Angles, Shape & Geometry — 11+ Topic Guide

Part of the GrammarMock topic guides. The hard maths papers (3 and 5) carry the heaviest geometry load, with diagrams.

The facts your child must know cold

GL geometry questions are mostly one fact plus one calculation. The child who knows the facts instantly spends their time on the calculation; the child who doesn't loses the question entirely. Non-negotiable memory items:

Angle facts

• Angles on a straight line = 180°
• Angles around a point = 360°
• Angles in a triangle = 180°
• Angles in a quadrilateral = 360°
• Vertically opposite angles are equal
• Each hour mark on a clock face = 30° (360 ÷ 12)

Interior angles of regular polygons — derive, don't memorise: sum = (sides − 2) × 180°, then divide by the number of sides. Pentagon: 3 × 180 ÷ 5 = 108°. Hexagon: 4 × 180 ÷ 6 = 120°. Octagon: 6 × 180 ÷ 8 = 135°.

Area & perimeter

• Rectangle: area = l × w, perimeter = 2(l + w)
• Triangle: area = ½ × base × height
• Square from area: side = √area (know your squares to 15² = 225)
• Cuboid volume = l × w × h; cube surface area = 6 × side²

Symmetry: a regular polygon with n sides has n lines of symmetry.

The compound-shape method (guaranteed to appear)

L-shapes and T-shapes with labelled sides appear on nearly every hard GL paper. Two valid methods — teach both, let your child pick:

1. Split: cut the L into two rectangles, find each area, add.
2. Subtract: complete the big rectangle, subtract the missing corner.

For perimeter of compound shapes, the reliable method is to trace around the outside with a finger, adding every side. The trap: unlabelled sides. If the full width is 15 and one horizontal piece is 6, the other is 15 − 6 = 9 — children must deduce missing sides before adding. This deduction step IS the question.

Clock-angle questions (the classic hard finisher)

"What is the angle between the hands at 4:40?"

• Minute hand: 40 minutes = 40 × 6° = 240° from 12
• Hour hand: at 4:00 it sits at 4 × 30° = 120°; in 40 minutes it moves 40/60 × 30° = 20° further, so 140°
• Angle between: 240 − 140 = 100°

The trap everyone falls into: treating the hour hand as parked at the 4. It moves. Practising three of these makes the pattern permanent.

Coordinates

• Reading and plotting in all four quadrants — (x, y), "along the corridor, up the stairs"
• Reflection in the x-axis: (x, y) → (x, −y). In the y-axis: (x, y) → (−x, y)
• Area of rectangles from coordinates: subtract x's for width, subtract y's for height. Watch negative coordinates: from x = −3 to x = 5 is 8 units, not 2.

The two "stretch" facts for hard papers

Top-quartile papers (and some superselectives) reach for:

• Pythagoras: in a right triangle, the two short sides squared add to the long side squared. Know the classic triples: 3-4-5, 5-12-13, and their doubles (6-8-10). "Diagonal 13, one side 5 → other side 12" should be recognition, not calculation.
• Working backwards from area/volume: "a cube has surface area 294 cm² — what's its volume?" One face = 294 ÷ 6 = 49, side = 7, volume = 343. The chain (surface → face → side → volume) is the skill.

Practice plan

• Days 1-2: angle facts drills (parent asks, child answers — 90 seconds a day until instant)
• Days 3-4: compound shapes, both methods, 5 shapes a day
• Day 5: clock angles × 3, coordinates × 5
• Day 6: Pythagoras triples + backwards area/volume
• Day 7: the geometry sections of GrammarMock Maths Paper 3 or 5 under time