2024 JPJC J1 EYE Revision Package_Qn

JC1 H2 Math Year-End Exam Revision Package \ Pg 1 2024 JC1 H2 Mathematics (9758) Year-End Examination Revision Package Name:______________________________ Class:__________ Contents Topical Revision Page Topic 1: Vectors 3 Topic 2: Graphing Techniques I & II 6 Topic 3: Equations & Inequalities 9 Topic 4: Functions 11 Topic 5: Differentiation Techniques & Applications 13 Topic 6: Integration Techniques 16 Paper Revision Revision Paper A 18 Revision Paper B 23 Revision Paper C 29 Revision Paper D 33 Answer Key 39 Worked solutions will be uploaded on JPJC Math Google Site on 30/8 (Topical 1-3), 9/9 (Topical 4-6), 18/9 (Revision A-D)

JC1 H2 Math Year-End Exam Revision Package \ Pg 2 INFORMATION FOR STUDENTS JC1 H2 Mathematics Year-End Examination: 27 Sept 2024 (Fri) SCHEME OF EXAMINATION PAPERS For the year-end examination in H2 Mathematics, it will be a 3 hour paper consisting of about 10 to 13 questions of different lengths and marks based on the following Pure Mathematics topics: Topic 1: Vectors Topic 2: Graphing Techniques I & II Topic 3: Equations and Inequalities Topic 4: Functions Topic 5: Differentiation Techniques & Applications Topic 6: Integration Techniques (Chp 1 to 8 of Lecture Notes) The total number of marks is 100. Candidates will be expected to answer all questions. USE OF GRAPHIC CALCULATOR (GC) The use of GC without computer algebra system will be expected. The examination papers will be set with the assumption that candidates will have access to GC. As a general rule, unsupported answers obtained from GC are allowed unless the question states otherwise. Where unsupported answers from GC are not allowed, candidates are required to present the mathematical steps using mathematical notations and not calculator commands. For questions where graphs are used to find a solution, candidates should sketch these graphs as part of their answers. Incorrect answers without working will receive no marks. However, if there is written evidence of using GC correctly, method marks may be awarded. Students should be aware that there are limitations inherent in GC. For example, answers obtained by tracing along a graph to find roots of an equation may not produce the required accuracy.

JC1 H2 Math Year-End Exam Revision Package \ Pg 3 H2 Mathematics Year-End Exam Revision Package JC1- 2024 Topic 1: Vectors 1. [CJC/2016/Promo/3] The position vectors of the points A , B and C with respect to the origin O are a , b and c respectively. Point C is on AB produced such that 5 3 .AB AC Given that 2a ci , a is a unit vector and the angle AOB is π 3 , show that 16 5b . [5] 2. [HCI/2016/Promo/7] Relative to the origin O, three distinct fixed points A, B and C have position vectors a , b and c respectively. It is known that b is a unit vector, 3a , 2c and angle AOC = 60 . (i) State the geometrical interpretation of b