Page 107 - ADVANCED MATH F.5

Form Five Form Five

2. Use Examples 5.53 to 5.56 in the Student’s Book to guide
students on how to obtain expansions of the given expressions.
Engage students to use mathematical software to verify the
given expansion for the given examples.
n FOR ONLINE READING ONLY
3. Instruct students to attempt Exercise 5.9 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 5.9

4
1. (a) 32x + 5 240xz + 4 720x z + 32 1080xz + 23 810xz + 243 z 5
(b) a − 7 7a b + 6 21a b − 5 2 35a b + 43 35a b − 34 21a b + 25 7ab − 6 b 7

+
(c) 32x + 5 160x + 3 320x + 320 160 + 32
x x 3 x 5
2. (a) 140 2 (b) 24476 (c) 40 2 (d) 98 .
3. 1 10x+ + 55x + 2 210x + 3  ; 1.106

4. (a) 1.0743 (b) 1 279.2 (c) 7272.2
5. m = − 9 and n = 46

7. 32 80y+ + 80y + 2 40y + 3 10y + 4 y 5 ; 32.08008
8. 1 024 1280y+ + 720y + 2 240 ; 1159y 3

9. 4 28c− + 85c − 2 146c + 3 155c + 4 
27 3 1
10. 81a − 4 54a b + 3 a b − 22 ab + 3 b 4 ; 757335.0625
2 2 16

Binomial expansion for fractional and negative indices

Teaching steps
1. Guide students in groups to discuss the modified binomial
theorem when n is negative or a fraction, the modified binomial
theorem is given by,
1 n ( nn − ) 1 ( nn − 1 )(n − 1 )(n − ) 2 ( nn − 1 )(n − 2 )(n − ) 3
(1 x+ ) = + x + x + 2 x + 3 x + 4 
0! 1! 2! 3! 4!
101
Mathematics for Advanced Secondary Schools

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ADVANCED MATH F.5 TG CHAPTERS.indd 101