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PERAK STATE EDUCATION DEPARTMENT PERAK STATE ADDITIONAL MATHEMATICS PROJECT WORK 2016
PERAK STATE EDUCATION DEPARTMENT
PERAK STATE
ADDITIONAL MATHEMATICS
PROJECT WORK
2016
PERAK STATE Additional Mathematics Project Work 2016
1 Teacher’s Guide
Assignment 1
PART 1
Brief history of John Napier and his contributions in developing the concept and uses of
logarithm.
PART 2
1. Definition of indices and logarithm with examples.
2. Brief description of a real life example of each type of function.
The design of the poster must fulfil the following criteria:
(i) done on A4 paper,
(ii) shows clearly the two functions involved,
(iii) contains coloured images.
Assignment 2
PART 1
(a)(i) & (ii)
(b) (i) One graph is the reflection of the other graph in the y-axis.
(ii) Properties
1. a 0 = 1
2. a x > 0 for all values of x.
3. 0 < x < 1 : x → ∞, ax → 0
x → – ∞, ax → ∞
x > 1 : x → ∞, ax → ∞
x → – ∞, ax → 0
PERAK STATE Additional Mathematics Project Work 2016
2 Teacher’s Guide
Assignment 2
PART 2
(a)(i) & (ii)
y
(b) (i) One graph is the reflection of the other graph in the x-axis.
(ii) Properties
1. loga 1 = 0
2. loga x is only defined for x > 0
3. 0 < a < 1 : x → 0, loga x → ∞,
x → ∞, loga x → – ∞
a > 1 : x → 0, loga x → – ∞,
x → ∞, loga x → ∞
Assignment 3
PART 1
1. Record the values of logarithms in Table 1.
2. Make the six sets of Ruler A and Ruler B using graph papers.
Ruler A
Ruler B
y = log2 x
y = log0.5 x
10
3 3.5 2.5 2 1.5 1 4 4.
5
5 6 6.5 7 7.5 8 8.5 9 9.5
2.5 2 1.5 1 3 3.5 4 4.5 5 6 6.5 7 7.5 8 8.5 9 9.5
10
PERAK STATE Additional Mathematics Project Work 2016
3 Teacher’s Guide
PART 2
Students paste Ruler A along Ruler B in the correct position to get the required product or
quotient and state the relevant law of logarithm.
Example:
(a) 2 3
(d) 9 ÷ 2
Law of logarithm : lg 2 + lg 3 = lg ( 2 3 )
Hence, 2 3 = 6
2 1
3 1
6
lg 3
lg 2
lg 2 + lg 3 = lg 6
Ruler A
Ruler B
Law of laogarithm : lg 9 – lg 2 = lg ( 9 ÷ 2 )
Hence, 9 ÷ 2 = 4.5
2 1
9 1 4.5
lg 2
lg 9
Ruler A
Ruler B
lg 9 – lg 2 = lg 4.5
PERAK STATE Additional Mathematics Project Work 2016
4 Teacher’s Guide
Assignment 4
METHOD 1
Construct table for the values of n, 1 +1
𝑛 and (1 +
1
𝑛)
𝑛using calculator, electronic spreadsheet or
any suitable software. The values of n chosen must be suitable and sufficient to estimate the value of
e correct to three decimal places.
METHOD 2
Construct the following table using calculator, electronic spreadsheet or any suitable software.
* At least 7 terms are required to estimate the value of e correct to 3 decimal places.
The value of e obtained by both method must be 2.718 [ correct to three decimal places ]
Assignment 5
CHALLENGE 1
(a) 1.2297 ppb
(b) 1.6599 ppb
34.98 %
CHALLENGE 2
(a) 6.8 billion
(b) 8.632 billion
(c) T = 58.1, year 2059
n Sn
PERAK STATE Additional Mathematics Project Work 2016
5 Teacher’s Guide
Assignment 6
CHALLENGE 1
(a) 8.2
(b) 5 times
CHALLENGE 2
(a) Acid : Q [pH = 5.5] and S[pH = 2.4] Alkali : P [pH = 8.1] and R[pH = 7.3]
Justification : acid pH < 7 , alkali pH > 7
(b) 2.846 × 10 – 3 mol / cm3
Assignment 7
(a) Plot the graph of log N against t
(b) (i) 1995
(ii) t > 25.6
(iii) 77.88%
(c) N = 1995( 0.881 t )
Assignment 8
1. (a) h = 8k3
(b) 3x y + 3
2. (a) (i) −1
2 (ii)
3
4
(b) (i) 1 (ii) 1
3. (a) 𝑥+1
𝑦 (b)
2𝑦
𝑦2−𝑥2
4. 𝑥3𝑦1
2
5. 55 log2 3
PERAK STATE Additional Mathematics Project Work 2016
6 Teacher’s Guide
Assignment 9
1. (a) −1
2
(b) x = 3
(c) 1.585
2. (a) 7
6
(b) x = 1
2
3. 𝑙𝑜𝑔3 (2𝑥+5
𝑥2 )
(a) x = 10
(b) 𝑥 = 5
3
4. x = 3.414, y = 10.24 ; x = 0.5858 ; y = 1.757
5. m = 19 683 , 𝑛 =1
3
Assignment 10
Student should
1. identify the line number for every mistake and stating the corresponding mistake,
Problem Line number and mistake
1 Line 1 : ( 3m 3 n ) 2 = 3m 6 n 2
Line 2 : n 2 ÷ n – 4 = n 2 – 4
2 Line 1 : 2 ( 3 x ) = 6 x
3 Line 1 : log3 3 ( x – 1 ) = log3 3x – 3
4 Line 1 :
x
x
2
2
log
)127(log = log 2 ( 7x – 12 – x )
2. solve each problem correctly.
Assignment 11
Creative reflection is encouraged : mind maps, poems, songs, PowerPoint presentation etc which must
be related to the awesome applications of Additional Mathematics.
