Top 200 Vocabulary for JC 2 H2 Mathematics Syllabus | A-Level 9758 Pure Mathematics, Statistics and Paper 2

JC2 H2 Mathematics vocabulary for Singapore A-Level students: 200 carefully defined terms, covering the questions students ask about syllabus 9758, Pure Mathematics, Probability and Statistics, the graphing calculator and exam explanations. Choose a topic below to find a word immediately.

The 2027 H2 Mathematics syllabus has two three-hour papers worth 50% each. Paper 1 is Pure Mathematics; Paper 2 combines 40 marks of Pure Mathematics and 60 marks of Probability and Statistics. This glossary connects words with mathematical decisions, not merely memorisation.

Quick information:

200 distinct, individually explained terms in ten groups.
SEAB H2 Mathematics code 9758; check the syllabus for your exact exam year.
Paper 1: Pure Mathematics; Paper 2: Pure Mathematics plus Probability and Statistics.
Includes worked problems, common confusions, four-week revision, FAQs and authoritative references.

This independently written teaching selection is not an official SEAB list of compulsory vocabulary or a substitute for its published syllabus.

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The top 200 H2 Mathematics vocabulary words, with meanings

1. Mathematical language

quantity — amount that can be counted or measured.
variable — symbol whose value can change.
constant — value held fixed in a calculation.
parameter — number selecting a particular member of a model family.
coefficient — numerical multiplier of an algebraic term.
expression — combination of mathematical symbols and operations.
equation — statement of equality between two expressions.
identity — equality true for every permitted input.
inequality — comparison using less than or greater than.
solution set — all values satisfying the original conditions.
domain — permitted inputs of a function.
range — outputs actually possible for the stated domain.
function — rule assigning exactly one output per permitted input.
mapping — correspondence between inputs and outputs.
input — argument supplied to a function.
output — value returned by a function.
inverse function — function reversing a suitable one-to-one mapping.
composite function — one function applied after another.
one-to-one — property in which distinct inputs have distinct outputs.
domain restriction — limitation of allowed inputs, sometimes enabling an inverse.

2. Graphs and algebra

root — input where a function is zero.
intercept — point where a graph meets an axis.
asymptote — line approached by a graph in limiting behaviour.
vertical asymptote — vertical line near which output becomes unbounded.
horizontal asymptote — horizontal line approached for very large input magnitude.
oblique asymptote — slanting line approached at large input magnitude.
turning point — point where a curve reverses its increasing or decreasing trend.
stationary point — point where first derivative equals zero.
axis of symmetry — line dividing a graph into mirror images.
reflection — transformation across a stated mirror axis.
translation — transformation shifting points by fixed distances.
stretch — transformation multiplying distances along a direction.
modulus function — function containing absolute value, for example |f(x)|.
piecewise function — function with different rules on separate intervals.
parametric equation — coordinate equation involving another parameter.
intersection — point lying on two specified graphs.
simultaneous equations — equations to solve under shared conditions.
quadratic discriminant — b²−4ac, indicating the number of distinct real quadratic roots.
approximate solution — numerical estimate close to the exact solution.
extraneous root — candidate that fails the original equation.

3. Sequences and complex numbers

sequence — ordered terms indexed by position.
series — sum of a collection of ordered terms.
nth term — expression for the value at position n.
recurrence relation — rule generating later terms from earlier ones.
arithmetic progression — sequence with fixed difference.
common difference — fixed change between arithmetic terms.
geometric progression — sequence with fixed ratio.
common ratio — multiplier between successive geometric terms.
partial sum — sum of the first specified number of terms.
sum to infinity — limiting total of a convergent infinite series.
convergence — approach towards a finite limit.
divergence — failure to approach a finite limit.
imaginary unit — number i with i²=−1.
complex number — number a+bi for real a and b.
real part — real component a in a+bi.
imaginary part — real coefficient b in a+bi.
complex conjugate — a−bi when the original number is a+bi.
complex modulus — distance from the origin in an Argand plane.
complex argument — directed angle locating a complex number.
Argand diagram — coordinate plane for real and imaginary components.

4. Three-dimensional vectors

scalar — quantity described by a number without direction.
vector — quantity with magnitude and direction.
position vector — vector from chosen origin to a point.
displacement vector — vector from one position to another.
direction vector — nonzero vector pointing along a line.
unit vector — vector with magnitude one.
magnitude — nonnegative vector length.
collinearity — multiple points lying on one straight line.
scalar product — dot product involving lengths and cosine of angle.
vector product — cross product perpendicular to the original vectors.
perpendicularity — right-angle relation, often established using dot product.
parallelism — same or opposite direction, indicated by scalar multiples.
normal vector — vector perpendicular to a plane.
vector equation of line — position vector plus scalar times direction vector.
Cartesian equation of plane — plane of form ax+by+cz=d.
plane intersection — set of common points of two planes.
skew lines — nonparallel three-dimensional lines that do not meet.
foot of perpendicular — nearest projection point on a line or plane.
point-to-plane distance — shortest perpendicular distance between point and plane.
ratio theorem — vector rule for internal division of a line segment.

