CEnT-S mathematics
Mathematics opens the test: fifteen questions in thirty minutes, the joint largest section and the first thing you see. It also has the clearest boundaries of the five, and knowing where they fall saves weeks of preparation.
What the section covers
Numbers and percentages
Ratio and proportion, percentage increase and decrease, and reverse percentages. A price reduced by 25% is 75% of the original, so recovering the original means dividing rather than adding the percentage back.
Algebra
Linear and quadratic equations, inequalities, and systems of two equations. For quadratics, the sum and product of the roots are −b/a and c/a, which answers a whole class of questions without solving anything.
Analytic geometry
The straight line, the circle, distance between points, midpoints and perpendicularity. The equation of a circle gives r² on the right-hand side, so an answer left unsquare-rooted is a radius that is wrong by a lot.
Functions and their graphs
Reading a graph, and the transformations: translation, reflection and stretch. A vertical translation adds a constant to every output, which is easy to state and easy to forget when the question asks for a value.
Exponentials and logarithms
The logarithm laws, exponential growth and decay, and doubling time. A growth factor is not a number of periods; it has to be turned into one first.
Combinatorics and probability
Permutations and combinations, and the difference between them. Equally likely outcomes, and the fact that a total on two dice is not equally likely — a total of nine can be reached four ways and a total of twelve only one.
Descriptive statistics
Mean, median, mode, and frequency distributions, including working backwards from a mean to a missing value.
What is not on the syllabus
Trigonometry is not listed. Neither is differentiation nor integration.
This matters more than it sounds, because sample papers for English TOLC-I, the test CEnT-S replaced, did include trigonometry. Preparation material written for TOLC-I therefore overshoots, and time spent on sine rules is time taken from the topics that actually appear. Check the date on anything you study from: if it predates November 2025, it was written for a different test. Full CEnT-S syllabus →
Two minutes a question, no calculator
Thirty minutes across fifteen questions is exactly two minutes each, and no calculator is permitted. The arithmetic is therefore designed to be manageable: square roots are of perfect squares, divisions come out clean, and the numbers in a probability question are small enough to count.
If a calculation turns into a long decimal, the method is usually wrong rather than the arithmetic hard. That is a useful signal to have during the test.
The formulas are not supplied either. The quadratic formula, the distance formula, the equation of a circle and the logarithm laws all have to be memorised. Full formula list →
Where marks are lost
Answering the wrong question. In a system of equations, x and y are both on the page and only one is asked for. In a ratio problem, the largest share and the difference between the largest and smallest are different numbers, and both will be among the options.
Percentage base. A 20% rise followed by a 20% fall does not return to the starting price, because the two percentages are taken on different amounts. The final price is 4% lower, and "unchanged" is always one of the options.
Dropping a term. The intercept of a line of best fit applies at every value of x, not only at zero. The half in s = ½at² comes from the speed rising steadily from rest, and leaving it out doubles the answer.
Each of these produces a wrong answer that looks plausible, which with a quarter-mark penalty is expensive. How the penalty changes what is worth guessing →
Practise the section
Fifteen original mathematics questions
Under the real thirty-minute limit, calculator-free, with every answer explained.
Start practice →