1 TJC H2 JC1 MYA 20219758/01 1A particular country ordered 11 million doses of vaccines to protect its population against rubella, hepatitis A and chicken pox. The country spent 244.25 million dollars in purchasing r million doses of rubella vaccines, a million doses of hepatitis A vaccines and c million doses of chicken pox vaccines. The cost of each dose of rubella vaccine is $6.50, hepatitis A vaccine $21 and chicken pox vaccine $27.50. Furthermore, it is known that the country had purchased 0.5 million more doses of hepatitis A vaccines than of rubella vaccines. Find how much more the country spent on chicken pox vaccines than on the other two types of vaccines combined. Solution Marker’s Comments 1r+ a+ c= 11 ----- (1) 6.5r + 21a+ 27.5c= 244.25 ----- (2)a = r+ 0.5 – r + a= 0.5 ----- (3) From GC, 2, 2.5, 6.5rac6.5 (27.5) – 2 (6.5) – 2.5 (21) = 113.25 The country spent $113.25 million more on chicken pox vaccines than on the other two types combined. Note: If 2 000 000 or 2 million doses of rubella vaccines has been purchased, then r= 2, not 2x106. Need to answer to the question in context.
2 TJC H2 JC1 MYA 20219758/01 2 (a)Find the vector uwhich has a magnitude of 2 units and is in the same direction as the vector i + k, where i, jand kare unit vectors along the x-axis, y-axis and z-axis respectively. State the geometrical relationship between uand the y-axis.  (b) The position vectors of points A and B, relative to the origin O, are aand brespectively and the angle AOBis . The point Mdivides ABin the ratio :1.(i) Write down OMin terms of , aand b.  (ii)The points C and D lie on OA and OBextended respectively such that OC= pOAand OD= qOB, where pand qare real numbers. It is also given that aand bare both unit vectors. If OMis perpendicular to CD, show that cos, where 0.pqqpqp Solution Marker’s Comment (a) 11120201111uSince 12 01uis parallel to the x-zplane, hence uis perpendicular to the y–axis. Common errors: 112 0 or 2110uMany students wrote uincorrectly as vector 1. parallel to the y-axis; 2. lies on plane contain y-axis; or 3. make an angle of 45 degree with the y-axis. (b)(i)1()11baOMbaMajority of the students answer this correctly. Common errors include or 1OMbabaAlternative ThinkingUnit vector along y-axis= j10201010uj, hence uis perpendicular to the y–axis.Did not convert to unit vector.Carelessly write down the vector.
3 TJC H2 JC1 MYA 20219758/01 (b)(ii)Given OCp OAand ODq OBSince OMis perpendicular to CD, 0OMCD1()()01baqbpa221()()01q bp b aq a bp a22(cos)(cos)0q bp a bq a bp a Since 1(unit vectors)ab()()cos0qppq cos, where 0.