algebra

1. Lecturer: Miss Rasvini
GROUP MEMBERS:
ANN HII SIANG SAN AA141577
HO WEN HUI AA140851
MARY ISABEL TING HUI PENG AA140126
SIA WAN LING AA140361

2. Sarah saves her money to buy a new hand
phone. The first month she save RM50. Each
month there after, her savings increase by
RM20. How much money she will have saved
in the 12th month? What is the total saving
after 12 months?

3. PROBLEM FORMAT
Sarah saves her money to buy a new hand phone. The first month she saves
RM50. Each month thereafter, her savings increase by RM20. How much money
she will have saved in the 12th month. What is the total saving after 12 months?
FILA TABLE
Facts Ideas Learning Issues Resources Needed
1. Sarah saves her
money to buy a
new hand phone.
2. She saves RM50
during the first
month.
3. Her savings
increase by
RM20 each
month.
1. Arimethic series
is involved.
2. First term, a, is
RM50.
3. Common
difference, d, is
RM20.
4. The amount
ofmoney saved in
12thmonth is 푇12,
which is the 12th
term.
5. The total saving
after 12 months
is 푆12, which is
the sum of the
1. Which series is
involved?
2. What is the
first term?
3. What is the
common
difference?
4. What is the
total money
saved in the
12th month?
5. What is the
total savings
after 12
months?
1. Internet.
2. Library books.

4.  The arithmetic series is 50, 70, 90….
 Given the first term, a, is RM 50 and the common difference,
d, is RM 20.
 Formula for calculating the value of a term in an arithmetic
series is: 푇푛 = 푎 + 푛 − 1 푑
 푇12 = 50 + 12 − 1 20
= 50 + 11 20
= 50 + 220
= 270
 Therefore, Sara saved up to RM270 during the 12th month.

5.  There are two formulas for calculating the sum of the terms in an
arithmetic series:
 First formula: 푆푛=
푛
2
2푎 + 푛 − 1 푑
 푆12 =
12
2
2 50 + 12 − 1 20
= 6 100 + 11 20
= 6 100 + 220
= 6 320
= 푅푀1920
 Second formula: 푆푛=
푛
2
(푎 + 푙)
 푆12 =
12
2
50 + 270
= 6 320
= 푅푀 1920
 Therefore, the total savings after the 12 months is RM1920.

6. Find the root of 푥4 - 5 = 0 over the
interval [1,2] by using secant method.
Iterate until |f (푥푖)| <ε = 0.005.

7. PROBLEM FORMAT
FILA TABLE
Facts Ideas Learning Issues Resources Needed
1. Which method is
involved?
2. How to find the
root?
3. Which formula
should be used?
4. What are the
intervals of the
root?
1. Internet.
2. Library Books.
3. Youtube.

8.  Iteration formula:
푥푖+2 =
,  푥푖푓 푥푖+1 − 푥푖+1푓(푥푖 )
푓 푥푖+1 − 푓(푥푖 )
Calculator formula:퐴퐷 − 퐵퐶 ÷ 퐷 − 퐶
 푖 = 0, 푥0 = 1
푓 푥0 = 14 − 5
= −4
 푖 = 1, 푥푖 = 2
푓 푥1 = 24 − 5
= 11
 푖 = 0, 푥0+2 =
1×11 − 2×−4
11—4
= 1.2667
푓 푥2 = 1.26674 − = −2.4255
 푖 = 1, 푥1+2 =
2×−2.4255 −(1.2667×11)
−2.4225−11
= 1.3992
푓(푥3) = 1.39924 − 5
= −1.1672
푖 푥푖 푓(푥푖 )
0 1 -4
1 2 11
2 1.2667 -2.4255
3 1.3992 -1.1672
4 1.5221 0.3675
5 1.4927 -0.0353
6 1.4953 -0.0007

