GCSE AQA Higher Further Maths · Topic 6 of 6
Choose a subtopic. Geometry covers Core geometry knowledge, Understand and construct geometrical proofs using formal arguments, Sine and cosine rules in scalene triangles, and Use of Pythagoras' theorem in 2D and 3D in GCSE AQA Higher Further Maths. 16 lessons in 10 subtopics.
Revise Geometry for GCSE AQA Higher Further Maths, including Core geometry knowledge and Understand and construct geometrical proofs using formal arguments.
16
Lessons
10
Subtopics
Geometry has 10 subtopics, including:
16 lessons, grouped by subtopic.
Go back to the full GCSE AQA Higher Further Maths topic list, or practise this topic with past-paper questions.
Geometry covers Core geometry knowledge, Understand and construct geometrical proofs using formal arguments, Sine and cosine rules in scalene triangles, and Use of Pythagoras' theorem in 2D and 3D in GCSE AQA Higher Further Maths. 16 lessons in 10 subtopics.
Pythagoras' theorem states that in a right-angled triangle with legs a and b and hypotenuse c, a² + b² = c². The Pythagoras in 2D and 3D notes cover this in full.
The core circle theorems are: the angle at the centre is twice the angle at the circumference; angles in the same segment are equal; opposite angles in a cyclic quadrilateral sum to 180°; the alternate segment theorem; and the radius results, that a tangent is perpendicular to the radius and the perpendicular from the centre bisects a chord. The Circle Theorems notes cover this in full.
Volume of a cylinder = π × r² × h, because a cylinder is a circular prism. The Area, Perimeter, Surface Area and Volume notes cover this in full.
SOH-CAH-TOA is the mnemonic for the three trigonometric ratios in a right-angled triangle: sin θ = opposite ÷ hypotenuse, cos θ = adjacent ÷ hypotenuse, and tan θ = opposite ÷ adjacent. The Trigonometry Review notes cover this in full.
Total surface area of a cylinder = 2πrh + 2πr²: the curved surface plus two circular ends. The Area, Perimeter, Surface Area and Volume notes cover this in full.
The graph of y = sin x is a smooth wave through (0°, 0), peaking at (90°, 1), crossing zero at (180°, 0), troughing at (270°, −1) and returning to (360°, 0). The Sketching Sine, Cosine, and Tangent Graphs notes cover this in full.
The graph of y = cos x is the same wave shape as sine but starts at its peak: (0°, 1), crossing zero at (90°, 0), troughing at (180°, −1), crossing zero at (270°, 0) and peaking at (360°, 1). The Sketching Sine, Cosine, and Tangent Graphs notes cover this in full.
Area of a trapezium = ½(a + b)h, where a and b are the parallel sides and h is the perpendicular height. The Area, Perimeter, Surface Area and Volume notes cover this in full.