5. Differentiation and rates

derivative — instantaneous rate of change.
first derivative — function used to study local increasing or decreasing behaviour.
second derivative — derivative of a derivative, indicating concavity.
differentiability — existence of a derivative at a point.
tangent — line sharing the curve’s local slope.
normal — line perpendicular to the tangent.
gradient — slope of a line or curve.
chain rule — differentiation of a nested function.
product rule — differentiation of a product.
quotient rule — differentiation of a fraction of functions.
implicit differentiation — finding derivatives without explicitly solving for y.
parametric differentiation — obtaining dy/dx from a parameter.
critical point — candidate point requiring examination for extreme behaviour.
local maximum — value not smaller than nearby values.
local minimum — value not larger than nearby values.
point of inflexion — point where concavity switches.
first derivative test — classification using sign changes of the derivative.
second derivative test — classification using the sign of the second derivative.
optimisation — finding maximum or minimum under constraints.
connected rates — linking multiple time derivatives through an equation.

6. Integration and differential equations

antiderivative — function that differentiates to the integrand.
indefinite integral — family of antiderivatives with arbitrary constant.
definite integral — signed accumulated value between fixed bounds.
constant of integration — free additive constant in indefinite integration.
substitution — change of variable used in integration.
integration by parts — method reversing the product rule.
partial fractions — decomposition of rational expressions into simpler fractions.
signed area — net area above minus area below an axis.
enclosed area — nonnegative area within given boundaries.
volume of revolution — volume formed by rotating a planar region.
Maclaurin series — power series expansion about zero.
truncation error — difference caused by stopping an infinite approximation.
small-angle approximation — approximation valid for small angles in radians.
order of approximation — highest retained power in a series approximation.
differential equation — equation involving an unknown function and its derivatives.
separation of variables — splitting suitable differential equations for integration.
general solution — solution family containing free constants.
particular solution — specific member satisfying additional conditions.
initial condition — stated starting value determining constants.
rate model — equation expressing how a quantity changes.

7. Probability and counting

sample space — all possible outcomes of an experiment.
event — set of outcomes of interest.
complement — outcomes in which an event does not happen.
union — outcomes belonging to at least one specified event.
intersection of events — outcomes shared by specified events.
mutually exclusive — events that cannot occur simultaneously.
independent events — events not affecting one another’s probabilities.
conditional probability — probability given an observed condition.
tree diagram — branches showing sequential outcomes.
Venn diagram — overlapping regions showing relationships among events.
addition rule — probability formula correcting for overlap.
multiplication rule — formula using conditional probabilities to find joint events.
fundamental counting principle — multiplying alternatives across stages.
permutation — ordered selection or arrangement.
combination — selection where order does not matter.
factorial — product of positive integers to n, with 0!=1.
repetition allowed — condition permitting the same option multiple times.
circular arrangement — ordered placement around a circle allowing for rotations.
at least one — one or more occurrences, often solved using complement.
exactly k — precisely k occurrences.

8. Random variables and distributions

random variable — numerical outcome determined by chance.
discrete variable — variable with countably many possible values.
continuous variable — variable modelled across a real interval.
probability distribution — assignment of probabilities to random-variable outcomes.
probability mass function — probabilities at individual discrete values.
probability density — function whose area gives interval probabilities.
expectation — probability-weighted average.
variance — expected squared deviation from the mean.
standard deviation — square root of variance.
linear transformation of variable — new variable of the form aX+b.
binomial distribution — success count in fixed independent trials.
Bernoulli trial — one trial with success and failure outcomes.
success probability — fixed chance of success per trial.
binomial parameters — trial count n and success chance p.
normal distribution — continuous symmetric bell-shaped model.
standard normal — normal distribution with mean zero and variance one.
z-score — distance from mean measured in standard deviations.
normal percentile — cutoff with a stated proportion below it.
tail probability — probability beyond a stated threshold.
distributional assumption — condition required to justify a probability model.

