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SELECTIVE SIXTH-FORM ENTRY

16+ Maths & Physics.
Make your thinking count.

One-to-one online tuition with Raphael, a Westminster alumnus with four A*s. Learn to choose an approach, apply the underlying ideas and explain your reasoning.

Book a free 15-min callSee exactly what’s included ↓
£75 / 60-minute session£300 / four sessions in total

THE SUBJECTS, THE REASONING, THE NEXT STEP

Preparation shaped
around your child.

Entrance assessments can ask pupils to use familiar ideas in unfamiliar ways. Lessons explore the reasoning behind a solution, alongside the subject knowledge needed to reach it.

  • Maths: algebra, geometry and problem-solving, matched to the relevant published assessment requirements.
  • Physics: applying concepts, interpreting information and explaining a chain of reasoning.
  • Subject interview practice: discussing an approach, responding to a prompt and checking an answer.

Schools assess different subjects and use different formats. On the parent call, we confirm the target school, planned subjects and where this tuition fits.

A focused diagnostic.

The first paid session lasts 60 minutes. I look at where your child gets stuck: knowledge, interpreting a question, choosing a method or checking the result. You receive a concise written summary of strengths, priority gaps and suggested practice. We use it to shape the next lesson; it is not a prediction of an admissions decision.

Continue if it helps.

The optional programme is four 60-minute sessions in total, including the diagnostic, for £300. It includes targeted practice, manageable homework and concise feedback. I model an approach, then reduce support as your child tackles related questions. Additional 60-minute sessions are £75 each, subject to availability.

There is no requirement to commit to the full programme before trying the diagnostic.

Read the Westminster preparation guide ↗

Try six worked Maths and Physics problems ↗

Explore academic interview preparation ↗

SEE THE THINKING

A question is a starting point.
The explanation is the lesson.

Explore a short example of how I would guide a pupil from a first attempt towards independent reasoning.

ORIGINAL MATHS EXAMPLE

The same perimeter.
The same area?

A rectangle has a perimeter of 24 cm. Could its area be greater than 36 cm²?

10 cm26 cm20 cm²36 cm²

Examples suggest an answer. How do we know it holds for every rectangle?

01 · Find a way into the problem

Ask: “What does the perimeter tell us about two adjacent sides?” They add to 12 cm. Calling one side x makes the other 12 − x.

That is the first useful move: translate the words into a relationship.

02 · Explain why the answer must hold

The area is x(12 − x) = 36 − (x − 6)².

A square cannot be negative, so the area cannot exceed 36 cm². Equality occurs at x = 6. We have moved from testing a few cases to explaining every case.

03 · Try a fresh question independently

Now change the perimeter to 28 cm. What is the greatest possible area? Can your child explain why, without following the previous working line by line?

Check: the sides add to 14; the area is 49 − (x − 7)², so the maximum is 49 cm².

What I’m looking for: choosing a representation, explaining a step and transferring the idea to a new question.

ORIGINAL PHYSICS EXAMPLE

Half below the water.
What can we infer?

A uniform solid block floats at rest with half its volume submerged. What does this tell us about its density?

A rule to use: upthrust equals the weight of the displaced water.

Assume still water and neglect surface tension and the upthrust from air.

01 · Start with the physical picture

Ask: “If the block is at rest, what must be true about the vertical forces?” Its weight is balanced by upthrust. Half the block’s volume displaces water.

02 · Connect the picture to an equation

For a block of volume V, its weight is ρblockVg. The displaced water weighs ρwater(V/2)g.

Equating these and cancelling Vg gives ρblock = ρwater/2: the block has half the density of the water.

03 · Change the situation and check

What if three quarters of the block were submerged? Its density would be three quarters of the water’s density.

Could a uniform solid block denser than water float this way? No: even complete submersion would not displace enough water to balance its weight under these assumptions.

What I’m looking for: using a supplied rule, balancing forces and checking whether the conclusion makes physical sense.

Illustrative teaching material, not an official entrance question, predicted exam content or a pupil result. Actual questions and the amount of guidance are matched to your child.

CHECKED 20 OCTOBER 2026

The current
assessment window.

These dates concern September 2027 entry. Always use the school’s own correspondence to confirm your child’s arrangements.

ST PAUL’S SCHOOL, LONDON · 16+

6 November 2026

Written examinations. Interviews: 21 November. The 30 September application deadline has passed.

Official assessment dates ↗
HARROW · 16+

7 or 14 November 2026

Standard-route shortlisted assessments; initial tests have already taken place. Harrow publishes a separate late-entry route.

Official routes and dates ↗

Current preparation is most relevant to pupils already registered or shortlisted for these assessments. Tuition cannot reopen an application or secure an offer.

WHAT USEFUL FEEDBACK LOOKS LIKE

Specific priorities.
Practical next steps.

The plan should make it easier to understand both the progress made and the work still to do.

ILLUSTRATIVE EXAMPLE11+ / 13+ MATHS

Your diagnostic summary.

A sample of the feedback format, not a real pupil’s results.

Starting point

Confident with whole-number calculations. Unsure how to organise the information in a multi-step word problem.

Priority

Draw or list the known information before choosing a calculation. Explain what the question is asking.

Next practice

Three word problems. For each: identify what is known, choose a representation, solve, then check the original conditions.

Review

Try a fresh question next lesson. Can the pupil choose a representation and explain it with fewer prompts?

Specific enough to guide practice. Clear enough to discuss together.

TALK DIRECTLY WITH YOUR CHILD’S TUTOR

Your free
15-minute parent call.

Tell me your child’s year group, target schools and next assessment. We’ll discuss where they need help and whether my tuition is a good fit.

  1. Choose a time

    Use the live calendar and check the time zone.

  2. Talk with Raphael

    Discuss priorities, lesson times and your questions on Google Meet.

  3. Decide on the next step

    If it fits, arrange one paid diagnostic. There is no obligation to continue.

For parents and guardians. No payment is taken for this call. School reports are not needed.

FREE PARENT CALL WITH RAPHAEL

A clear place
to start.

15 minutesGoogle Meet£0
Choose a time on Calendly

Opens Calendly. Your call is booked once you complete its confirmation.

What should I share when booking?

Your child’s year group, target schools and main concern are enough. Add an assessment date if you know it, using Calendly’s optional preparation box.

If you choose a first lesson

60 minutes with a diagnostic, written priorities and follow-up practice.

11+ / 13+ £6516+ £75

No compulsory package. Terms agreed before payment.

How your information is handled

Talk with Raphael15 minutes · FreeBook free call