Skip to content

Course home

1.5 Trigonometry

1.5 Trigonometry

EasyMediumHard
123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596979899100101102103104105106107108109110111112113114115116117118119120121122123124125126127128129130131132133134135136137138139140141142143144145146147148149150151152153154155156157158159160161162163164165166167168169170171172173174175176177178179180181182183184185186187188189190191192193194195196197198199200201202203204205206207208209
Question 102

An ecologist monitors the population of Arctic hares, HHH hundreds, on a remote island at various times ttt months after a monitoring project began. The recorded data follows a cyclic pattern based on seasonal availability of vegetation. The researcher models this population using the equation:

H(t)=6.52cos⁡(2π(t−2.5)10.5)+14.34 H(t) = 6.52 \cos\left( \frac{2\pi(t - 2.5)}{10.5} \right) + 14.34 H(t)=6.52cos(10.52π(t−2.5)​)+14.34
a.

Find the minimum population of hares predicted by the model. Give your answer to the nearest whole hare.

[3]
b.

Find the duration of the longest continuous period during the first 21 months of the project (from t=0t=0t=0 to t=21t=21t=21) where the population predicted by the model is above 18 hundred. Give your answer in months to one decimal place.

[4]
c.

A different colony of hares in a more sheltered valley is found to have a more stable population with less variation between peaks and troughs, though it maintains the same average population and peak times. A student suggests refining the model for this sheltered colony by increasing the value 6.52 to 7.80. Explain whether this refinement is appropriate.

[2]
Markscheme

1.5 Trigonometry Questions

  1. A Level
  2. /Maths
  3. /1.5 Trigonometry

317 exam-style questions on OCR A Level Maths 1.5 Trigonometry, covering 1.5.1 Definitions for all arguments, 1.5.2 Sine and cosine rules, 1.5.3 Area of a triangle, 1.5.4 Radian measure (A-level only), 1.5.5 Small angle approximations (A-level only), 1.5.6 Graphs of basic trigonometric functions, 1.5.7 Exact values in radians (A-level only), 1.5.8 Reciprocal and inverse trigonometric ratios (A-level only), 1.5.9 Graphs of reciprocal and inverse functions (A-level only), 1.5.10 Trigonometric identities, 1.5.11 Further trigonometric identities (A-level only), 1.5.12 Double angle and compound angle formulae (A-level only), 1.5.13 Geometrical proofs of formulae (A-level only), 1.5.14 Harmonic form Rcos / Rsin (A-level only), 1.5.15 Trigonometric equations, 1.5.16 Proof involving trigonometric functions (A-level only), and 1.5.17 Trigonometric functions in context. Each one has a worked solution and a mark scheme showing where the marks go.

Question bank