Traps
How CDS Maths costs you marks when you know the maths
A wrong answer loses a third of a mark, and there are 1.2 minutes a question. So two of the traps below are about the paper, not the mathematics: guessing blind, and staying too long. The rest are the slips that produce the wrong options CDS reuses from paper to paper.
- trap shapes
- 15
- strands affected
- 3
- playbooks hit by the widest trap
- 3
- paper-wide, not chapter-specific
- 1
Cornerstone traps — where the most marks go
The two paper-wide traps — the blind guess and the time sink — plus the slips that cost marks in the five largest chapters.
The blind guess — worth nothing on average, and it adds risk
Paper-wide — not tied to any one chapter
How it happens
A right answer earns 1 mark and a wrong one loses 1/3. Guessing blind among four options, you are right one time in four: 1/4 × 1 − 3/4 × 1/3 = 0. So a blind guess gains nothing on average, and across a paper it only adds spread to your score. Students from exams with no negative marking guess everything; students scared of the penalty guess nothing. Both lose marks.
The check
Guess only after ruling out at least one option. With three options left a guess is worth +1/9 of a mark on average; with two left, +1/3. Rule out options on sight — wrong units, a sign that cannot be right, a value outside a range — and then commit.
The four-minute question on a 1.2-minute paper
Affects: Trigonometry, Mensuration 2D, Algebraic Identities
How it happens
100 questions in 120 minutes is 1.2 minutes each, and every question pays the same 1 mark. The HARD questions pool in a few pages: in Trigonometry, maximum/minimum and eliminating θ hold 29 of its 46 HARD questions, and Algebraic Identities is 39% HARD. A question that feels close for four minutes costs the three easy ones you never reach.
The check
Two passes. On the first, answer everything you can see through in under a minute and mark the rest. On the second, return to the marked ones in order of how close you were. If a question has not opened up in about two minutes, rule out what you can and move on.
An option that cannot be true
Affects: Trigonometry, Number System
How it happens
Distractors are often values that the question's own conditions forbid: sin θ greater than 1, a negative length, a probability above 1, a remainder larger than the divisor, a non-integer count of divisors. They look plausible because they come from a common slip in the working.
The check
Before solving, check each option against the range the answer must lie in. This is the cheapest way to rule out an option — and on this paper, ruling one out is what makes a guess worth taking.
Mixed units in mensuration
Affects: Mensuration 2D, Mensuration 3D
How it happens
Dimensions come in cm and m in the same question, volumes are asked in litres, and costs are per square metre while sides are in cm. The arithmetic is right and the answer is off by a factor of 100 or 1000 — and that answer is usually one of the options.
The check
Convert everything to one unit before any formula. 1 m² = 10,000 cm², 1 m³ = 1,000,000 cm³, 1 litre = 1000 cm³.
Scaling a length but not the area
Affects: Triangles, Mensuration 2D, Mensuration 3D
How it happens
For similar figures, areas go as the square of the side ratio and volumes as the cube. Doubling the radius of a sphere multiplies its volume by 8, not 2. The distractor is always the linear ratio.
The check
Name what is being compared — length, area or volume — and raise the ratio to 1, 2 or 3 before choosing.
HCF × LCM = product, used for three numbers
Affects: Number System, Polynomials
How it happens
HCF × LCM = a × b holds for two numbers only. Applied to three numbers it gives a wrong answer that is still one of the options. For polynomials it holds only up to a constant factor.
The check
For three numbers, factorise each into primes and build the HCF and LCM from the powers.
Quick-win traps — cheap marks lost to a slip
These sit in the cheapest chapters, and each is a slip in method, not a hard question. The wrong answer is always among the options.
Average speed taken as the average of speeds
Affects: Time, Speed and Distance, Averages
How it happens
Over equal distances at u and v, the average speed is 2uv/(u + v), not (u + v)/2. The arithmetic mean is always an option, and it is always wrong unless the times are equal.
The check
Average speed is total distance over total time. For equal distances, use 2uv/(u + v).
A percentage of the wrong base
Affects: Percentage, Profit and Loss, Data Interpretation, Ratio, Proportion and Variation
How it happens
If A is 25% more than B, B is 20% less than A — not 25%. Successive changes do not add: +20% then −20% is a 4% fall. Profit is on cost price, discount on marked price. In a chart question, 'percentage increase' is on the earlier year.
The check
Write down the base before computing. For two successive changes, use a + b + ab/100.
Adding days instead of rates
Affects: Time and Work
How it happens
If A takes 10 days and B takes 15, together they do not take 25 days, or 12.5. Work adds as rates: 1/10 + 1/15 = 1/6, so 6 days.
The check
Turn every worker into work per day, add, then invert. For two workers, ab/(a + b).
Half-yearly compounding at the yearly rate
Affects: Simple and Compound Interest
How it happens
Compounded half-yearly, the rate halves and the number of periods doubles. Using the annual rate for n periods gives an option that is close enough to look right.
The check
Use R/2 and 2n for half-yearly, R/4 and 4n for quarterly.
Changing data and keeping the old spread
Affects: Statistics
How it happens
Adding a constant to every value shifts the mean, median and mode but leaves the range and standard deviation unchanged. Multiplying by k multiplies all of them by k. The median needs the data in order first.
The check
Ask whether the change adds or multiplies, and apply it only to the measures it moves.
Selective traps — algebra and geometry
Algebra and the smaller geometry chapters: a dropped term, a sign, a root that breaks the domain, and the case the question did not name.
x² + 1/x² taken as k²
Affects: Algebraic Identities, Surds and Indices
How it happens
From x + 1/x = k, squaring gives x² + 2 + 1/x² = k², so x² + 1/x² = k² − 2. Dropping the middle term gives k², which is always an option. The cube has the same trap: x³ + 1/x³ = k³ − 3k.
The check
Expand the square in full, including the middle term, every time.
Same side or opposite sides — the question may not say
Affects: Circles, Heights and Distances
How it happens
Two parallel chords can lie on the same side of the centre or on opposite sides; two observers can stand on the same side of a tower or on either side. The distances subtract in one case and add in the other, and both answers can appear as options.
The check
Draw both cases. If only one matches an option, that is the answer; if both do, reread the stem for the word that decides it.
A root that breaks the domain
Affects: Logarithms, Quadratic Equations
How it happens
Solving a log equation often ends in a quadratic, and one of its roots makes a logarithm's argument zero or negative. The option listing both roots is wrong.
The check
Put every root back into the original equation and reject any that makes a log's argument non-positive.
The sign of the sum of roots
Affects: Quadratic Equations, Polynomials
How it happens
For ax² + bx + c = 0 the sum of roots is −b/a. Dropping the minus sign gives an option with the right size and the wrong sign. The same slip happens with the remainder theorem when dividing by (x + a): put x = −a.
The check
Write the equation in standard form first, then read the sign off it.
Two habits cover most of this page
Before you solve
Check the options first
Rule out anything out of range, in the wrong units or with the wrong sign. It often leaves one option, and when it does not, it makes a guess worth taking.
On the paper
Two passes, no blind guesses
Answer the quick ones first and mark the rest. Leave a question only if you cannot rule out a single option — at a third of a mark per wrong answer, that is the one guess not worth making.