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LearnEdexcel4MA12016 specificationPapers 1F, 2F · Foundation tierGeometry and trigonometry

Papers 1F, 2F · Module

Geometry and trigonometry

11 subtopics≈ 335 min in total

Start the module: Angles and polygons Open graphing calculator

Angles and polygons
A handful of angle facts (straight lines $180^\circ$ , points $360^\circ$ , triangles $180^\circ$ , and the three parallel-line pairs) solve almost every angle problem. For polygons, start with the exterior angles: they always add up to $360^\circ$ .
≈ 30 min
Circle theorems
Eight short theorems describe how angles behave in a circle. Learn each one with its exact wording, spot which one a diagram is using, and give it as your reason.
≈ 35 min
Similarity and congruence
Similar shapes are enlargements of each other: same angles, all lengths multiplied by the same scale factor $k$ . Areas then scale by $k^2$ and volumes by $k^3$ . Congruent shapes are identical: $k=1$ .
≈ 30 min
Bearings, scale drawings and symmetry
A bearing is an angle measured clockwise from north, written with three figures. To reverse a bearing, add or subtract $180^\circ$ . Map scales turn real distances into drawn ones, and symmetry describes how a shape fits onto itself.
≈ 25 min
Constructions and loci
A locus is the set of all points that obey a rule. Points a fixed distance from a point make a circle; equidistant from two points, the perpendicular bisector; equidistant from two lines, the angle bisector. Ruler-and-compass constructions draw these exactly, and you leave the arcs to show your method.
≈ 30 min
Perimeter, area and units
Perimeter is the distance around a shape; area is the space inside it. Five area formulas cover almost every straight-sided shape, and compound shapes are just these pieces added or subtracted. When converting area units, square the length conversion.
≈ 30 min
Circles, arcs and sectors
Circumference $2\pi r$ and area $\pi r^2$ . A sector is a fraction $\dfrac{\theta}{360}$ of the circle, so its arc and area are that fraction of the circumference and area. Its perimeter is the arc plus two radii.
≈ 30 min
Prisms and cylinders
A prism has the same cross-section all the way through, so its volume is cross-section area $\times$ length. A cylinder is a prism with a circular cross-section. Surface area is the total area of every face: unfold the solid into a net and add.
≈ 30 min
Pyramids, cones and spheres
A pyramid or cone holds exactly one third of the prism with the same base and height. A sphere has volume $\tfrac43\pi r^3$ and surface area $4\pi r^2$ . Composite solids are built from these pieces: add the volumes, and count only the outside surfaces.
≈ 35 min
Pythagoras' theorem
In a right-angled triangle, the square on the hypotenuse equals the sum of the squares on the other two sides: $a^2+b^2=c^2$ . Add the squares to find the hypotenuse; subtract to find a shorter side.
≈ 25 min
Right-angled trigonometry
Label the sides opposite, adjacent and hypotenuse relative to the angle. Then SOHCAHTOA tells you which ratio links the two sides you know (or want). Use the ratio to find a side, or the inverse function to find an angle.
≈ 35 min