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ESAT Mathematics & Physics · Distractor guide

Seven of the eight answers are built from a mistake.

We took apart every maths and physics question from the eight ENGAA papers (2016–2023) that sit inside the current ESAT specification: 273 questions and 1,484 wrong options. Each wrong option was traced back to the mistake that produces it. This guide turns those mistakes into short routines you can run under exam conditions.

ENGAA 2021 · Q2 Air is compressed at constant temperature until its pressure rises by 20%. New density?
A0.69ρUpside down
B0.80ρUpside down
C0.83ρUpside down
D1.00ρMisconception
E1.20ρanswer
F1.44ρPower slip

76% of wrong options trace to a named mistake45% are execution slips on a correct plan31% answer a different question0.9% are plain arithmetic slips

Where the wrong answers come from

Every wrong option in the set was classified by the mistake that reproduces it. 1,122 of the 1,484 wrong options could be reproduced by a specific mistake; the rest are fillers with no systematic route. The chart counts each traced option once, by its main mistake.

Reading31%The working is right, but for a different question or with a condition dropped.
Answered a different question13.2%
Stopped early8.9%
Ignored a condition4.3%
Misread the graph2.6%
Misjudged a statement2.0%
Model20%The wrong formula or physical idea is chosen before any calculation starts.
Wrong formula or wrong situation11.9%
Misconception8.0%
Execution45%The plan is right, then a systematic slip: a sign, a reciprocal, a power, a factor.
Sign or direction flip12.2%
Upside down9.2%
Power slip8.7%
Lost or extra factor8.1%
Algebra slip6.9%
Bookkeeping4%Units, prefixes and plain arithmetic.
Units or powers of ten3.0%
Arithmetic slip0.9%

Most traps are slips on the right plan

45% of traced options come from a sign, a reciprocal, a power or a lost factor. The student knew what to do. These are the easiest marks to protect, because the Outline step catches most of them before you calculate.

A third answer a different question

34% of questions include an option that answers a different question, and 27% include a value you pass through on the way. Your working can be flawless and still land on one of these.

Matching an option proves nothing

Only 0.9% of distractors are arithmetic slips. Examiners build the wrong options from systematic mistakes, so they are designed to be matched. If your answer matches none of the options, check your arithmetic first.

Eight options usually means three decisions

26% of traced options stack two or more mistakes. Wrong options are often combinations: sign × factor × formula. Settle each decision separately and every decision removes half of what is left.

Reading the grid

Three real questions whose options are built from independent yes/no decisions. Scan the options first, name the decisions, then settle them one at a time.

ENGAA 2020 · Q15Maths · Trigonometry · Expressions

Triangle PQR with altitude QS onto PR; PS = x, PQ = y, QR = z, angle QRS = 61°. Express z.

  1. A√(y²+x²)·sin61
  2. B√(y²−x²)·sin61
  3. C√(y²+x²)·cos61
  4. D√(y²−x²)·cos61
  5. E√(y²+x²)/sin61
  6. F√(y²−x²)/sin61
  7. G√(y²+x²)/cos61
  8. H√(y²−x²)/cos61
ENGAA 2020 · Q8Physics · Electromagnetism & transformers · Statements

A 20 cm rod (weight 0.40 N) lies across rails 12 cm apart in a 0.50 T field into the page; a 2.4 A current flows. Find the initial acceleration and its direction (diagram: + terminal on the upper rail).

  1. A0.36 left
  2. B0.36 right
  3. C0.60 left
  4. D0.60 right
  5. E3.6 left
  6. F3.6 right
  7. G6.0 left
  8. H6.0 right
ENGAA 2020 · Q33Maths · Differentiation · Solution sets

Find all p for which y = x³ + 3√5·p·x² + 3px + 13 has two distinct turning points.

  1. Ap<0 or p>0.2
  2. Bp≤0 or p≥0.2
  3. C0<p<0.2
  4. D0≤p≤0.2
  5. Ep<0 or p>1.2
  6. Fp≤0 or p≥1.2
  7. G0<p<1.2
  8. H0≤p≤1.2

SPOTS: the routine for every question

Five steps, in this order, on every question. The first three take well under a minute and usually remove most of the options before any real calculation. Each step targets particular mistakes; the figure shows what share of traced wrong options those mistakes produce.

