Mathematics
Core concepts
VWO mathematics spans algebra (factorising, solving equations, exponentials and logarithms), functions and graphs (domain, range, transformations, asymptotes), calculus (differentiation, tangents, extrema, integration for areas), geometry (trigonometry, sine and cosine rules, vectors, circles), probability and statistics (conditional probability, binomial and normal distributions, hypothesis testing), and combinatorics.
Traps examiners set
- Forgetting to state the domain restriction when solving equations with roots or logarithms, producing extraneous solutions.
- Mixing degrees and radians in trigonometric work.
- Using the wrong tail in normal-distribution questions; always sketch the curve and shade the required area.
- Rounding intermediate values too early, which shifts the final answer outside the marking tolerance.
- In hypothesis tests, confusing the significance level with the p-value.
Rule of thumb
Write down what is given, what is asked, and which formula links them before calculating. Show the substitution explicitly; method marks are awarded for the correct formula even when arithmetic slips.
Worked example
Solve 2^(x+1) = 5·3^x. Take logarithms: (x+1)log2 = log5 + x·log3. Rearrange: x(log2 − log3) = log5 − log2, so x = (log5 − log2)/(log2 − log3) ≈ −2.21. Note that dividing by a negative logarithm flips nothing but does change the sign of the result; check by substitution.
Exam technique
Annotate graphs, label axes, and give units. For proof questions, work from the given to the required, one justified step per line.