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Paper 2 · Q7GraphsQuadraticsTrig: find x

Find x. Give your answer to 3 significant figures.

35°10 cmxsin 35° = x10x = 10 × sin 35°x = 10 × 0.819x = 8.19 cmthat's cos 35°!x = 10 × 0.574 = 5.74 cm

Solve 2x² + 5x − 3 = 0 by factorising.

2x² + 5x − 3 = 0(2x  )(x  ) = 0 ??× to make −6, + to make 56 and −12x² + 6x − x − 3 = 02x(x + 3) − 1(x + 3) = 0(2x − 1)(x + 3) = 0x = ½ or x = −3

Sketch y = 2 sin x + 1 for 0° ≤ x ≤ 360°.

sin x = −½ ⇒ x = 210°, 330°

7The curve C has equation y = x³ − 6x² + 9x + 2

(a) Find dy/dx.[2 marks]

(b) Find the coordinates of the stationary points of C.[4 marks]

dy/dx = 3x² − 12x + 93x² − 12x + 9 = 0x² − 4x + 3 = 0(x − 1)(x − 3) = 0 ⇒ x = 1, x = 3x = 1: y = 1 − 6 + 9 + 2 = 6x = 3: y = 27 − 54 + 27 + 2 = 4(1, 6) and (3, 4)M1 A1M1 A1A1A0recheck: this is 2
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A tutor that works on your page, not in a chat box

Drop in a screenshot of the question, or handwrite it straight onto the canvas. Every time you ask, the tutor looks at your whole board, handwriting and all, so it always knows exactly where you're up to.

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Circles, ticks, arrows and whole diagrams, drawn on like a pen right next to your working. Tap a mark in the chat and the board jumps straight to it.

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Pythagoras Vectors

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Simultaneous equations Trig: find x
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Nearly there. Look at the last line: if 4 − 2y = 0, is y positive or negative?
Ticks Circled −2 Note

Diagrams, drawn exactly

Ask for a triangle, a graph or a bearing and the tutor draws it from the maths, so every length, angle and curve is where it should be.

Cosine rule Bearings
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Cosine rulex² = 12² + 9² − 2(12)(9) cos 58°

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Drop in a PDF and work straight on the page. The tutor marks it the way an examiner would, method marks and all, and shows you where the missing marks went.

Paper 1 · Q4 Paper 1 · Q3
Paper 1 done!
Redo 4(b) tomorrow
2/3

Hints first, answers last

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Straight lines Quadratics
I'm stuck

No problem. Start with what you know: how far does the line go up from A to B?

8 up, and 4 across?

Exactly. So the gradient is up ÷ across. What do you get?

Check my work Give me a hint I'm stuck

The little things that add up

Solve 2sin²x + 3cos x = 3 for 0° ≤ x < 360°.

2(1 − cos²x) + 3cos x = 32cos²x − 3cos x + 1 = 0(2cos x − 1)(cos x − 1) = 0x = 60°, 0°
Looking at your board
Used sin²x = 1 − cos²x Factorised the quadratic cos x = ½ also gives 300°

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One tap and the tutor scans everything on your board, then tells you what's right, where it slipped and why, step by step. It streams in as it writes, so you're never left waiting.

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7 Solve 3(x − 4) = 2x + 5

8 Solve 5(2x + 1) = 3x − 9

3x − 12 = 2x + 5x = 17
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Take a photo of a textbook or worksheet, or drop or paste one in, and it lands right on your board. Work underneath it and the tutor reads both.

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add the heightAdded it to the same diagram

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Say "add the height" or "label the angles" and the tutor updates the diagram it already drew, in the same spot, instead of starting a new one.

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Why not just use a chatbot?

It does everything a chatbot can. Then it works through the maths with you, on your page.

ChatbotPrivate tutorletsMath
Your workingCan't see it. You upload it and explain the problem, exam board and syllabus every timeOnly sees it in your booked hour The AI tutor sees your canvas, all the time
FeedbackA paragraph you have to match back to your working line by lineMistakes wait until your next session Ticks, crosses and notes on the exact line, as you work
Past papersWork on paper, then type or upload answers to get feedbackMarking either uses up your paid hour or waits until next session Write straight on the PDF and get detailed marking on the paper itself
DiagramsGenerated in the chat, so you scroll back up to find them while you workSketched on paper, gone when the session ends Drawn on your board beside your working, and edited in place when you ask
AnswersOften hands you the full solution, so you copy instead of learnDepends on the tutor, and only while they're there Teaches you when you're stuck, or shows a fully laid-out solution if you want one
AvailabilityAny timeLimited slots, booked in advance Any time
CostAbout $25/month for a paid plan, and it still can't see your pageAbout £25-£55 an hourFrom about £10/month, with a generous free tier and a free week of full access
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Everything students and parents ask us before they start.

Does it just give my child the answers?

No. The tutor starts with a hint and only goes further when the student asks. Its job is to find the step that went wrong and help them fix it, so the method is still there in the exam.

What maths does it cover?

GCSE and A-level maths: algebra, trigonometry, graphs, calculus, vectors, probability and the rest. If you can write it on paper, you can write it on the board.

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No. It works in the browser with a mouse, a trackpad or a finger. A tablet and stylus feels most like paper, so that's what we'd recommend if you have one.

How is this different from asking a chatbot?

You don't type maths. You write your working the way you would on paper, and the tutor reads your handwriting, then circles, ticks and draws on the board itself. It answers with hints rather than a finished solution.

Can I use my own past papers?

Yes. Drop a PDF onto the board and work straight on the page. The tutor marks it the way an examiner would, method marks and all.

What happens when my weekly time runs out?

The question you're on always finishes, even if it takes you slightly over. You'll get a warning at 80%, and the allowance resets every week.

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