Figure Maths

GCSE & A-level maths revision. free lessons, real mark schemes, timed mock papers.

[Figure Maths @FigureMaths]

№ 001 — have a go before you scroll. Worked solution in the reply.

[Figure Maths @FigureMaths]

The answer is 4.

Raise 2 to the whole product and each log lifts it by exactly one integer: 3 → 4 → 5 → … → 16.

So 2^P = 16, and P = 4.

The 14 is bait — that is just how many logs there are. № 010

[Figure Maths @FigureMaths]

Fourteen logs. No calculator. The answer is one digit. № 010

[Figure Maths @FigureMaths]

∛3 — about 1.442.

Not 3: that is 3^27, about 7.6 trillion. The trick is the exponent, not the base. If x³ = 3, the whole tower collapses to x³ = 3.

If you said 3, the base got you.

More like this: https://t.co/H2BEnUeTAQ

[Figure Maths @FigureMaths]

Looks impossible. It isn't. What is x? № 009

[Figure Maths @FigureMaths]

123.

Square: x² + 1/x² = 7. Cube: x³ + 1/x³ = 18. Multiply those and you get x⁵ + 1/x⁵ — plus an unwanted x + 1/x. So 7 × 18 − 3.

If you said 126, the cross terms got you.

More like this: https://t.co/H2BEnUeTAQ

[Figure Maths @FigureMaths]

You never need to know x. № 008

[Figure Maths @FigureMaths]

If you have a Year 11 starting this week: the maths year is shorter than it looks. Mocks in November, real papers in May. Roughly 30 teaching weeks between them, minus holidays.

The students who cope best build a small weekly revision habit now, not at Easter.

[Figure Maths @FigureMaths]

Three. x = 2, x = 4 — and one more near x = −0.77.

For negative x, 2^x is tiny but still positive, and x² comes back down to meet it: sign change between −1 and 0.

If you said two, you stopped at the easy pair.

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[Figure Maths @FigureMaths]

How many solutions does this equation have?

Nearly everyone misses one.

№ 007

[Figure Maths @FigureMaths]

How many solutions does this equation have?

Nearly everyone misses one.

№ 007

[Figure Maths @FigureMaths]

x = 2, 3, 4, 5, 6, 7 — six of them, consecutive.

Base 1: x = 2, 5. Base -1 with an even power: x = 3, 4. Power 0, base non-zero: x = 6, 7.

If you found two, you solved the base and stopped.

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[Figure Maths @FigureMaths]

How many integers x make this true?

Take your time — almost nobody gets them all.

№ 006

[Figure Maths @FigureMaths]

@purtle_ja Both right — there are more.

[Figure Maths @FigureMaths]

This June, a grade 4 in Edexcel GCSE Maths (Higher tier) needed 50 marks out of 240. That's 21%.

Not because students got worse — the papers are genuinely hard, and boundaries move to match.

Every board's 2026 boundaries: https://t.co/ByQ0hrcdR0

[Figure Maths @FigureMaths]

x = 72°.

If you said 90°, you trusted your eyes — nothing in a regular pentagon makes those diagonals perpendicular.

Isosceles triangles: each diagonal makes 36° with the sides. Exterior angle: 36° + 36°.

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[Figure Maths @FigureMaths]

No numbers given. None needed. What is x?

№ 005

[Figure Maths @FigureMaths]

x = 32°.

Angle at the centre is twice the angle at the circumference: AOB = 2 × 58° = 116°. OA and OB are radii, so triangle OAB is isosceles: x = (180° − 116°) ÷ 2 = 32°.

If you said 58°, you assumed OAB = ACB — that's the trap.

More like this: https://t.co/H2BEnUeTAQ

[Figure Maths @FigureMaths]

Most people get this wrong. What is x?

№ 004

[Figure Maths @FigureMaths]

The trap: multiplying by 2x only. The inside derivative is the WHOLE bracket — every term differentiates, so it's ×(2x + 3). Full working below.

More questions like this: https://t.co/H2BEnUeTAQ

[Figure Maths @FigureMaths]

№ 003 — have a go before you scroll. Worked solution in the reply.