9.  푖 = 2, 푥2+2 =
1.2667×−1.1672 −(1.3992×−2.4255)
−1.1672− −2.4255
= 1.5221
푓 푥4 = 1.52214 − 5
= 0.3675
 푖 = 3, 푥3+2 =
1.3992×0.3675 − 1.5221×−1.1672
0.3675—1.1672
= 1.4927
푓 푥5 = 1.49274 − 5
= −0.0353
 푖 = 4, 푥4+2 =
1.5221×−0.0353)−(1.4927×0.3675)
−0.0353−0.3675
= 1.4953
푓 푥6 = 1.49534 − 5
= −0.0007
 Since 푓 푥6 = −0.0007 < 휀 = 0.005, so the
root of 푓 푥 = 푥4 − 5 is ≈ 푥6 = 1.4953.
푖 푥푖 푓(푥푖 )
0 1 -4
1 2 11
2 1.2667 -2.4255
3 1.3992 -1.1672
4 1.5221 0.3675
5 1.4927 -0.0353
6 1.4953 -0.0007

10. A contest has ten cash prizes totalling RM17
000. The winner of the tenth prize receives
RM800 and the difference between successive
prizes are the same. Find the values of the
first prize and the fifth prize.

11. PROBLEM FORMAT
A contest has ten cash prizes totalling RM17 000. The winner of the tenth prize
receives RM800 and the difference between successive prizes are the same. Find the
values of the first prize and the fifth prize.
FILA TABLE
Facts Ideas Learning Issues Resources Needed
1. A contest has ten
cash prizes.
2. The total of the
cash prizes is
RM17 000.
3. The winner of the
tenth prize receives
RM800.
4. The difference
between the
successive prizes is
the same.
1. Arithmetic series
is involved.
2. The total of the
ten cash prizes,
RM17 000, is the
sum of the
arithmetic series.
3. The amount of
the tenth prize,
RM800, is the
10th term.
4. The amount of
the first prize is
the 1st term.
5. The amount of
the fifth prize is
the 5th term.
1. Which series is
used for the
solution?
2. What is the first
term?
3. How to find the
common
difference?
4. What is the
formula used to
calculate the sum
of the cash prizes
and the amount
of one prize.
1. Internet.
2. Library Books.

12.  From the question, we can conclude that
 푆10 = 푅푀17 000
 푇10 = 푅푀 800
 Formulas used in this question:
 푆푛 =
푛
2
2푎 + 푛 − 1 푑
 푇푛 = 푎 + 푛 − 1 푑
 푆10 =
10
2
1 2푎 + 10 − 1 푑
17000 =
10
2
2푎 + 10 − 1 푑
17000 = 5 2푎 + 9푑 17000
= 10푎 + 45푑
 푇10 = 푎 + 10 − 1 푑
800 = 푎 + 10 − 1 푑
800 = 푎 + 9푑
푎 = 800 − 9푑
1
2

13. 2 1
Substitute into :
 17000 = 10 800 − 9푑 + 45푑
17000 = 8000 − 90푑 + 45푑
17000 = 8000 − 45푑
17000 − 8000 = −45푑
9000 = −45푑
푑 = −200
 To find 푇1:
푎 = 800 − 9 −200
푎 = 800 − −1800
푎 = 2600
∴ 푇ℎ푒 푣푎푙푢푒 표푓 푡ℎ푒 1푠푡 푡푒푟푚 푖푠 푅푀2600.
푎 = 2600 , 푑 = −200
 푇푛 = 푎 + 푛 − 1 푑
푇5 = 2600 + 5 − 1 −200
푇5 = 2600 + 4 −200
푇5 = 2600 − 800
푇5 = 1800
∴ 푇ℎ푒 푣푎푙푢푒 표푓 푡ℎ푒 푓푖푓푡ℎ 푡푒푟푚 푖푠 푅푀1800.

14. Using both bisection and secant method,
find the root of 푒푥 + 2−푥 + 2 cos 푥 = 0 in the
interval [1,2]. Show all your calculation in
three decimal places.

15. PROBLEM FORMAT
FILA TABLE
Facts Ideas Learning Issues Resources
Needed
1. Which method is
used?
2. How to find the
root?
3. What is the
interval for the
root?
4. Which formula is
involved?
1. Internet.
2. Library Books.

18.  Abd. Wahid Md Raji et al. (2010). Matematik
Asas, Jilid I&II. Jabatan Matematik, Fakulti
Sains, UTM.
 James, S.(2001). Intermediate Algebra.
Boston: McGraw Hill.
 Howard Anton. (1994) Elementary Linear
Algebra. New York. Wiley.