Page 207 - ADVANCED MATH F.5

Form Five Form Five

8. Using Figures 9.8 and 9.9 in the Student’s Book guide students
through discussions to derive the formula for calculating the
length of an arc of a function in the Cartesian coordinate system.
Allow students to share alternative methods of deriving the
FOR ONLINE READING ONLY
formula for calculating the length of an arc.
9. Assist students through discussion to develop formulae for
calculating the length of an arc for functions given by parametric
equations and when given in polar coordinates.

10. Use Examples 9.72 to 9.75 in the Student’s Book to guide
students and assist them in calculating the length of an arc
expressed in Cartesian coordinate system, parametric, and in
polar form. Engage students to use mathematical softwares to
verify the solutions of Examples 9.72 to 9,75 in the students Book.
11. Require students to attempt Exercise 9.13 in the Student’s
Book. Advise students to submit their work and check the
correctness of their answers, and provide them constructive
feedback. Encourage students to explore additional resources,
such as online tutorials, or reference books, to deepen their
understanding and for further practice.

Answers to Exercise 9.13

1 1
1. square units 2. abπ square units
3 2
π 9
3. square units 4. (1 e− − 2 ) square units
2 2
80
5. 18 square units 6. square units
π

 1 4π − 33 
7. 3 square unitsπ 8.   −   squareunits
 2 24 

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Mathematics for Advanced Secondary Schools

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ADVANCED MATH F.5 TG CHAPTERS.indd 201
ADVANCED MATH F.5 TG CHAPTERS.indd 201 30/06/2024 18:02:54