Page 93 - ADVANCED MATH F.5

Form Five Form Five

6. In groups, discuss how to involve students in deducing the
formula for the sum of the first n natural numbers through
Activity 5.2 in the Student’s Book. Furthermore, through
discussion, ask students to deduce the sum of the squares of
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the first n natural numbers. Use Examples 5.7 and 5.8 in the
Student’s Book, to assist students in deducing the sum of the
given expressions.
7. Instruct students through Activity 5.3 in the Student’s Book to
derive the formula for the sum of the cubes of the first n natural
numbers. Advice students to present their findings on flip chart,
post them on classroom walls and allow them to do gallery
walk for more inputs. Use Example 5.9 in the Student’s Book,
to assist students in deducing the sum of the given expressions.

8. Require students to attempt Exercise 5.1 in the Student’s Book.
Advise students to submit their work, check the correctness of
their answers, and provide them constructive feedback.

Answers to Exercise 5.1

5 14 7  1  k 1 −
1. (a) ∑ (3k + 5) (b) ∑ 2k (c) ∑ 32  
k= 1 k= 1 k 1 =  2 
11 6 1 n
(d) ∑ k 2 (e) ∑ k (f) ∑ ( ) 1 k− k 2
k 1 = k= 1 2 k 1 =

2. (a) 456 78 9+ + + ++ (b) 29 70 145+ +
(c) 2 10 24 44 70 102 140− − − − − − −
(d) 3 7 15 31 63 127 255−− − − − − −
1 1
(e) + + 1 2 4 8 16 32 64 128+++ + + + +
4 2
63 42
3. (a) 156 (b) (c) (d) 380 (e) 1
2 5

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Mathematics for Advanced Secondary Schools

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ADVANCED MATH F.5 TG CHAPTERS.indd 87