JABATAN PENDIDIKAN NEGERI PERAK
2015
PERAK STATE
ADDITIONAL MATHEMATICS
PROJECT WORK
TEACHER’S GUIDE
Disediakan oleh :
PERAK CEMERLANG
Sektor Pengurusan Akademik
Jabatan Pendidikan Negeri Perak
Perak State Additional Mathematics Project Work : Teacher’s Guide
2015
WORKSHEET 1
The design must fulfill the following criteria:
(i)
done on A4 paper
(ii)
based on various types of triangles
(iii)
in colour
(iv)
include the words ‘ Happy Birthday ’
WORKSHEET 2
*
Any suitable conjecture given in the form of a relationship between the sum of the lengths
of any two sides and the length of the remaining side of a triangle.
*
Suggested example of Table 1 created using MS EXCELL:
a
b
c
Number of triangles
that can be formed
a+b
c
a+c
b
b+c
a
*
Table 1 must show all the 20 combinations of a, b and c with 14 combinations yielding
triangles.
*
Make a conclusion about the conjecture made by analyzing the data from the Table 1.
*
Prove a < b + c, b < a + c and c < a + b by using the fact that cos  ≤ 1.
WORKSHEET 3
Findings must show that only one distinct triangle can be constructed for Case 2 : SAS.
WORKSHEET 4
*
Findings must show that the number of triangles possible are 0, 1 or 2.
*
Suggested conclusion:
Condition
c < b sin C
c = b sin C
b sin C < c < b
c  b
JPN PERAK
Number of triangles possible
0
1
2
1
Page 1
Perak State Additional Mathematics Project Work : Teacher’s Guide
2015
WORKSHEET 5
1.
Cosine rule and its proof
2.
Students must use only the Cosine rule to arrive at the following answers.
3.
(a)
 P = 24.15˚ / 24˚ 9’ ,  Q = 54.9˚ / 54˚ 54’,  R = 100.95˚ / 100˚ 57’
(b)
AB = 10.82 cm,  A = 46.10˚ / 46˚ 6’ ,  B = 73.90˚ / 73˚54’
Using the cosine rule and the formula s = r to arrive at the answer AC = 10.52 cm.
WORKSHEET 6
1.
Sine rule and its proof
2.
Students must use only the Sine rule to arrive at the following answers.
3.
(a)
 B = 46.42˚ / 46˚25’ ,  A = 58.58˚ / 58˚ 35’ , BC =7.068 cm
(b)
 P = 129.53˚ / 129˚ 32’ ,  R = 10.47˚ / 10˚28’ , PQ = 1.414 cm
Using the sine rule and the formula s = r to arrive at the answer  = 2.50 rad.
WORKSHEET 7
1.
Area of triangle = ½ ab Sin C and its derivation.
2.
Case 1 : SAS
(a)
Case 2 : SSS
9.922 cm2
Case 3 : SSA
(a)
3.
20 cm2
9.254 cm2
(b)
20.84 cm2
(b)
47.33 cm2 or 9.08 cm2
Using the sine rule and the formula A =½ r 2 to arrive at the answer 92.52 cm2
JPN PERAK
Page 2
Perak State Additional Mathematics Project Work : Teacher’s Guide
2015
WORKSHEET 8
1.
2.
3.
4.
5.
Impossible
The lengths of the sides of the triangle = 6 cm, 10 cm, 3 cm and 6 + 3 < 10
Impossible
AC = 7 cm and thus the length of wire must be 20cm. The 19 cm-wire is 1 cm short.
Impossible
The measurements will result in sin  RPQ > 1
Impossible
The shortest distance between L and M = 80 sin 40o = 5.96 km
Impossible
Suggested methods:
1.
Solve simultaneous equations and found that there are no real roots
2.
Show that the maximum area possible is only 6.25 km2 which is less than the
required 6.5 km2 by using
(a)
the algebraic method,
(b)
differentiation.
WORKSHEET 9
(a)
Solve 3 inequalities formed from a, a + d and a + 2d to arrive at the condition – ⅓ a < d < a
(b)
Solve 3 inequalities formed from a, ar and ar2 to arrive at the condition 0.618 < r < 1.618
Construct any suitable example for each case.
JPN PERAK
Page 3
Perak State Additional Mathematics Project Work : Teacher’s Guide
2015
WORKSHEET 10
(a)
(b)
AC = 70 m
(i)
Ambiguity in triangle ACD
4 266.61 – 1 968.78 = 2 297.83 m2
(ii)
Arun’s land
Abil’s land
WORKSHEET 11
Creative reflection is encouraged : mind maps, poems, songs, powerpoint presentation …………
JPN PERAK
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