Huh Lab Maths › IGCSE Maths › Geometry
Topic 4 of the Cambridge IGCSE Mathematics (0580) syllabus: from angles and bearings to similarity and the circle theorems. Here is what each part asks, a practice question for each, and the mistakes that cost the most marks.
Each part with one practice question, made by the same engine your child plays. Parts marked Extended are for the Extended paper only.
A solid has 4 faces, 6 edges and 4 vertices.
Which solid could it be?
tetrahedron. A tetrahedron has 4 faces, 6 edges and 4 vertices. (cube: 6, 12, 8.)
The questions for this part come with a picture or are played as a game, so they are best tried in Huh Lab.
The bearing of B from A is 210°.
What is the bearing of A from B?
030°. Turn round: add 180° if the bearing is under 180°, take 180° away if it is over. 210° − 180° = 030°.
Two similar shapes have lengths in the ratio 1 : 3.
The small one has volume 7 cm³.
Find the volume of the large one.
189 cm³. Volumes scale by 3³ = 27: 7 × 27 = 189 cm³.
PA and PB are tangents to a circle with centre O.
Angle APB = 70°. Find angle AOB.
110. A tangent meets the radius at 90°, so angles OAP and OBP are both 90°. The angles of quadrilateral OAPB add to 360°: AOB = 360 − 90 − 90 − 70 = 110°.
Two parallel lines are crossed by a third line.
One angle is 110°. What is its co-interior angle?
70°. Co-interior (allied) angles sit between the parallel lines on the same side. They add to 180°: 180 − 110 = 70°.
In a cyclic quadrilateral, one angle is 90°.
What is the opposite angle?
90°. Opposite angles of a cyclic quadrilateral add to 180°. 180 − 90 = 90°.
Tangents from a point P touch a circle at A and B.
Angle APB = 56°. Find angle PAB.
62°. PA = PB (tangents from one point), so triangle PAB is isosceles. Its base angles are (180 − 56) ÷ 2 = 62°.
Huh Lab checks every wrong answer against known mistakes like these, and goes back to the step behind the one your child keeps making.
Name the rule that makes them equal. If there is no rule, work it out.
A back bearing is a half turn: add or subtract 180°, never 360° minus.
A triangle drawn on a diameter always has a right angle on the circle.
Alternate (Z) and corresponding (F) angles are EQUAL. Nothing to subtract.
Lengths × 3 means areas × 9 and volumes × 27. Square or cube the scale factor.
Mark the right angles where the tangents touch the circle before adding angles.
A quadrilateral cuts into two triangles, so its angles add up to 2 × 180 = 360°.
In 47 the 4 is four TENS. Say the number aloud in tens and ones.
Short rounds on any topic, a new question every time, the exact mistake found, and a report to you after every session.
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