9. Sampling and statistical decisions

population — full group of units being studied.
sample — subset used to infer something about a population.
simple random sample — every subset of fixed size having equal selection probability.
sample mean — average of observed sample values.
sampling distribution — distribution of a statistic across repeated samples.
standard error — standard deviation of a statistic’s sampling distribution.
null hypothesis — reference claim used by a hypothesis test.
alternative hypothesis — competing claim for which evidence is sought.
significance level — prespecified type I error threshold.
test statistic — computed quantity used in a test decision.
critical region — values leading to rejection of the null.
critical value — boundary of a test’s rejection region.
p-value — probability under the null of equally or more extreme data.
one-tailed test — test with a directional alternative.
two-tailed test — test with an alternative in either direction.
type I error — rejecting a null hypothesis that is true.
type II error — not rejecting a null hypothesis that is false.
statistical conclusion — decision interpreted in relation to the stated hypotheses.
practical significance — real-world importance of an estimated difference.
sample size — number of observational units used.

10. Regression, models and communication

bivariate data — paired observations of two variables.
scatter diagram — graph of the observed coordinate pairs.
correlation — strength and direction of statistical association.
Pearson coefficient — numerical measure of linear correlation.
linear regression — fitting a straight line to predict a response.
least-squares line — line minimising summed squared vertical errors.
residual — observed minus predicted response.
interpolation — prediction within the observed input range.
extrapolation — prediction beyond the available input range.
outlier — unusually distant observation.
mathematical model — simplified description based on mathematical relationships.
assumption — condition under which a model or method applies.
constraint — restriction on feasible values.
validity — suitability of conclusions under real-world conditions.
graphing calculator — approved device assisting numerical and graphical methods.
exact form — unrounded symbolic answer.
significant figures — digits expressing reported numerical precision.
interpretation — meaning of a calculated answer in its original context.
justification — reasoning showing why a claim follows.
reasonableness check — checking signs, units and plausible sizes.

How JC2 Mathematics vocabulary works in a question

Words identify the operation before a student calculates. Domain asks what inputs are permitted; range asks what outputs are actually attainable. For f(x)=√(x−2), the real domain is x≥2 and the range is y≥0. Even a student who remembers square roots can lose marks by answering the wrong set question.

Likewise, an instruction asking for “at least one success” describes a different event from “exactly one success”. With four independent attempts and success probability 0.2 each, P(at least one success)=1−0.8⁴=0.5904. The complement is the efficient route; “exactly one” would require a binomial term instead.

Finally, a p-value is calculated under the null hypothesis. It is not the probability that the null hypothesis is true. A sensible A-Level conclusion relates the test outcome to the stated real-world claim and avoids confusing statistical significance with practical importance.

Six recurring misconceptions

Terms	What to check
Stationary / turning point	Not every stationary point is a maximum or minimum.
Independent / mutually exclusive	These are different probability conditions and should not be interchanged.
Variance / standard deviation	Multiplying X by a multiplies variance by a² and standard deviation by \|a\|.
Correlation / causation	Association alone does not establish what causes what.
Interpolation / extrapolation	Outside-range predictions need extra caution.
Exact / rounded	Preserve exact values until approximation is requested.

A four-week vocabulary revision plan

Week 1: learn entries 1–80 in batches; draw diagrams for graphs, sequences, complex numbers and vectors. Test each term in a school question.
Week 2: practise entries 81–120 in calculus and explain why a particular derivative or integral method applies.
Week 3: learn entries 121–180 while practising probability events, distributions and the words used in hypothesis-test conclusions.
Week 4: finish entries 181–200 and attempt mixed, timed Paper 1 and Paper 2 questions. Keep an error log linking every mistake to a concept.

Four weeks is an organisational schedule rather than a promise of mastery. Repair JC1 algebra or foundational statistics where needed before intensifying timed work.

Frequently asked questions

Does the 9758 syllabus include polar-form complex numbers?

No. SEAB 9758 includes Cartesian-form complex numbers and Argand diagrams but excludes polar and exponential forms of complex numbers. Avoid transferring H2 Further Mathematics topics by accident.

Which examination paper tests Probability and Statistics?

Paper 2 has 60 marks of Probability and Statistics and 40 marks of Pure Mathematics. Paper 1 covers Pure Mathematics.

Can a graphing calculator replace written methods?

The syllabus expects an approved graphing calculator without computer algebra, but specified questions require mathematical steps or graph sketches. Show the reasoning where necessary.

Is this an official mandatory list?

No. These are 200 helpful study terms curated against published topics. The official SEAB syllabus has priority.

How should a student memorise these terms?

Use definition, example and contrast: for every new term, state an example and one common wrong interpretation, then solve a related question.

How can parents help?

Ask your student to explain one term aloud and show where it mattered in a marked solution. Understanding is more useful than reciting hundreds of words at speed.

Official syllabus and further eduKate reading

Sources checked 6 November 2026. Verify future exam-year changes with SEAB. Not an official government publication.