UBC MATH 101 EXAM QUESTIONS AND ANSWERS GRADED A+ 2026

UBC MATH 101 EXAM QUESTIONS AND
ANSWERS GRADED A+ 2026




For a function to be differentiable, it must... - ANS -it has to be continuous

- the limit from the left has to equal the limit from the right

-



cscθ - ANS 1/sinθ



secθ - ANS 1/cosθ



cotθ - ANS cosθ/sinθ



sin²θ + cos²θ = 1 - ANS x² + y² = (radius of unit circle)



tan²θ + 1 = sec²θ - ANS (sin²θ/cos²θ) + (cos²θ/cos²θ) = (1/cos²θ)



1 + cot²θ = csc²θ - ANS (sin²θ/sin²θ) + (cos²θ/sin²θ) = (1/sin²θ)



sin(x ± y) - ANS sin(x)cos(y) ± cos(x)sin(y)
@COPYRIGHT 2026/2027 ALL RIGHTS RESERVED
1

, cos(x ± y) - ANS cos(x)cos(y) ∓ sin(x)sin(y)



tan(x ± y) - ANS [tan(x) ± tan(y)] ÷ [1 ∓ tan(x)tan(y)]



sin(2x) - ANS 2 sin(x) cos(x)



equivalent to sin(x ± x)



cos(2x) - ANS cos²(x) - sin²(x)



equivalent to cos(x ± x)



cos(2x) - ANS 2 cos²(x) - 1



equivalent to cos²(x) - [sin²(x) = 1 - cos²(x)]



cos(2x) - ANS 1 - 2 sin²(x)



equivalent to [cos²(x) = 1 - sin²(x)] - sin²(x)



tan(2x) - ANS 2 tan(x) ÷ [1 - tan²(x)]



equivalent to tan(x ± x)


@COPYRIGHT 2026/2027 ALL RIGHTS RESERVED
2