How to Take This Test

You get 15 minutes for 25 questions, the same 36 seconds a question that Tier 1 gives you. Most trigonometry questions take one or two lines once the right value or identity comes to mind, so revise these first:

  • The table for 0∘0^\circ, 30∘30^\circ, 45∘45^\circ, 60∘60^\circ and 90∘90^\circ, both ways round: sin⁡30∘=cos⁡60∘=12\sin 30^\circ = \cos 60^\circ = \frac{1}{2}, tan⁡30∘=13\tan 30^\circ = \frac{1}{\sqrt{3}} and tan⁡60∘=3\tan 60^\circ = \sqrt{3}.
  • The three squared identities and the pairs they give, such as (sec⁡θ+tan⁡θ)(sec⁡θ−tan⁡θ)=1(\sec\theta + \tan\theta)(\sec\theta - \tan\theta) = 1, which turns one given sum into the matching difference.
  • For two angles that add up to 90∘90^\circ: sin⁡A=cos⁡B\sin A = \cos B, tan⁡Atan⁡B=1\tan A \tan B = 1, and sin⁡2A+sin⁡2B=1\sin^2 A + \sin^2 B = 1.
  • The triplets 3, 4, 5; 5, 12, 13; 8, 15, 17; 7, 24, 25 and 20, 21, 29, so that one ratio gives all six without working.
  • In the second quadrant only sin⁡θ\sin\theta and cosec⁡θ\operatorname{cosec}\theta are positive, and asin⁡θ+bcos⁡θa\sin\theta + b\cos\theta always stays between −a2+b2-\sqrt{a^2 + b^2} and a2+b2\sqrt{a^2 + b^2}.

How to take it:

  • Set a 15-minute timer and do all 25 in one go, without notes or a calculator.
  • Marking is +2 for a right answer and −0.50 for a wrong one; a question left blank scores 0.
  • If an identity has not opened up in about 40 seconds, put θ=45∘\theta = 45^\circ (or 30∘30^\circ) into the question and the options; if two options still agree, mark it and come back later.
  • Read the explanations only when the time is over.

Your score. Count 2 for each right answer and take off 0.5 for each wrong one; the total is out of 50. For example, 19 right, 4 wrong and 2 left blank gives 38 − 2 = 36.

Score (out of 50) What to do next
40 or more Trigonometry is ready for the exam. Keep the values quick with one of this chapter's PYQ Practice Sets each week.
30 to 39.5 The methods are in place, but a few questions slip. Check the tag on each wrong answer and redo the quiz of that concept section; for identities and conditions that means Identities and Simplification or Values from a Condition, Maximum and Minimum.
20 to 29.5 You know most of the facts but take too long to use them. Go through Shortcuts & Speed Methods and Solved Questions, redo Practice Sets 1 and 2, and sit this test again a few days later.
Below 20 Start again from the concept sections, Angles, Radians and Trigonometric Ratios, Standard Angles and Complementary Angles, Identities and Simplification, Values from a Condition, Maximum and Minimum and Allied, Compound and Double Angles, with their quizzes, before more timed work.

About guessing: Chapter 0 shows that a pure guess in Tier 1 gains about 0.125 marks on average, and ruling out one option first lifts that to about 0.33, so a guess after one elimination is worth making. Trigonometry options are often easy to rule out: a sine or cosine above 1 cannot be right, no ratio of an acute angle is negative, a second-quadrant cosine must carry a minus sign, and a check at θ=45∘\theta = 45^\circ removes any identity option that does not match there.