Mathematics
Mathematics in the FMRDA Medicine Admission exam tests algebra, functions, trigonometry, introductory calculus, probability, and statistics. The emphasis is on accurate manipulation and choosing the shortest valid method, not on lengthy proofs.
Algebra and functions
Quadratic equations can be solved by factorisation, completing the square, or the formula x = [−b ± √(b² − 4ac)]/(2a). The discriminant b² − 4ac determines the number of real roots: positive gives two, zero gives one repeated root, negative gives none. For logarithms, log(ab) = log a + log b and log(a/b) = log a − log b; the base must be positive and not 1, and the argument must be positive.
Calculus
Differentiate powers with d/dx(xⁿ) = nxⁿ⁻¹. The derivative gives gradient; setting it to zero locates stationary points, and the second derivative distinguishes maximum from minimum. Integrate powers with ∫xⁿ dx = xⁿ⁺¹/(n+1) + C for n ≠ −1. Definite integrals give signed area; split the interval where the curve crosses the axis.
Probability and statistics
For equally likely outcomes, P(A) = favourable outcomes/total outcomes. For independent events, P(A and B) = P(A)P(B). For mutually exclusive events, P(A or B) = P(A) + P(B). Without replacement, update the denominator after each draw. Mean = sum of values/n; median is the middle ordered value; mode is the most frequent value.
Worked example
Solve 2^(x+1) = 8^(x−2). Write 8 as 2³, so the right side is 2^(3x−6). Equate exponents: x + 1 = 3x − 6. Then 7 = 2x, so x = 3.5. Checking: left exponent 4.5; right exponent 3(3.5) − 6 = 4.5, so the solution is valid.
Traps that cost marks
- Squaring both sides can introduce extraneous roots; always check in the original equation.
- Forgetting domain restrictions for logs and square roots.
- Mixing degrees and radians in trigonometric equations.
- Using P(A) + P(B) for non-mutually-exclusive events without subtracting P(A and B).
- Treating the median as the midpoint of the range rather than the middle ordered value.