1. A. 2. The Learning Hall Mathematics Class IX-X Aug 26, 2018 How to get FULL MARKS in Long Problems in Mathematics (4-5 Marks) ? Long Problems (4-5 Marks) often create a lot of stress amongst students, as it is DIFFICULT to get FULL MARKS. A step by step approach will help students to get there. 1. 2. 3. 4. 5. 6. 7. 8. 9. Read the Question carefully, and try to understand the deliverables Start with the Problem Statement Draw diagrams, wherever possible, and name them. Follow the sequential steps in answering the problem — Don't SKIP Steps Number the important equations with (i), (ii), (iii) etc. Mention Referrals (Pythagoras Theorem, ASA Congruency etc.), wherever applicable Gradually come to the Solution Statement Highlight the final Answer with a Box etc. Remember Full Marks will be given, IF AND ONLY IF — All steps are correct — All referrals are correct — The Final Answer is correct S O
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In the given fig., ray OS stands on a line POQ. Ray OR and ray OT are angle bisectors of angle POS and angle SOQ respectively. If angle POS = x, find angle ROT Ray OS stands on the line POQ A. ROS = 1/2 SOQ= 1/2 (1800- 900 _ SOT = 1/2 3. A. Therefore, Z But, Therefore Z POS + POS = x = 1800 - Now bisects Z Therefore, Z POS And, Now ROT = — 1800 SOQ - x POS = ROS SOT - x/2 +900 900 If x = r sin A cos C, y = r sin A sin C, z = r cosA, Prove that r2 = + Y2 + z2 We know that x = r sin A cos C Therefore, = r2 sin2 A cos2 C Similarly, y = r sin A sin C Therefore, Y2 = r2 sin2 A sin2 C Similarly, z = r cos A Therefore, z2 = r2 cos2 ---------------(ii)
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By (i) + (ii)+ (iii), we get + Y2 +z2= r2 sin2 A (sin2C + cos2 C) + r2cos2A = r2 sin2A Xl + r2 cos2A ( Since sin2C + cos2C = 1) = r2 (sin2A+ cos2A) ( Since sin2A + cos2A = 1) Therefore,
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