How to Take This Test

Twenty-five questions in 15 minutes leaves 36 seconds for each, as in the exam. The mix follows a Tier 1 paper on this chapter: mostly one tower and one angle, shadows, ladders and kite strings, with a few on two angles, two heights and a moving car or plane. Keep the 1:3:21 : \sqrt{3} : 2 and 1:1:21 : 1 : \sqrt{2} triangles in your head before you start, along with the rule that from 30∘30^\circ to 60∘60^\circ the distance walked is twice the distance left.

  • Start a 15-minute timer and work straight through, with no notes and no calculator.
  • Marking: +2 for each right answer, −0.50 for each wrong one, and 0 for a question left blank.
  • For any question with two angles or two heights, draw a rough sketch first; it takes a few seconds and shows at once whether two distances add or subtract.
  • Look at the explanations only after the time is up.

Your score. Take 2 marks for each right answer and subtract half a mark for each wrong one; the total is out of 50. Say you get 18 right and 5 wrong and leave 2: your score is 36 − 2.5 = 33.5.

Score (out of 50) What to do next
40 or more Heights and distances is ready for the exam. Keep it fresh with one of this chapter's PYQ Practice Sets every week or two.
30 to 39.5 The triangles are in place, but some questions still slip. Check the tag on each wrong answer and redo that concept section's quiz: two angles and moving objects are in Two Angles and Moving Objects, statues and pairs of towers in Two Heights: Towers, Buildings and Statues.
20 to 29.5 You can solve most of these, but not yet at 36 seconds each. Work through Shortcuts & Speed Methods and Solved Questions, redo Practice Sets 1 and 2, and take this test again after a few days.
Below 20 Go back to Angles of Elevation and Depression and Shadows, Ladders, Strings and Slopes, with their quizzes, before more timed practice.

On guessing: in Tier 1 a blind guess is worth only about +0.125 marks a question on average, while a guess made after ruling out one option is worth about +0.33, so guess only when you can rule out at least one. In this chapter that is often quick: a 60∘60^\circ angle needs a height greater than the distance and a 30∘30^\circ angle a smaller one, a slant length (a ladder, a string or a line of sight) is longer than either of the other two sides, and a speed has to be in the unit the question asks for.