  1. Scan the options 10 s

    Before solving, read the options as data. Ask what changes from one option to the next: a sign, a factor of 2, a power of ten, sin or cos, < or >. Each thing that changes is a decision you will have to get right. Eight options usually means three yes/no decisions (2 × 2 × 2).

    Exposes the grid behind the 26% of wrong options that stack more than one mistake.

  2. Pin the ask 10 s

    Underline the exact quantity asked for, its unit and every condition word: total, each, change, wasted, distinct, NOT, without replacement, greatest. Then list the values you will pass through on the way. Any option equal to one of those stage values is a trap for students who stop early.

    Catches 31% of traced wrong options: Different questionStopped earlyIgnored a conditionGraph misreadStatement misjudged

  3. Outline the answer 15 s

    Predict before you calculate: the sign, the rough size (order of magnitude), whether it is bigger or smaller than a value you were given, and what it must contain (a √3? f in the denominator?). Every option that breaks the outline is gone without full working.

    Catches 33% of traced wrong options: Sign flipUpside downPower slipUnits

  4. Trap-aware solve most of the time

    Solve by the shortest route. At each step where a named slip is possible (squaring, taking reciprocals, a ½ or a 2, converting units, choosing a formula), stop and check it on purpose. The topic playbooks below list the slips each topic is built on.

    Catches 35% of traced wrong options: Wrong formulaMisconceptionFactor slipAlgebra slip

  5. Stress-test the survivor 15 s

    Substitute a simple value, check a limiting case, or check the units. Matching an option proves little, because most wrong options are built to be matched. If your answer matches no option, look for an arithmetic slip first: examiners almost never build distractors from them.

    Catches 0.9% of traced wrong options: Arithmetic

Algorithms by answer format

The shape of the option set decides the fastest way to strike options. Recognise the format while you Scan, then run its algorithm.

Numbers · 158 questions

Magnitude ladder

Looks like: Eight numbers, often with units: 0.160 J … 864 000 J.

  1. Sort the options and look for families: values ×10 or ×1000 apart (units trap), ×2 or ½ apart (factor trap), a value and its square or root (power trap), reciprocals (upside-down trap).
  2. Estimate the order of magnitude with rounded numbers. Strike every option in the wrong decade.
  3. Pin the ask: of the stage values you pass through (before, after, useful, wasted, one object, both objects), which is the final one? Strike the other stage values.
  4. Inside the surviving family, settle the remaining factor (½, 2, π, g) with the exact formula.
  5. Check bounds: a loss is less than the input, a share is less than the total, efficiency is below 100%.
ENGAA 2022 · Q8Physics · Energy, work & power · Numbers

A motor takes 0.800 kW at 60% efficiency for half an hour. Find the energy wasted.

  1. A0.160 J
  2. B0.240 J
  3. C160 J
  4. D240 J
  5. E576 J
  6. F864 J
  7. G576 000 J
  8. H864 000 J
ENGAA 2023 · Q4Physics · Electric circuits · Numbers

All three resistors in the circuit are identical. A battery drives a branch containing an ammeter and one resistor. A switch connects a second branch in parallel, made of the other two resistors in series. With the switch open the ammeter reads 1.0 A and the battery supplies 1.0 W. Find the ammeter reading and the battery's power output once the switch is closed.

  1. A0.67 A, 0.67 W
  2. B0.67 A, 1.3 W
  3. C0.67 A, 1.5 W
  4. D0.67 A, 2.0 W
  5. E1.0 A, 1.0 W
  6. F1.0 A, 1.5 W
  7. G1.0 A, 2.0 W
  8. H1.0 A, 3.0 W

Playbooks by topic

Each topic leans on its own few mistakes. Learn the traps for the topic, and use the matching checks during the Trap-aware solve step.

Maths
Physics

Maths · 22 questions

Indices, surds and logarithms

Traps to expect

  • Squaring a bracket term by term: (a − b)² written as a² − b², losing the cross term 2ab.
  • Applying a power to something outside the bracket, or adding exponents where they should be multiplied.
  • Log laws turned into the wrong operation: log A − log B = 2 read as A − B = 9 instead of A ÷ B = 9; log₂3 confused with log₃2.
  • (log x²)² treated as 2(log x)² instead of 4(log x)².

