S475 1 Subsidiary Mathematics Uace Samplepaper 2026 Guide

© 2026 Uganda National Examinations Board Turn Over UGANDA NATIONAL EXAMINATIONS BOARD Uganda Advanced Certificate of Education S475/1 SUBSIDIARY MATHEMATICS SCORING GUIDE FOR THE SAMPLE PAPER Page 2 of 12 In response to the tasks, the candidate is expected to: correctly identify the relevant concepts to manipulate in response to the task(s) in the scenario, select and ap ply (a)correct method(s) to correctly manipulate the concepts identified, and correctly interpret accurate outputs from correctly identified and manipulated concepts to justify/inform decision. 𝑺𝑬𝑪𝑻𝑰𝑶𝑵 𝑨 ITEM 1 Task 𝑃𝑜𝑖𝑛𝑡𝑠: 𝐵 (−70,30), 𝐴 (90,30), 𝑆 (0, 0) 𝐿𝑒𝑡 𝛽 𝑏𝑒 𝑡ℎ𝑒 𝑎𝑛𝑔𝑙𝑒 𝑏𝑒𝑡𝑤𝑒𝑒𝑛 𝑆𝐵⃗⃗⃗⃗⃗ 𝑎𝑛𝑑 𝑆𝐴⃗⃗⃗⃗⃗ . 𝑆𝐴⃗⃗⃗⃗⃗ = (90 30) 𝑆𝐵⃗⃗⃗⃗⃗ = (−70 60) 𝑆𝐴⃗⃗⃗⃗⃗ ⋅𝑆𝐵⃗⃗⃗⃗⃗ = (90 30) . (−70 60) = −6300 + 1800 = −4500 −4500 = (√{902+ 302}⋅√{(−70)2+ 602} )𝑐𝑜𝑠𝛽 −4500 = (√{9000 }⋅√{8500 } )𝑐𝑜𝑠𝛽 −4500 = 8746 .4278 𝑐𝑜𝑠𝛽 𝑐𝑜𝑠 𝛽 = −0.5145 𝛽 = 120.96∘ ≈121.0𝑜 𝑇ℎ𝑒𝑟𝑒𝑓𝑜𝑟𝑒 𝑎 𝑡ℎ𝑖𝑟𝑑 𝑠𝑝𝑒𝑎𝑘𝑒𝑟 𝑖𝑠 𝑛𝑒𝑒𝑑𝑒𝑑 𝑠𝑖𝑛𝑐𝑒 𝑡ℎ𝑒 𝑎𝑛𝑔𝑙𝑒 𝑏𝑒𝑡𝑤𝑒𝑒𝑛 𝑡ℎ𝑒 𝑠𝑜𝑢𝑛𝑑 𝑝𝑟𝑜𝑗𝑒𝑐𝑡𝑖𝑜𝑛𝑠 𝑆𝐴⃗⃗⃗⃗⃗ 𝑎𝑛𝑑 𝑆𝐵⃗⃗⃗⃗⃗ 𝑖𝑠 121.0𝑜 𝑤ℎ𝑖𝑐ℎ 𝑖𝑠 𝑚𝑜𝑟𝑒 𝑡ℎ 𝑎𝑛 90𝑜 2𝑠𝑖𝑛2𝜃 + 𝑐𝑜𝑠𝜃 = 1 𝑈𝑠𝑖𝑛𝑔 {𝑠𝑖𝑛2𝜃 = 1 − 𝑐𝑜𝑠2𝜃} 𝑔𝑖𝑣𝑒𝑠 2 (1 − 𝑐𝑜𝑠2𝜃)+ 𝑐𝑜𝑠𝜃 = 1 2 − 2 𝑐𝑜𝑠2𝜃 + 𝑐𝑜𝑠𝜃 = 1 Page 3 of 12 2𝑐𝑜𝑠2𝜃 − 𝑐𝑜𝑠𝜃 − 1 = 0 𝐿𝑒𝑡 𝑎 = 2, 𝑏 = −1, 𝑐 = −1. 𝑈𝑠𝑖𝑛𝑔 𝑡ℎ𝑒 𝑞𝑢𝑎𝑑𝑟𝑎𝑡𝑖𝑐 𝑓𝑜𝑟𝑚𝑢𝑙𝑎: 𝑐𝑜𝑠 𝜃 = {−𝑏 ± √{𝑏2− 4𝑎𝑐}} {2𝑎} 𝑐𝑜𝑠 𝜃 = {−(−1)±√{(−1)2− 4 × 2 × (−1)}} {2 × 2 } cos 𝜃 = {1 ±√{9}} {4} = {1 ± 3 } {4} 𝐸𝑖𝑡ℎ𝑒𝑟 𝑐𝑜𝑠 𝜃 = 1 𝑜𝑟 𝑐𝑜𝑠 𝜃 = −1 2 𝜃 = 0∘ 𝑜𝑟 𝜃 = 120𝑜 𝐹𝑜𝑟 𝑞𝑢𝑎𝑙𝑖𝑡𝑦 𝑠𝑜𝑢𝑛𝑑, 𝑡ℎ𝑒 𝑚𝑖𝑐𝑟𝑜𝑝ℎ𝑜𝑛𝑒 𝑠ℎ𝑜𝑢𝑙𝑑 𝑏𝑒 𝑝𝑟𝑜𝑗𝑒𝑐𝑡𝑒𝑑 𝑎𝑡 0∘ 𝑡𝑜 𝑡ℎ𝑒 ℎ𝑜𝑟𝑖𝑧𝑜𝑛𝑡𝑎𝑙. 𝑰𝑻𝑬𝑴 𝟐: 𝑻𝑨𝑺𝑲 (𝒂) 𝑇(𝑥)= 200000 − 1500 𝑥2 …