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ESAT Paper 4 Worked Solutions: The Final Check
Keep Paper 4 for the last week before the test: sit it under exam conditions, then move on to full timed papers of 27 questions a module.
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This is a sample: five questions of each module, and a full module runs to 27, written for one school at a time. Full timed papers, 27 questions a module, are in ESAT practice, free to start.
Available Subject Modules
Select a module below to view step-by-step worked solutions and timing benchmarks:
Mathematics
Surds, similar shapes and scale factors, parallel and perpendicular lines, completing the square, and the reciprocal graph. 5 questions, worked in full.
Difficulty: ★★★☆☆ Time: 7 min 24 s
Advanced Mathematics
Indices, surds, the discriminant, where a line meets a curve, and sequences from a recurrence. 5 questions, worked in full.
Difficulty: ★★★☆☆ Time: 7 min 24 s
Physics
A circuit with diodes, the force on a current in a magnetic field, average speed, weight and drag, and wave terms. 5 questions, worked in full.
Difficulty: ★★☆☆☆ Time: 7 min 24 s
Chemistry
Protons, neutrons and electrons, atomic and mass number, the rate of a reaction, and calorimetry. 5 questions, worked in full.
Difficulty: ★★★☆☆ Time: 7 min 24 s
Biology
The cell cycle, aerobic and anaerobic respiration, and the motor neurones that drive breathing. 5 questions, worked in full.
Difficulty: ★★★☆☆ Time: 7 min 24 s
How to use Paper 4
The final check. Sit it under exam conditions in the last week before the test.
More
Sit the modules you are taking back to back, with no notes, and read the worked solutions only after the last one. Then set each answer against your Paper 1 baseline, question by question, to see what your preparation has fixed and what needs a last look.
Every one of the 25 questions published here carries a full worked solution: five from each of the five modules. The rest of each module is written for one school at a time and is not published, which is what makes a commissioned pack worth commissioning.
If you want practice with no gaps in it at all, the practice questions by topic are complete throughout. Why we publish the gap rather than quietly close it is explained in our Quality Assurance standards.
Where to go next
- Still losing marks on one skill after Paper 4? Book a lesson on exactly that skill: 1-to-1 ESAT tutoring.
- Sit a full module against the clock: ESAT practice has full timed papers, 27 questions a module, free to start.
- Recognise the method before you calculate: our ESAT methods.
- Check what is actually examinable: the specification tables count every assessable sub-topic from the official document.
- Revise formulas and exam tactics: the ESAT Essentials guide.
- Work one topic at a time: practice by topic files every question under the specification topic and skill it tests.
- Teaching a cohort rather than sitting the test? ESAT mock papers for schools carry all 27 questions in every module, with worked solutions and mark schemes, and each pack is written for one school and issued to no other.
For individual preparation. The free question sets on this site are for a candidate working on their own. They are not licensed for a school, college or tutoring provider to print and run with a class, to republish or resell, or to fold into a course sold by another provider. A school sitting a timed mock with a class needs a paper written for its own candidates and used nowhere else: a commissioned pack, which comes with mark schemes and a syllabus reference.