Checks that strike them

  • Rewrite every term as a power of the same prime and add exponents base by base.
  • Evaluate options roughly (√2 ≈ 1.41, √3 ≈ 1.73). The sign and size of the answer kill most surd distractors.
  • Put n = 0 or n = 1 into index expressions and compare with the options.
  • Before simplifying a squared or cubed bracket, count its cross terms.
ENGAA 2016 · Q3Maths · Indices & surds · Expressions

Expand and simplify (√3 - √2)^2.

  1. A1-2sqrt3sqrt2
  2. B5-2sqrt2sqrt3
  3. C2sqrt3-2sqrt2
  4. D1
  5. E5-√2sqrt3
  6. F13-2sqrt2sqrt3
  7. G5+2sqrt2sqrt3
  8. H5
ENGAA 2022 · Q1Maths · Indices & surds · Expressions

Simplify y multiplied by the square of (3 x^(1/2) z / y³).

  1. A3xz²/y⁴
  2. B3xz²/y⁵
  3. C9x^(1/2)z²/y⁵
  4. D9xz²/y⁴
  5. E9xz²/y⁵
  6. F9x^(5/2)z²/y⁵

Distractor atlas

All 273 in-specification questions with every wrong option explained. Filter by mistake type to practise spotting one trap at a time. Detective mode hides the explanations until you click an option. Questions are paraphrased; open the official paper for the full wording and diagrams.

273 questions

  • ENGAA 2016 · Q1Maths · Equations & inequalities · Solution sets

    Solve the linear inequality -8 < 6 - x/2 for x.

    1. Ax<4Sign flipmoved 6 across with the wrong sign: x/2 < 8-6 = 2, x<4
    2. Bx>4Sign flipSign flipx<4 route plus flipped inequality
    3. Cx<20Algebra slipdoubled 6 but not -8 when clearing the fraction: -8<12-x gives x<20
    4. Dx>20Algebra slipSign flipx<20 route with inequality reversed
    5. Ex<22Algebra slipdoubled -8 but not 6: -16<6-x gives x<22
    6. Fx>22Algebra slipSign flipx<22 route with inequality reversed
    7. Gx<28Answer
    8. Hx>28Sign flipreversed the inequality when dealing with -x/2 (either flipped unnecessarily or twice)
  • ENGAA 2016 · Q2Physics · Radioactivity & nuclear · Qualitative

    Pb-214 (Z=82) decays to Pb-210 (Z=82); which set of alpha/beta emissions achieves this?

    1. A3 alphaMisconceptionwrong alpha bookkeeping: 3 alpha removes 12 nucleons and 6 protons (gives 202/76)
    2. B2 alpha + 1 betaMisconception2 alpha removes 8 nucleons (A=206) and Z ends at 79
    3. C2 alpha + 2 betaMisconceptionStopped earlybalances Z (82) but mass number becomes 206; only checked the proton number
    4. D1 alpha + 2 betaAnswer
    5. E3 betaMisconceptionunclearthinks beta reduces mass number; 3 beta leaves A=214 and raises Z to 85
  • ENGAA 2016 · Q3Maths · Indices & surds · Expressions

    Expand and simplify (√3 - √2)^2.

    1. A1-2sqrt3sqrt2Sign fliptook 3 - 2 = 1 for the squared terms (subtracted b²)
    2. B5-2sqrt2sqrt3Answer
    3. C2sqrt3-2sqrt2Power slipdoubled each term instead of squaring
    4. D1Algebra slip(a-b)² = a² - b² = 3-2
    5. E5-√2sqrt3Factor slipdropped the 2 in the cross term 2ab
    6. F13-2sqrt2sqrt3Power slipsquared 3 and 2 (9+4=13) instead of the surds
    7. G5+2sqrt2sqrt3Sign flipcross term with + instead of -
    8. H5Algebra slip(a-b)² = a² + b², cross term omitted
  • ENGAA 2016 · Q4Physics · Energy, work & power · Statements

    A straight line through the origin with gradient 5 (y=10 at x=2, SI units). Which two of four described relationships (KE vs v in free fall for 10 kg; PE vs height for 20 kg; v vs t for 20 kg under 100 N; work vs distance for a 5 N force at constant speed) could it show?

