SHS3 Additional Mathematics · Semester 2, Week 2
Principle of Calculus
Full lesson notes coming
Notes for this lesson are being prepared. The curriculum details below are complete and ready to use for your planning.
Curriculum details
- Strand
- Calculus (Strand 3)
- Sub-strand
- Principle of Calculus (3.1)
- Content standard
- 3.3.1.CS.1 - Demonstrate conceptual understanding of the rules and techniques of integration to select and apply them. appropriately to a function. 3.3.1.LO.1 Identify and apply the integration rules to evaluate integrals.
- Indicator
- 3.3.1.LI.1 - Identify and apply the integration rules to evaluate integrals.
- Suggested placement
-
Semester 2, Week 2
(Week 22 of the year)
Our suggestion, laid out in curriculum order across three terms of twelve weeks. NaCCA does not fix the week, so follow your school's scheme of learning.
- Curriculum reference
- NaCCA curriculum document, p. 508
Exemplars (from the NaCCA curriculum)
Talk for Learning, Think-pair-share, Experiential Learning and Group Work/Collaborative Learning. Activity 1: With reference to a real life instances of derivative functions, learners work in mixed-ability groups to discuss the concept, importance and basic rules of integration. Rules of Integration - Power Rule - Sum rule - Difference rule - Multiplication by constant Example 1: Which rule of integration is applicable and why? 5. 6. 7. 8. Example 2 Evaluate the antiderivative of the following; 9. 10. 11. 12. 13. Definite Integral: Learners should be aware that from the fundamental theorem of calculus, if is continuous on the interval, and let be an antiderivative of . Then 14. Where, Theorem ( Integral Theorems) 15. If are two antiderivatives of the same function, then and differ by a constant. In other words, there is a constant such that 16. If for all, then for some constant . 17. Let be a continuous nonnegative function for. Let be the area of the region under the graph of the function from to the number. The is an antiderivative of Activity 2: Evaluating integrals Learners will be working in convenient groups (ability, mixed-ability, mixed gender or pairs etc.) to evaluate integrals. Example 1: Evaluate the following integrals 18. 19. 20. 21. Solution: d. Note: that for questions b and c, the length of the limits of integration for a) is 6-2=4 and that of the b) is 6-0=6. What is the integral value for questions b and c.? Are the same? Why? Teaching and Learning Resources: - Reading resource colour pens - Notebook - Graph sheets - Mathematical sets, - Technological tools. - Curriculum - Card boards Assessment (3.3.1.AS.1). The document marks these depth-of-knowledge levels for this indicator: Level 1 Recall; Level 2 Skills of conceptual understanding.