ESAT Specification: Every Module and Topic, with Examples

The ESAT specification is UAT-UK's list of every topic the Engineering and Science Admissions Test can examine, organised into five modules: Mathematics 1, Mathematics 2, Physics, Chemistry and Biology. Most courses that use the ESAT require Mathematics 1 and two further modules, and every module assumes the content of Mathematics 1. Below is a summary of the topics in each module, with notes on what the specification leaves out, an original example question for each module and a way to turn the specification into a revision plan.

How the ESAT is structured

Each module has 27 multiple-choice questions in 40 minutes and is timed separately, so time left over at the end of one module does not carry into the next. The test is taken on computer with an erasable booklet for working, and calculators are not allowed. Each correct answer scores one mark, with no marks deducted for wrong answers, and each module is reported separately on a scale from 1 to 9.

Students choose their modules when they book and cannot change them afterwards without cancelling and rebooking. Which courses require which modules is covered in the ESAT guide.

The five modules and their topics

The specification, published as the ESAT Content Specification, labels its topics M for Mathematics 1, MM for Mathematics 2, P for Physics, C for Chemistry and B for Biology.

Throughout every module, students are expected to know the SI unit for each quantity mentioned and the standard prefixes from nano to giga, and to be comfortable with negative indices in units, such as m s⁻¹ for velocity.

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What the specification leaves out

The specification is precise about some exclusions, and knowing them saves revision time:

• Mathematics 1: candidates are not expected to recall or use the sine or cosine rules, and formal set theory notation is not required for probability, although Venn diagrams and tree diagrams are.
• Mathematics 2: differentiation from first principles is excluded, points of inflexion are not examined, and no question needs the change of base formula for logarithms.
• Chemistry: in organic chemistry, reaction mechanisms and carbocation stability are not required.

Students should read the full wording of each topic, since the line between what is included and what is left out is often drawn within a topic. For example, MM1 includes the Factor Theorem and the Remainder Theorem and algebraic division by linear and quadratic expressions.

Original example questions for each module

The questions below were written for this guide in the style of the ESAT. Each is answerable without a calculator in about 90 seconds, which is the average time available per question.

Mathematics 1: ratio and algebra

"

The ratio of boys to girls in a club is 3 : 5. After 6 more boys join, the ratio becomes 3 : 4. How many girls are in the club?
A. 24 B. 32 C. 40 D. 45 E. 48

The answer is C. Writing the numbers as 3k boys and 5k girls, the new ratio gives (3k + 6) ÷ 5k = 3 ÷ 4, so 12k + 24 = 15k and k = 8. There are 5 × 8 = 40 girls.

Mathematics 2: differentiation

"

The curve y = x³ − 6x² + 9x + 2 has two stationary points. What is the distance between them?
A. 2 B. 4 C. 2√5 D. 2√13 E. 6

The answer is C. The derivative is 3x² − 12x + 9 = 3(x − 1)(x − 3), so the stationary points are at x = 1 and x = 3, giving the points (1, 6) and (3, 2). The distance between them is √(2² + 4²) = √20 = 2√5.

Physics: electricity

"

A 6 Ω resistor and a 3 Ω resistor are connected in parallel, and this combination is connected in series with a 4 Ω resistor across a 12 V supply of negligible internal resistance. What is the current in the 3 Ω resistor?
A. 2/3 A B. 1 A C. 4/3 A D. 2 A E. 3 A

The answer is C. The parallel pair has a resistance of (6 × 3) ÷ (6 + 3) = 2 Ω, so the total is 6 Ω and the supply current is 2 A. The potential difference across the parallel pair is 2 A × 2 Ω = 4 V, so the current in the 3 Ω resistor is 4/3 A. Option D is the supply current, a common slip.

Chemistry: quantitative chemistry

"

Magnesium burns completely in oxygen to form magnesium oxide. What mass of magnesium oxide forms from 6.0 g of magnesium? (Relative atomic masses: Mg = 24, O = 16)
A. 4.0 g B. 8.0 g C. 10 g D. 12 g E. 20 g

The answer is C. The equation is 2Mg + O₂ → 2MgO, so each mole of magnesium gives one mole of magnesium oxide. 6.0 g of magnesium is 0.25 mol, which gives 0.25 mol of MgO with a molar mass of 40 g mol⁻¹, so 10 g.

Biology: inheritance

"

In a species of plant, the allele for tall stems (T) is dominant to the allele for short stems (t). A heterozygous tall plant is crossed with a short plant, and 120 seeds from the cross are grown. About how many of the plants would be expected to be heterozygous?
A. 0 B. 30 C. 60 D. 90 E. 120

The answer is C. The cross is Tt × tt, so half of the offspring are expected to be Tt and half tt. Half of 120 is 60. Option B comes from treating the cross as Tt × Tt and taking the Tt share as a quarter, when in that cross it would be a half.

Turning the specification into a revision plan

The specification works best as a checklist. A simple method is to go through every numbered topic in the modules being sat and mark each one in three ways: secure, covered at school but rusty, or not yet covered. The third group needs teaching or self-study first, and the second group needs practice questions.

UAT-UK publishes an ESAT Guide for each module, with explanations and worked examples, and the Mathematics 2 notes are shared with the TMUA. The ESAT past papers page explains which parts of the old ENGAA and NSAA papers match each module, and the ESAT preparation plan sets out the weeks before the test.

Related guides

• ESAT guide: modules, scoring and which courses require it
• ESAT past papers
• ESAT scores and results
• TMUA specification
• Oxford physics entry requirements
• University admissions tests in the UK: which test for which course
• Super-curricular activities for engineering

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