    1. A1 and 2Statement misjudgedMisconceptionaccepts 1 (KE vs v is a parabola, not linear) and 2 (gradient mg = 200, not 5)
    2. B1 and 3Statement misjudgedMisconceptionaccepts 1 (thinks KE ∝ v); rejects 4
    3. C1 and 4Statement misjudgedMisconceptionaccepts 1; rejects 3
    4. D2 and 3Statement misjudgedFactor slipaccepts 2 (linear but gradient 200, ignoring the numbers) and rejects 4
    5. E2 and 4Statement misjudgedFactor slipaccepts 2 by checking shape only, not gradient; rejects 3
    6. F3 and 4Answer
  • ENGAA 2016 · Q5Maths · Ratio, proportion & percentages · Ratio / scaling

    Given Q:R = 5:2 and R:S = 3:10, find Q:S in simplest form.

    1. A1:2Wrong formulaignored R and paired Q=5 with S=10 directly
    2. B2:1Wrong formulaUpside down5:10 route written backwards
    3. C3:4Answer
    4. D3:25Upside downdivided the ratios instead of multiplying: (5/2)/(3/10) = 25/3, then inverted to 3:25
    5. E4:3Upside downcorrect value written as S:Q
    6. F25:3Upside downdivided instead of multiplied: (5/2)÷(3/10) = 25/3
  • ENGAA 2016 · Q6Physics · Radioactivity & nuclear · Statements

    Three diagrams show a particle hitting U-235 and producing two daughter nuclei plus neutrons (1: proton in, Ba-144, Kr-89, 2n; 2: neutron in, Xe-137, Sr-96, 3n; 3: neutron in, Br-87, La-145, 3n). Which could represent fission?

    1. AnoneStatement misjudgedArithmeticunclearrejects 2 (miscounts nucleons or neutrons)
    2. B1 onlyStatement misjudgedMisconceptionunclearaccepts proton-induced 1 (Z and A not conserved) and rejects 2
    3. C2 onlyAnswer
    4. D3 onlyStatement misjudgedStopped earlychecks only proton numbers (3 balances Z=92) and misjudges 2
    5. E1 and 2Statement misjudgedMisconceptionaccepts 1: ignores that incoming particle is a proton and A is not conserved (236 vs 235)
    6. F1 and 3Statement misjudgedMisconceptionunclearaccepts 1 and 3, both of which fail nucleon conservation
    7. G2 and 3Statement misjudgedStopped earlyaccepts 3 by checking only Z (35+57=92) or forgetting the incoming neutron in the mass count (235 = 87+145+3)
    8. H1, 2 and 3Statement misjudgedMisconceptionthinks any split into two nuclei plus neutrons is valid, no conservation check
  • ENGAA 2016 · Q7Maths · Probability & statistics · Numbers

    A club of 20 has mean age 28; two new members raise the mean by 2. Find the mean age of the new pair.

    1. A20Wrong formulaused 20 people in the new total: 20×30 − 560 = 40, halved = 20
    2. B22Fillerno clear route (number of members)
    3. C30Different questiongave the new mean of the club
    4. D40Wrong formulaFactor slip20×30 − 560 = 40 not halved, or just the 40-year extra (20×2) without adding the new mean
    5. E50Answer
    6. F52Factor slip30 + 22×2/2 = 52: used 22 members for the extra years
  • ENGAA 2016 · Q8Physics · Electric circuits · Numbers

    A 5 Ω resistor and a 3–15 Ω variable resistor are in series with a 24 V battery; find the maximum power in the 5 Ω resistor.

