Page 152 - ADVANCED MATH F.5

Form Five Form Five

3. Guide students through discussion to use the notation of limit
to describe the behaviour of graphs as the variable approaches
a certain point.
4. Assist students through discussion to perform Activity 8.1 in the
FOR ONLINE READING ONLY
Student’s Book, on the application of limits in finding derivatives
of functions. Ask them to discuss how to use the gradient
of a secant line to approximate the slope of the tangent line.

5. Guide students through discussion to continue with the process
of differentiation until the first principle of differentiation is
()
( fx h+ ) − fx
′
( ) lim=
understood to be fx .
h → 0 h
6. Ask students through group discussions to perform Activity 8.2
in the Student’s Book on illustrating the concept of the derivative
of a function from first principles. Advise students to present
their findings in manila cards, post them on the classroom walls,
then conduct galley walk for improvements.
7. Use Examples 8.1 to 8.4 in the Student’s Book, to guide students
to find the derivative of each of the given functions. Engage
students to use mathematical software to verify answers for the
given examples. Advise students to share their findings.
8. Require students to attempt Exercise 8.1 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 8.1

′
1. (a) () 5fx = (e) fv ′ () 2=
′
(b) ft ′ () 3t= 2 − 2t (f) fx = (3 x ) − 2
()
−
(c) fx = − 3 (g) f ′ () 5t = kt 4
()
′
′
() 4x=
(d) fx − 3 (h) ′ () = ( ) − 1 2
2x
fx
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Mathematics for Advanced Secondary Schools
30/06/2024 18:02:36
ADVANCED MATH F.5 TG CHAPTERS.indd 146
ADVANCED MATH F.5 TG CHAPTERS.indd 146 30/06/2024 18:02:36