GEOMETRY AND TRIGONOMETRY

Use Pythagoras in 2D (a² + b² = c²)

A right-angled triangle has sides 3 cm and 4 cm. Find the hypotenuse.

Use Pythagoras in 3D (a² + b² + c² = d²)

A cuboid has sides 3 cm, 4 cm, 12 cm. Find space diagonal.

Use SOHCAHTOA (sin, cos, tan)

In a right-angled triangle, hypotenuse = 10 cm, angle = 30°. Find opposite side.

Use sine rule (a/sinA = b/sinB)

In triangle ABC, a=7, b=10, angle A=30°. Find angle B.

Use cosine rule (a²=b²+c²−2bc cosA)

Find side c in triangle with a=5, b=6, angle C=60°.

Find area of triangle using trig (½ab sin C)

Triangle with sides 8 cm, 11 cm, angle 45°. Find area.

Use circle theorems (angle at centre = 2 × angle at circumference)

Angle at centre = 100°. Find angle at circumference.

Use alternate segment theorem (angle between tangent & chord)

Find angle in segment where tangent meets circle.

Find equation of a circle (x−h)² + (y−k)² = r²)

Circle centre (3,−2) radius 5. Find equation.

Find length of an arc (rθ in radians)

Circle radius 7 cm, angle 60°. Find arc length.

Find area of sector (½ r² θ)

Circle radius 5 cm, angle 90°. Find sector area.

Find radius or angle from sector area

Sector area = 20 cm², radius = 5 cm. Find angle in radians.

Use bearings (angle measured clockwise from North)

Ship travels on bearing 045°. Draw path.

Find gradient of a line (change in y ÷ change in x)

Line passes (1,2) and (5,10). Find gradient.

Find perpendicular gradient (negative reciprocal)

Line has gradient 3. Find perpendicular gradient.

Find equation of a line (y = mx + c)

Line through (0,3) gradient 2. Find equation.

Transformations – translation (add vector)

Translate triangle A(1,2), B(3,4) by vector (2,−1).

Transformations – reflection (mirror across axis/line)

Reflect point (3,5) across y = x.

Transformations – rotation (around point, clockwise/anticlockwise)

Rotate (2,3) 90° clockwise about origin.

Transformations – enlargement (scale factor, centre)

Enlarge triangle by scale factor 2 about origin.

Find perimeter of composite shapes (add all sides)

Rectangle 5×3 and triangle base 5 height 4. Find perimeter.

Find area of composite shapes (sum of areas)

Same rectangle + triangle. Find area.

Find surface area of prism/cylinder/cone

Cylinder radius 3 height 10. Find surface area.

Find volume of prism/cylinder/cone

Same cylinder. Find volume.

Use similarity (same shape, scale factor)

Two similar triangles, sides 3 cm and 6 cm. Find missing side.

Use congruence rules (SSS, SAS, ASA, RHS)

Prove triangles congruent using SAS.

Find midpoint of a line (average coordinates)

Points (1,2) and (5,6). Find midpoint.

Use vector notation to describe points

AB = (3,4). Find position vector of B relative to origin.

Solve vector problems (addition/subtraction)

A = (2,3), B = (5,1). Find A + B.

Use loci (set of points equidistant from line/point)

Construct locus 3 cm from a line segment.