus lesson the student will know how to choose an appropriate volume formula, re-arrange an expression to suit the formula, and then calculate a result to a prescribed accuracy. |
| 15 | Calculus – Trapezoidal and Simpson’s rules | The Trapezium rule and Simpson’s rule |
| Objective: On completion of the Calculus lesson the student will know how to calculate sub-intervals, set up a table of values, then apply the Trapezoidal Rule, or Simpson’s Rule to approximate an area beneath a curve. |
| 16 | Exam | Exam – Topic 7 – Differential Calculus |
| Objective: Exam |
