Advanced level 2025 BAEBOC Pure mathematics with mechanics guide

Advanced level 2025 BAEBOC Pure mathematics with mechanics guide

Advanced level 2025 BAEBOC Pure mathematics with mechanics guide

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i) 4x−10ydxdy​=3xdxdy​+3y ⇒dxdy​=3x+10y4x−3y​

mT​=3(−2)+10(2)4(−2)−3(2)​=−6+20−8−6​=14−14​=−1

$y-2=-1(x-(-2))\Rightarrow y-2=-x-2\Rightarrow y=-x$

ii) a) y=(cos(x1/2

))2 dxdy​=2cos(x1/2)⋅(−sin(x1/2))⋅21​x−1/2=−x​sin(x1/2)cos(x1/2)​=−2x​sin(2x​)​

b) y=ln[1−x2sin4x​]3=3ln(1−x2sin4x​)=3(4ln∣sinx∣−ln∣1−x2∣)=12ln∣sinx∣−3ln∣1−x2∣ dxdy​=12sinxcosx​−31−x2−2x​=12cotx+1−x26x

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