Geometry (Higher)

Edexcel 1MA1 G

GCSE Maths (1MA1) · Higher · exam-style practice, examiner-report intelligence and the tools that drill it.

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The topic on one screen

Every circle-theorem answer needs the theorem NAMED as the reason — 'angle at the centre is twice the angle at the circumference', not just the number.
Alternate segment theorem is the one that gets forgotten: the angle between a tangent and a chord equals the angle in the alternate segment.
Cosine rule for three sides, or two sides and the INCLUDED angle; sine rule otherwise. Choose by what is opposite what.
Exact trig values are non-calculator marks — know sin and cos of 0, 30, 45, 60, 90 degrees, and tan of 0, 30, 45, 60 (tan 90 is undefined).
Similar shapes: area scales by $k^2$ , volume by $k^3$ . Find the length ratio $k$ first, then square or cube it.
3D trig: find a right-angled triangle inside the solid, redraw it flat, and it becomes ordinary Pythagoras or SOHCAHTOA.

Where students actually lose marks

Circle-theorem marks are for the reasoning as much as the value — a correct angle stated without naming the theorem can drop the communication mark.

Edexcel 1MA1 mark-scheme conventions (geometrical reasoning)

Rounding an intermediate cosine-rule value before the final step is a standard accuracy loss — keep full calculator accuracy until the last line.

Edexcel 1MA1 Higher — recurring trigonometry error

On similar solids, applying the length ratio $k$ to a volume instead of $k^3$ (or $k$ to an area instead of $k^2$ ) is the classic lost-marks error.

Edexcel 1MA1 Higher — recurring similarity error

Try it — exam-style

Medium

2 marks

ORIGINAL

A, B and C are points on a circle, centre O. Angle $AOC = 130^\circ$ (the angle at the centre standing on arc AC). B lies on the major arc. Work out angle $ABC$ , giving a reason.

Medium

3 marks

ORIGINAL

In triangle $ABC$ , $AB = 8$ cm, $AC = 5$ cm and the included angle $BAC = 52^\circ$ . Work out the length of $BC$ , to 3 significant figures.

Medium

3 marks

ORIGINAL

In triangle $ABC$ , angle $A = 42^\circ$ , angle $B = 63^\circ$ and side $a$ (opposite $A$ ) $= 6.5$ cm. Work out the length of side $b$ , to 3 significant figures.

Medium

2 marks

ORIGINAL

A triangle has two sides of length 10 cm and 7 cm with an included angle of $68^\circ$ . Work out its area, to 3 significant figures.

Medium

2 marks

ORIGINAL

A sector of a circle has radius 12 cm and angle $30^\circ$ at the centre. Work out the exact arc length, then give it to 3 significant figures.

Hard

3 marks

ORIGINAL

Two solid cones are mathematically similar. The smaller has surface area $50\text{ cm}^2$ and volume $24\text{ cm}^3$ . The larger has surface area $200\text{ cm}^2$ . Work out the volume of the larger cone.

Medium

2 marks

ORIGINAL

In triangle $OAB$ , $\overrightarrow{OA} = \mathbf{a}$ and $\overrightarrow{OB} = \mathbf{b}$ . $M$ is the midpoint of $AB$ . Express $\overrightarrow{OM}$ in terms of $\mathbf{a}$ and $\mathbf{b}$ , simplified.

Questions are written in the style of past Edexcel papers (source shown on each) — never copied from them.

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Drill it properly

Circle Theorems

Each theorem with its reason, drilled until you name it automatically.

Formulae to Memorise

Sine rule, cosine rule, area and the exact trig values worth knowing cold.

GCSE maths flashcards

Theorem reasons and the rule-choosing decisions, as recall prompts.

Stuck on geometry (higher)?

Geometry is where reasoning marks are won or thrown away — I teach how to write the reason the mark scheme wants, and your first lesson is free.

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