lab451.0

Exams

Interview

PricingArchiveAbout
lab451.0
Everything you need. All at once.

Designed to lift You upPrepare with lab45

From real-style mocks to syllabus-aligned drills, lab45 gives you the tools Oxbridge admits wish they had.

Your edge starts here.

See how Review, Drill, Library, and My Exams work together — real-style ESAT mocks, diagnostics, saved questions, and the sets you own.

✦ THE LAB45 STANDARD

Built for the Exam That Matters Most.

Every mock, every question, every difficulty calibration traces back to what the real ESAT actually demands. Nothing here exists because it was convenient to make.

Mocks Engineered From the Source

Built from live ESAT data, calibrated to the current syllabus and weighted to real difficulty distributions. No recycled legacy material, no guesswork on what the exam actually demands.

Mocks Engineered From the Source

One Hub for Every Attempt

Scores, trends, weak-topic drill, saved questions — one place. Every mock feeds the same workflow.

One Hub for Every Attempt

Built by People Who Cracked It

Written by the founders — Oxbridge students and Olympiad medalists who sat these exact exams. Every explanation teaches the reasoning pattern behind the question, so the next variant is never a surprise.

ESAT Score9.0

No Surprises on Exam Day

The interface mirrors the real ESAT. On test day, the only unfamiliar thing is your seat number.

No Surprises on Exam Day

⬡ Dashboard

Know exactly where you stand.

Review, Stories, Library, and Drill share one hub — every mock you finish updates the same place so you always know what to do next.

Question by question.

Every question you attempted, with the correct answer, explanation, and a save button if it's worth revisiting.

lab45.app/dashboard
/ESAT · Set 2 · Math 2 · Q5
Q5Math 2 · Set 2
Evaluate ∫0π/4sin⁡(2x) dx\int_{0}^{\pi/4} \sin(2x)\, dx∫0π/4​sin(2x)dx.
A
12\frac{1}{2}21​
B
22\frac{\sqrt{2}}{2}22​​
C
12\frac{1}{\sqrt{2}}2​1​
D
111
NotesSoon

Solution

To evaluate ∫0π/4sin⁡(2x) dx\int_{0}^{\pi/4} \sin(2x)\,dx∫0π/4​sin(2x)dx:

∫sin⁡(2x) dx=−12cos⁡(2x)+C\int \sin(2x)\,dx = -\frac{1}{2}\cos(2x) + C∫sin(2x)dx=−21​cos(2x)+C


Applying the limits:
[−12cos⁡(2x)]0π/4=−12cos⁡ ⁣(π2)+12cos⁡(0)=0+12=12\left[-\frac{1}{2}\cos(2x)\right]_{0}^{\pi/4} = -\frac{1}{2}\cos\!\left(\frac{\pi}{2}\right) + \frac{1}{2}\cos(0) = 0 + \frac{1}{2} = \frac{1}{2}[−21​cos(2x)]0π/4​=−21​cos(2π​)+21​cos(0)=0+21​=21​
✦ WHO LAB45 IS FOR

For Students Who Won't
Leave It to Chance.

ESAT Candidates

Preparing for Engineering, Natural Sciences, or Mathematics at Cambridge or Imperial — with mocks and a dashboard hub built around the live exam.

Physics study cover artwork

TMUA Candidates

Planning for Oxford, Warwick, or LSE? TMUA is on our roadmap; today the platform is ESAT-first, with the same quality bar as we expand.

Mathematics study cover artwork

Interview Candidates

STEM interview practice for Oxford and Cambridge is coming soon — quantitative reasoning that matches how those interviews really probe you.

Interview preparation cover artwork

Independent Learners

No tutor, no class — just mocks, drills, and a hub that shows where you stand: Review, Drill, Library, and My Exams in one signed-in workflow.

Independent study cover artwork

Second Attempt

You've sat it once. Now you know where it caught you out. Lab45 helps you fix the exact gaps that cost you last time.

Arrow cover artwork

ESAT Candidates

Preparing for Engineering, Natural Sciences, or Mathematics at Cambridge or Imperial — with mocks and a dashboard hub built around the live exam.

Physics study cover artwork

TMUA Candidates

Planning for Oxford, Warwick, or LSE? TMUA is on our roadmap; today the platform is ESAT-first, with the same quality bar as we expand.

Mathematics study cover artwork

Interview Candidates

STEM interview practice for Oxford and Cambridge is coming soon — quantitative reasoning that matches how those interviews really probe you.

Interview preparation cover artwork

Independent Learners

No tutor, no class — just mocks, drills, and a hub that shows where you stand: Review, Drill, Library, and My Exams in one signed-in workflow.

Independent study cover artwork

Second Attempt

You've sat it once. Now you know where it caught you out. Lab45 helps you fix the exact gaps that cost you last time.

Arrow cover artwork
✦ ARCHIVE

The notes behind
better preparation.

View all posts
⬡ All Pass

Unlock everything
Lab45 ships for ESAT.

One purchase covers every mock at bundle pricing, plus full access to our upcoming course, Library, and weak-topic drill as they launch — no second invoice when the platform grows.

Get All Pass
Lab45
All Pass
Mocks · Course · Library & drill
Best value

Every mock, one tier

All eight full-length ESAT mocks at bundle pricing — timed, exam-accurate, and cheaper than buying set by set.

Structured course access

Full access to our upcoming ESAT prep course the moment it goes live — same membership, no second purchase.

Library & drills included

Full access to Library (saved questions, filters) and topic drill as they roll out — built for how you revisit ESAT-level work.

Everything we ship

All Pass is the single unlock for Lab45 ESAT prep: mocks, dashboard hub, and every major feature we add on this track.

For Schools & Institutions

Bring the best ESAT prep to your school.

Give your students the same tools top candidates use — full mock sets, deep analytics, and a dedicated school dashboard — all under one licence.

Get in touch

FAQ

Common questions.

lab45

ESAT mocks and a dashboard hub — Review, Drill, Library, and My Exams.

Instagram @lab45.appYouTube @lab45appTikTok @lab45.appEmail lab45edu@gmail.com

Exams

  • ESAT Preparation
  • Mock Exams
  • Pricing
  • ESAT Courses

Resources

  • About
  • Archive
  • For Schools

Legal

  • Terms
  • Privacy Policy
  • Refund Policy
© 2026 lab45. Built by Oxbridge graduates for future Oxbridge graduates.
Designed and Developed by Yejun