Perak State Additional Mathematics Project Work : Teachers Guide

Perak State Additional Mathematics Project Work : Teachers Guide 2015

WORKSHEET 1The 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:abcNumber of triangles that can be formeda+bca+cbb+ca

*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 3Findings 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:ConditionNumber of triangles possible

c < b sin C0

c = b sin C1

b sin C < c < b2

c b1

WORKSHEET 51.Cosine rule and its proof2.Students must use only the Cosine rule to arrive at the following answers.(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 / 73543.Using the cosine rule and the formula s = r to arrive at the answer AC = 10.52 cm.

WORKSHEET 61.Sine rule and its proof2.Students must use only the Sine rule to arrive at the following answers.(a) B = 46.42 / 4625 , A = 58.58 / 58 35 , BC =7.068 cm(b) P = 129.53 / 129 32 , R = 10.47 / 1028 , PQ = 1.414 cm3.Using the sine rule and the formula s = r to arrive at the answer = 2.50 rad.WORKSHEET 71.Area of triangle = ab Sin C and its derivation.2.Case 1 : SAS(a)20 cm2(b)20.84 cm2Case 2 : SSS9.922 cm2Case 3 : SSA(a)9.254 cm2(b)47.33 cm2 or 9.08 cm23.Using the sine rule and the formula A = r 2 to arrive at the answer 92.52 cm2

WORKSHEET 81.Impossible The lengths of the sides of the triangle = 6 cm, 10 cm, 3 cm and 6 + 3 < 102.ImpossibleAC = 7 cm and thus the length of wire must be 20cm. The 19 cm-wire is 1 cm short.3.ImpossibleThe measurements will result in sin RPQ > 14.ImpossibleThe shortest distance between L and M = 80 sin 40o = 5.96 km5.ImpossibleSuggested methods:1.Solve simultaneous equations and found that there are no real roots2.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 a < d < a (b)Solve 3 inequalities formed from a, ar and ar2 to arrive at the condition 0.618 < r < 1.618Construct any suitable example for each case.

WORKSHEET 10(a)AC = 70 m(b)(i)Ambiguity in triangle ACD4 266.61 1 968.78 = 2 297.83 m2(ii)Aruns land

Abils land

WORKSHEET 11Creative reflection is encouraged : mind maps, poems, songs, powerpoint presentation JPN PERAKPage 1