Page 171 - ADVANCED MATH F.5

Form Five Form Five

Turning points and points of inflexion of a curve
Teaching steps

1. Guide students through discussions to brainstorm on turning
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points and points of inflexion of a curve.
2. For further practices, engage students in Activity 8.6 on
identification of turning points and points of inflexion. Advise
students to present their findings on a flip chart, then allow
them to make presentations for further improvement.
3. Instruct students to use Figure 8.3 in the Student’s Book
to investigate the concepts of turning points and points of
inflexion. Furthermore, allow students to discuss the important
steps for determining turning points.
4. Use Examples 8.63, 8.64 and 8.65 in the Student’s Book to
guide students to determine the turning points of the given
functions.
5. Assign students to attempt Exercise 8.16 in the Student’s
Book. Advise them to submit their work; check the correctness
of their answers, and provide them constructive feedback.

Answers to Exercise 8.16

⎞ 
)
1. ( 1, 3 and− ) ⎛ ⎜ 1 1 , − , − 15  3.75 2. (0, 0 and (4, 32− )

⎟ 
⎝ 2 2 4  ⎠ 
3. (5, 210 and− ) ( 1,6− )
⎛ 39 ⎞
1,
4. (a) (1, 9− ) (b) ⎜ , ⎟ (c) ( ) 2 and ( 1, 2−− )
⎝ 24 ⎠

5. (a) ⎛ ⎜ 1 76 ⎞ , ⎟ and ( 1,4− ) (b) ( 2,0 and− ) ⎛ ⎜ 2 256 ⎞ , ⎟
⎝ 3 27 ⎠ ⎝ 3 27 ⎠
)
(c) (2, 8− ) (d) (3, 4

165
Mathematics for Advanced Secondary Schools

30/06/2024 18:02:42
ADVANCED MATH F.5 TG CHAPTERS.indd 165
ADVANCED MATH F.5 TG CHAPTERS.indd 165 30/06/2024 18:02:42