    1. A7.2 WIgnored a conditionused the 15 Ω setting (min current 1.2 A): 1.2²×5 = 7.2
    2. B18 WWrong formulaunclearat max resistance, 1.2 A × 15 Ω = 18 (voltage across variable resistor / wrong product)
    3. C27 WDifferent questionpower in the 3 Ω variable resistor: 3²×3 = 27
    4. D45 WAnswer
    5. E72 WDifferent questiontotal power 24×3 = 72
    6. F75 WWrong formula15 V across 5 Ω divided by the 3 Ω: 15²/3 = 75 (voltage and resistance of different components)
  • ENGAA 2016 · Q9Maths · Ratio, proportion & percentages · Numbers

    A £15 000 scanner loses 20% of its value each year; by how much has its value fallen after 2 years?

    1. A£600Power slip15000×0.2² = 600
    2. B£3000Stopped earlyone year's depreciation only
    3. C£5400Answer
    4. D£6000Wrong formulasimple rather than compound: 40% of 15000
    5. E£9000Wrong formulaDifferent questionsimple depreciation, value left = 60%
    6. F£9600Different questiongave the remaining value not the reduction
    7. G£12 000Stopped earlyDifferent questionvalue after one year
  • ENGAA 2016 · Q10Physics · Space & other · Numbers

    Star power P = kR²T⁴; the Sun (4.0×10²⁶ W) has R increased 100-fold and T halved; find new P.

    1. A2.5 × 10²⁷ WPower slipR not squared: 100/16 = 6.25 -> 2.5 × 10²⁷
    2. B1.0 × 10²⁸ WPower slipPower slipR not squared and T only squared: 100/4
    3. C2.0 × 10²⁸ WPower slipPower slipno powers at all: 100/2
    4. D2.5 × 10²⁹ WAnswer
    5. E1.0 × 10³⁰ WPower slipT squared instead of 4th power: 10⁴/4
    6. F2.0 × 10³⁰ WPower slipT not raised to 4th power: 10⁴/2
    7. G2.5 × 10³³ WPower slipR raised to 4th power: 10⁸/16
    8. H1.0 × 10³⁴ WPower slipPower slipswapped exponents R⁴T²: 10⁸/4
  • ENGAA 2016 · Q11Maths · Trigonometry · Numbers

    A is 4 km due east of B; C is on bearing 330° from A and 060° from B. Find BC.

    1. A2 kmDifferent questionWrong formulafound AC = 4sin30° = 2 (other leg) or used sin for cos
    2. B2sqrt3 kmAnswer
    3. C4 kmMisconceptionassumed an isosceles/equilateral triangle, BC = AB
    4. D2sqrt5 kmWrong formulaPythagoras with AB as a leg: √(4²+2²)
    5. E4sqrt2 kmWrong formulauncleartreated as right isosceles with legs 4: √(32)
  • ENGAA 2016 · Q12Physics · Waves, sound & optics · Numbers

    A transverse wave has f = 5.0 Hz, wavelength 4.0 cm, amplitude 3.0 cm; how far does one particle of the medium move in one minute?

    1. A900 cmFactor slipA per oscillation: 300×3
    2. B1200 cmMisconceptiondistance the wave travels (v t = 20 cm/s × 60 s), i.e. treated particle as moving with the wave
    3. C1800 cmFactor slip2A per oscillation (one-way peak-to-trough only): 300×6
    4. D2400 cmMisconceptionFactor slipunclearused 2λ per oscillation: 300×8
    5. E3600 cmAnswer
    6. F4800 cmDifferent questionused wavelength as amplitude: 4×4 cm per cycle ×300

How this was made

Source papers

Section 1 of the Engineering Admissions Assessment (ENGAA), November 2016–2023, with the official answer keys, published by UAT-UK on its ESAT preparation page. ENGAA is the predecessor of ESAT, and its questions are of the ESAT type. Questions that the papers cross out as outside the ESAT specification (every Part B physics question) are excluded, leaving 273.

ESAT papers have eight options per question. The older ENGAA papers used here have four to eight, so some examples have fewer wrong options.

Official ESAT preparation materials and past papers

Classification

Each question was solved independently and checked against the key. Every wrong option was then reverse-engineered: a mistake counts as traced when applying it reproduces the option exactly (high confidence) or almost exactly (medium). Options no systematic mistake reproduces are marked as filler or unclear and left out of the percentages.

Every worked example on this page was re-checked by a second, independent pass against the paper images and keys. Question text is paraphrased, and option values are transcribed.

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