Score 90+ in FBISE Class 11 Math Unit 9 – key answers only!
HSA Notes Features
- 100% NBF/FBISE correct
- Ex 9.1–9.2 + Review solved
- Short exam-ready format
- Range, period, odd/even, graphs
- Free PDF download
- Trusted for high marks
Target Audience
FBISE + Punjab boards. Top schools: Beaconhouse, Roots, LGS, City School, Karachi Grammar, Aitchison, Lawrence, ICG, APS, FPS.
Unit 9 Key Solved Highlights
Ex 9.1 (Range & Period)
Q1(i) [0,4] → Max 4, Min 0
Q1(ii) [1/6, 7/6] → Max 7/6, Min 1/6
Q1(iii) [−9/5, 11/5] → Max 11/5, Min −9/5
Q1(iv) [32/5, 38/5] → Max 38/5, Min 32/5
Q2(i) Max 1, Min 1/7
Q2(ii) No finite max/min (asymptotes)
Q3(i) [−7,7], period 2π
Q3(ii) [−1,1], period 2π
Q3(iv) R, period 2
Q3(vi) [cos1, 1], period 2π
Q4(i) π
Q4(iii) 4π
Q4(vi) 2π
Ex 9.2 (Odd/Even & Graphs)
Q1(i) Odd
Q1(ii) Even
Q1(iii) Even
Q1(iv) Even
Q1(v) Odd
Q1(vi) Even
Q1(vii) Odd
Q1(viii) Odd
Q5(i) sin x = cos x → x = π/4 + kπ
Q5(ii) cos x = x → x ≈ 0.739
Q6 V(t) = 180 sin(112π t)
Q7 h(t) = −8.5 cos(π t / 25) + 10.5
Q8 h(t) = 4 cos(π t) + 16
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