Page 94 - ADVANCED MATH F.5

Form Five Form Five

1 1
4. (a) 2 (nn + (b) ( nn + 1 )(n + ) 5 (c) ( nn + 1) ( 3n + 2 23n + 46 )
1)
3 12
5
8
4
5. (a) ∑ k (2k − ) 1 (b) ∑ ( x− ) k 1 − (c) ∑ ky (d) ∑ (3k − 7)
∞
k
FOR ONLINE READING ONLY
k= 4 1 1 k 4 1 = k= 1 k= 1
(e) ∑ 2k + 1 (f) ∑ (3k − 2)(3k + 1)
k 1 = k 1 =
1 4
6. (a) 4, 8, 16 (b) 2, 6, 12 (c) 2, ,
11 1 2 15
(d) ,, (e) 1, − 4, 9 (f) 18, 300, 1,134
2 6 12

7. 1 ( nn + 1)(3n + 2 1ln 140),− 1 (7,997,000)
6 6

8. 48,124,960 9. 1,871,040

Proofs by mathematical induction
Teaching steps

1. In groups, guide students to discuss the concept of proof by
mathematical induction through Activity 5.4 in the Student’s
Book and other resources as suggested. Advise them to write
their work on a flip chart ready for presentations or gallery walk.
2. Use Examples 5.10, 5.11, and 5.12 in the Student’s Book to
guide students to discuss proof by mathematical induction.
3. Assign students to attempt Exercise 5.2 in the Student’s Book.
Advise students to submit their work, check the correctness of
their answers, and provide them constructive feedback.

Roots of polynomial functions
Teaching steps
1. Develop hands on activities that can be used to assist students
to realize the concept of general form of the polynomial

88
Mathematics for Advanced Secondary Schools

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ADVANCED MATH F.5 TG CHAPTERS.indd 88 30/06/2024 18:02:19
ADVANCED MATH F.5 TG CHAPTERS.indd 88