| 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 |
