1. 3 Formulas
3.1 Sequences
3.2 Introduction to Functions
3.3 Algebraic Fractions
3.4 Formulas and Method of Substitution
3.5 Change of Subject

2. 3.1 Sequences
A. Introduction to Sequences

3. 3.1 Sequences
B. Some Common Sequences

4. 3.1 Sequences
B. Some Common Sequences

5. 3.1 Sequences
B. Some Common Sequences

6. 3.1 Sequences
B. Some Common Sequences

7. 3.1 Sequences
B. Some Common Sequences

8. 3.1 Sequences
B. Some Common Sequences

9. 3.1 Sequences
C. General Terms

10. Example 1T 3 Formulas Solution:
Find the general term of each of the following sequences.
(a) 9, 18, 27, 36, … (b) 0.4, 0.8, 1.2, 1.6, …
Solution:
(a)
(b)

11. Example 2T 3 Formulas Solution:
Find the general term of each of the following sequences.
(a) 1, 2, 4, 8, … (b) 15, 14, 13, 12, …
Solution:
(a)
(b)

12. Example 3T 3 Formulas Solution:
Find the general term and the 9th term of each of the following sequences.
(a) 1, 2, 5, 8, ... (b) 1, 4, 9, 16, ...
Solution:
(a) 
 The general term

13. Example 3T 3 Formulas Solution:
Find the general term and the 9th term of each of the following sequences.
(a) 1, 2, 5, 8, ... (b) 1, 4, 9, 16, ...
Solution:
(b) 
 The general term

14. 3.2 Introduction to Functions

15. 3.2 Introduction to Functions

16. 3.2 Introduction to Functions

17. 3.3 Algebraic Fractions Note that expressions like and
are not called algebraic fractions because their denominators are constants.

18. Example 4T 3 Formulas Solution:
If p is a function of x such that p  4x  5, find the value of p corresponding to each of the following values of x.
(a) 6 (b) 5
Solution:
(a) When x  6, p  4(6)  5
(b) When x  5, p  4(5)  5

19. 3.3 Algebraic Fractions
A. Simplification

20. Example 5T 3 Formulas Solution:
Simplify the following algebraic fractions.
(a) (b)
Solution: 20

21. Example 6T 3 Formulas Solution:
Simplify the following algebraic fractions.
(a) (b)
Solution: 21

22. 3.3 Algebraic Fractions
B. Multiplication and Division

23. Example 7T 3 Formulas Solution: Simplify the following expressions.
(a) (b)
Solution: 23

24. 3.3 Algebraic Fractions
C. Addition and Subtraction

25. Example 8T 3 Formulas Solution: Simplify the following expressions.
(a) (b)
Solution:
(a)
(b) 25

26. Example 9T 3 Formulas Solution: Simplify the following expressions.
(a) (b)
Solution:
(a)
(b) 26

27. 3 Formulas
Example 10T
Simplify
Solution: 27

28. 3.4 Formulas and Method of Substitution

29. Example 11T 3 Formulas Solution: Consider the formula y = mx + c.
(a) Find the value of y when x = 4, m = 0.5 and c = 3.
(b) Find the value of x when y = 5, m = 2 and c = 7.
Solution:
(a)
(b) 29

30. Example 12T 3 Formulas Solution:
Consider the formula Find the value of h if T  121
and r  2.5.
Solution: 30

31. 3.5 Change of Subject

32. Example 13T 3 Formulas Solution:
Make u the subject of the formula 3k  4  5u.
Solution:
i.e., 32

33. Example 14T 3 Formulas Solution:
Make x the subject of the formula 3x  5ax  7hk.
Solution:  33

34. Example 15T 3 Formulas Solution: Make m the subject of the formula . 34

35. Example 16T 3 Formulas Solution: Make x the subject of the formula .
i.e., 35

36. Example 17T 3 Formulas Solution:
A bag of food is put into a refrigerator. The temperature T (in C) of
the food after time t (in hours) is given by the formula
(a) Make t the subject of the formula.
(b) How long will it take for the temperature of the food to become
–3C?
Solution:
(a)
(b)
∴ It takes 6 hours for the temperature of the food to become 3C. 36