CMA Foundation Paper 3 common mistakes
CMA Foundation Paper 3 · Understand the traps and how to avoid them.
When computing a simple or compound interest problem, substituting the annual rate directly into the formula without converting the time period to years (e.g., using t = 9 for 9 months, or t = 3 for 3 quarters), producing an answer several times too large.
Candidates pattern-match on the formula I = PRT/100 and treat every time figure as a year count, especially when the question states months or days in words rather than as a fraction.
What to do instead
Immediately after reading the question, write the time as an explicit fraction of a year (9 months = 9/12, 45 days = 45/365 or 45/366 as stated) before touching the formula, and check that the resulting interest is smaller than one year's interest when the period is under a year.
Applying the compound interest formula with the nominal annual rate and the number of years when compounding is more frequent than annual, instead of dividing the rate by the compounding frequency and multiplying the periods.
The formula A = P(1 + r)^n is memorised in its simplest form, and candidates do not register phrases such as 'compounded half-yearly' or 'quarterly' as signals to adjust both r and n.
What to do instead
Adopt a fixed two-line setup: state i = r/m and n = t x m explicitly, write them down, then substitute. Practise converting 'compounded quarterly at 8% for 2 years' into i = 0.02, n = 8 until it is automatic.
Solving a linear equation or word problem and stopping at the value of the variable, without translating back to the quantity the question actually asks for (e.g., reporting x when the question asks for the price of the second article, which is x + 15).
Cognitive load is spent on the algebra, and the final 'answer the question asked' step is skipped because the variable value feels like the finish line.
What to do instead
Before solving, write a one-line declaration of what the variable represents and a separate line stating what must be reported. After solving, substitute back into that target expression and verify the answer satisfies the original word conditions.
Treating a ratio or proportion problem as a direct proportion when the relationship is inverse, for example computing that more workers take proportionally more days to finish a job, or that a faster speed covers a fixed distance in more time.
Direct proportion is the default mental model, and the inverse case requires an extra reasoning step (product constant rather than quotient constant) that is easily bypassed under time pressure.
What to do instead
For every proportionality question, test one extreme: double the number of workers and ask whether the days should go up or down. If the product of the two quantities is fixed, set up x1y1 = x2y2 rather than x1/y1 = x2/y2.
In mensuration, mixing units within one calculation, such as substituting a radius in centimetres and a height in metres into the same volume formula, or reporting a volume in square units.
Questions often deliberately present dimensions in different units to test conversion, and candidates focus on the formula rather than the units attached to each number.
What to do instead
Convert all dimensions to a single unit as the first written step, and carry units through the calculation. Check the final unit against the type of measure: length, area squared, volume cubed.
Using the wrong mensuration relationship, for example applying the slant height of a cone where the perpendicular height is required, using the diameter as the radius, or using the curved surface area formula when total surface area (including the base) is asked.
Formulae for cylinder, cone and sphere look similar and are recalled as a blur; the words 'curved', 'total', 'slant' and 'perpendicular' are skimmed rather than read.
What to do instead
Draw a small labelled sketch for every mensuration item, mark which length is given and which is needed, and write the formula with named quantities (l for slant, h for perpendicular) before substituting numbers.
Differentiating or integrating a term and dropping the constant factor or the constant of integration, for example writing the derivative of 5x^3 as 3x^2, or giving the integral of x^2 as x^3/3 + C omitted entirely.
Attention is on the exponent rule, and the coefficient in front of the term is treated as decoration; the arbitrary constant is forgotten because it has no numerical role in a definite integral.
What to do instead
Apply the rule term by term in a written line, explicitly writing the coefficient before and after the operation. For indefinite integrals, make '+ C' a mandatory final token, and check by differentiating your answer back to the integrand.
Confusing marginal cost or marginal revenue with average cost or average revenue, and hence setting the derivative equal to price rather than to zero when asked to find the output that maximises profit.
The words 'marginal' and 'average' are both used in business contexts, and candidates substitute whichever function they remember rather than the one the optimisation condition requires.
What to do instead
State the optimisation condition in words first: profit is maximised where marginal revenue equals marginal cost, or where the derivative of the profit function is zero. Identify which function is given, derive the other if needed, then solve.
Computing a mean, median or mode from grouped frequency data without using class midpoints, or reading the modal class as the mode itself, or applying the median formula with the wrong cumulative frequency.
Ungrouped habits carry over into grouped data, and the median formula has several terms (lower boundary, cumulative frequency before the class, class frequency, class width) that are easy to misassign.
What to do instead
Build a table with columns for class, midpoint, frequency and cumulative frequency before computing anything. For the median, locate the class containing the N/2-th item from the cumulative column and label each term of the interpolation formula before substituting.
Interpreting a correlation coefficient as proof of causation, or misreading the sign and strength of r, for example calling r = -0.85 a weak relationship or assuming r = 0.9 means 90% of the variation is explained.
The coefficient is treated as a vague 'how related' score, and the distinction between r and r-squared, and between association and causation, is not reinforced during practice.
What to do instead
For every correlation result, state three things explicitly: sign (direction), magnitude band (strong, moderate, weak), and that r-squared, not r, is the proportion of variation explained. Add a one-line note that correlation alone cannot establish cause.