How to Take This Test

You have 15 minutes for 25 questions, about 36 seconds each, which is the pace of the real Tier 1 Maths section. At that speed the quick results have to be ready in your head: the centre-angle results (∠BIC=90∘+A2\angle BIC = 90^\circ + \frac{A}{2} for the incentre, ∠BOC=2A\angle BOC = 2A for the circumcentre, ∠BHC=180∘−A\angle BHC = 180^\circ - A for the orthocentre), the common Pythagorean triplets (3, 4, 5; 5, 12, 13; 8, 15, 17; 7, 24, 25; 20, 21, 29) and their multiples, the chord distance rule d2+(l2)2=r2d^2 + \left(\frac{l}{2}\right)^2 = r^2, the tangent length d2−r2\sqrt{d^2 - r^2}, and the two common tangents, d2−(R−r)2\sqrt{d^2 - (R - r)^2} for the direct one and d2−(R+r)2\sqrt{d^2 - (R + r)^2} for the transverse one. Make a ten-second sketch for every question; it stops most mix-ups about which angle or which arc is meant.

  • Time yourself for 15 minutes and finish in one go, with no breaks and no notes.
  • A right answer earns +2, a wrong one costs −0.50, and a skipped question scores 0.
  • Leave a long-looking question for later and come back if time is left. One stubborn angle chase can eat the time of three quick questions.
  • Open the explanations only when the 15 minutes are up.

Scoring. Score = 2 × (right answers) − 0.5 × (wrong answers), out of 50. So 21 right, 3 wrong and 1 skipped gives 42 − 1.5 = 40.5.

Your score (out of 50) What to do next
40 or more Geometry is ready for the exam. Go through the PYQ Practice Sets now and then so the centre angles and tangent formulas stay quick.
30 to 39.5 The base is sound, but marks are leaking. Sort your wrong and skipped questions by tag and redo the quiz of each section they point to. Wrong angles usually send you to Centres of a Triangle or the angle rules in Circles: Chords, Arcs and Angles; wrong lengths to chords, tangents and common tangents.
20 to 29.5 You know the results but they are slow. Go through Shortcuts & Speed Methods, especially the centre-angle table, chord distance and the common tangents, then Practice Sets 1 and 2, and take this test again a few days later.
Below 20 Go back to the six topic sections, Lines, Angles, Quadrilaterals and Polygons, Triangles: Angles, Sides, Congruence and Pythagoras, Centres of a Triangle, Similar Triangles and Proportionality, Circles: Chords, Arcs and Angles and Circles: Tangents, Secants and Two Circles, before you try more timed tests.

The tag on each question tells you where to look: lines and angles, polygons and quadrilaterals are in Lines, Angles, Quadrilaterals and Polygons; triangle angles and sides, congruence, and Pythagoras and right triangles are in Triangles: Angles, Sides, Congruence and Pythagoras; triangle centres, and inradius and circumradius are in Centres of a Triangle; similar triangles and proportionality theorems are in Similar Triangles and Proportionality; chords and arcs, angles in a circle and cyclic quadrilaterals are in Circles: Chords, Arcs and Angles; and tangents, and two circles and common tangents are in Circles: Tangents, Secants and Two Circles.

If more than 3 were wrong, slow down a little next time. On guessing, Chapter 0 works out the numbers: in Tier 1 even a blind guess is very slightly in your favour on average, and once you can rule out one option, a guess is clearly worth taking.