How to Take This Test

There are 25 questions and 15 minutes, about 36 seconds a question, which is the pace of the Tier 1 maths section. Solids usually need one step more than plane figures (a slant height, a radius worked back from a volume, a change of units), so have these ready before you start:

  • The triplets 3, 4, 5; 5, 12, 13; 7, 24, 25; 8, 15, 17 and 20, 21, 29, and their multiples such as 21, 28, 35, give the slant height of a cone or a pyramid without working.
  • 1 m³ =1000= 1000 litres and 1 litre =1000= 1000 cm³. A pipe's speed (in m per second or km/h) must be in the same length unit as its radius before you multiply.
  • When every length is multiplied by kk, surfaces are multiplied by k2k^2 and volumes by k3k^3. In ratio questions, volume goes as r2hr^2 h for cylinders and cones and as r3r^3 for spheres.
  • In melting and recasting the volume stays the same, and the π\pi or 43π\frac{4}{3}\pi usually cancels before any multiplying.
  • Options such as 154, 616, 1,386 or 5,544, and radii that are multiples of 7, mean π=227\pi = \frac{22}{7}; options written with π\pi in them mean you leave π\pi as it is.

How to take it:

  • Start a 15-minute timer and do the test in one sitting, without notes.
  • Marking is +2 for a right answer and −0.50 for a wrong one; a skipped question scores 0.
  • If a question needs more than three lines of working, mark it and come back after the quick ones. A toy or a recasting question can wait; a one-formula question should not.
  • Read the explanations only after the time is up.

Your score. Your score is twice the number right minus half the number wrong, out of 50. So 22 right, 2 wrong and 1 skipped comes to 44 − 1 = 43.

Score (out of 50) What to do next
40 or more This chapter is ready for the exam. Do one of this chapter's PYQ Practice Sets every week or so to keep the formulas and the triplets quick.
30 to 39.5 You know the methods, but a few marks are slipping away. Note the topic of each wrong answer and redo that section's quiz.
20 to 29.5 You know the formulas but reach for them too slowly. Work through Shortcuts & Speed Methods, then Solved Questions and Practice Sets 1 and 2, and take this test again after a few days.
Below 20 Go back to the six concept sections, Cuboid and Cube, Right Prisms and Pyramids, Cylinders and Hollow Cylinders, Cones and Frustums, Spheres and Hemispheres and Combined Solids, Melting and Recasting, and do their quizzes before more timed tests.

On guessing: in Tier 1 even a blind guess is very slightly in your favour on average (+0.125 marks, as Chapter 0 works out), and once you can rule out one option a guess is clearly worth taking (about +0.33 marks on average). In this chapter an option can often be ruled out on sight: a cone cannot hold more than the cylinder on the same base and height, the metal in a pipe is less than the whole outer cylinder, and a wire drawn from a small ball is metres long, not centimetres.