First-semester general mathematics papers for science students look broadly alike from school to school. Expect a written exam of about 2 to 3 hours. Some papers are entirely theory (worked) questions, often "answer any four or five of seven"; others have an objective section of multiple-choice questions followed by a theory section; a few large classes are examined mostly or wholly by multiple choice. Theory questions are usually split into parts worth 3 to 10 marks each, so one question can touch two or three topics.

Numbers and indices: classify numbers, convert recurring decimals, prove $\sqrt2$ irrational, evaluate fractional indices, simplify and rationalise surds, simplify logs and solve exponential or log equations.
Sets: list and combine sets, verify De Morgan's laws, and a three-set Venn diagram word problem (a favourite long question).
Sequences and series: AP and GP terms and sums, sum to infinity, a word problem on savings, salaries or growth, and a proof by induction.
Binomial theorem: an expansion, a specific coefficient, the term independent of $x$, or an approximation.
Quadratics and functions: solve by a named method, nature of roots, the $\alpha$, $\beta$ question, composite and inverse functions, and a sketch or plotted graph.
Trigonometry and complex numbers: radians, exact values, identities and compound angles, trig equations in a range, sine and cosine rules, complex arithmetic, modulus and argument.

The marks live in the working. Write the formula before the numbers, keep units on every line, show each region of a Venn diagram, label the parts of an induction proof, and finish each part with a clear final answer in the form asked (exact, surd form, or to the stated decimal places or significant figures). Use the method the question names: "by completing the square" answered by the formula usually scores very little.

A calm plan for the day: read the whole paper first and choose your questions before writing. Share your time by marks, and keep ten minutes at the end to re-check arithmetic. Know your calculator before exam day: the log and ln keys, powers and roots, and the DEG/RAD mode (degrees for most triangle and equation work, radians for arc length and sector area). Carry at least 4 significant figures through every step and round only at the end. In multiple-choice sections, estimate first (is the answer between 9 and 27?) and eliminate options that fail a quick check, such as a negative modulus, a negative length or a sine bigger than 1.