JC1 H2 Mathematics vocabulary begins with understanding functions, domains, ranges, graphs and mathematical notation. This guide explains 200 useful terms in plain English, so Singapore junior college students can read lectures, interpret questions and express reasoning accurately. The glossary follows the main themes of the SEAB H2 Mathematics syllabus 9758 for the 2027 A-Level examination.
Do not treat these 200 terms as a checklist to memorise in one sitting. The list includes JC1 foundations and concepts that many colleges teach later in JC2. Read the cluster connected to this week’s lesson, solve an example and explain the term without copying its definition.
- Find quickly: functions and inverses, transformations, equations, sequences, vectors, complex numbers, calculus, probability and statistics.
- Start with: domain, range, inverse, composition, gradient, stationary point, derivative and integration.
- Know the scope: this is an independent 200-term learning glossary, not an official or frequency-ranked SEAB word list.
Why JC1 Maths seems difficult even when the algebra looks familiar
Students often know a procedure but misunderstand the noun describing the task. ‘State the domain’ is not a request for a value of x. ‘Find the range’ asks about outputs, not permitted inputs. ‘Sketch’ usually means showing defining features, not merely reproducing a screen. Vocabulary changes what you are being asked to do.
The simplest repair method has three parts. Translate the term into a sentence you could say to a younger student. Connect it to a diagram, equation or worked solution. Finally, name an example that does not fit the definition. That last step makes the boundary clear.
Quick contents: all 200 H2 Mathematics terms
- Functions and mathematical language: 1–20
- Graphs and transformations: 21–40
- Equations and inequalities: 41–60
- Sequences and series: 61–80
- Vectors and three-dimensional geometry: 81–100
- Complex numbers: 101–120
- Limits and differentiation: 121–140
- Integration and differential equations: 141–160
- Probability and distributions: 161–180
- Statistics, inference and communication: 181–200
1. Functions and mathematical language (words 1–20)
Think of a function as a machine. Its formula tells you the rule, while its domain tells you which inputs the machine accepts.
- Function. A rule that assigns exactly one output to each permitted input.
- Domain. The set of inputs a function is allowed to accept.
- Range. The outputs a function actually produces over its stated domain.
- Codomain. The declared target set for outputs, sometimes larger than the range.
- Mapping. An assignment connecting inputs with outputs, often shown with arrows.
- Independent variable. The input whose value is selected, often represented by x.
- Dependent variable. The output determined by the input, often represented by y.
- One-to-one function. Distinct valid inputs always produce distinct outputs.
- Many-to-one function. Two or more distinct inputs can produce the same output.
- Inverse function. A rule reversing a one-to-one mapping, with input-output sets exchanged.
- Composite function. One function applied to the output of another function.
- Identity function. A function returning every input unchanged: I(x) = x.
- Piecewise function. A rule using different expressions on different portions of its domain.
- Modulus. Absolute value for a real number, or magnitude for a complex number.
- Parameter. A symbol fixed within one model but variable across a family of models.
- Constant. A specified quantity that does not vary inside the problem.
- Variable. A symbol standing for a changing or unknown quantity.
- Restriction. A stated limit on allowable inputs or values.
- Image. An output corresponding to a chosen input under a mapping.
- Preimage. An input or collection of inputs leading to a chosen output.
2. Graphs and transformations (words 21–40)
Before using the calculator, say what the graph should look like. A correct sketch must communicate shape, intercepts and restrictions.
- Cartesian plane. A coordinate system with perpendicular horizontal and vertical axes.
- Coordinate. A number locating a point along an axis.
- Intercept. A point where a graph meets a coordinate axis.
- Turning point. A position where a smooth curve switches between increasing and decreasing.
- Stationary point. A differentiable point at which the first derivative is zero.
- Local maximum. A function value at least as large as values sufficiently nearby.
- Local minimum. A function value no larger than values sufficiently nearby.
- Global maximum. The greatest value actually attained over the full stated domain.
- Global minimum. The smallest value actually attained over the full stated domain.
- Asymptote. A straight line approached by part of a curve in a limiting sense.
- Vertical asymptote. A vertical line approached as function values grow unboundedly.
- Horizontal asymptote. A horizontal line approached as inputs tend to infinity.
- Oblique asymptote. A sloping line approached by a curve far from the origin.
- Translation. A shift of a graph without a change in shape.
- Reflection. A transformation flipping a graph across a specified line.
- Stretch. A scale transformation changing distances in a specified direction.
- Symmetry. A graph property preserved under a reflection or rotation.
- Even function. A function satisfying f(−x) = f(x), symmetric about the y-axis.
- Odd function. A function satisfying f(−x) = −f(x), symmetric about the origin.
- Parametric equation. A coordinate expression defined using an additional parameter, often t.
3. Equations and inequalities (words 41–60)
Substitution may generate candidate roots, but only the original statement decides which are valid. Check excluded inputs first.
- Equation. A statement saying two expressions have equal values under stated conditions.
- Identity. An equality true throughout its valid domain.
- Inequality. A mathematical comparison using less-than or greater-than relationships.
- Solution set. All permitted values that make a statement true.
- Root. A value making a specified expression equal to zero.
- Multiplicity. The number of times a root occurs in a factorised polynomial.
- Polynomial. A finite sum of non-negative integer powers with constant coefficients.
- Rational function. A quotient of polynomials, excluding zeros of its denominator.
- Linear equation. An equation involving variables only to the first power.
- Quadratic equation. An equation of degree two, such as ax² + bx + c = 0.
- Cubic equation. An equation whose highest polynomial degree is three.
- Discriminant. For quadratics, b² − 4ac; its sign classifies real roots.
- Factorisation. Rewriting an expression as a product of simpler factors.
- Substitution. Replacing a symbol or expression with an equivalent value or new variable.
- Elimination. Combining simultaneous equations to remove an unknown.
- Extraneous solution. A candidate found during manipulation that fails the original statement.
- Interval notation. Brackets and parentheses used to express included or excluded endpoints.
- Sign diagram. A display showing where expressions are positive, negative or zero.
- Absolute-value inequality. A constraint on distance, such as |x − 2| < 3.
- Feasible region. All points satisfying every stated condition simultaneously.
4. Sequences and series (words 61–80)
Ask whether consecutive terms change by adding or multiplying. That one distinction determines which sequence model to investigate.
- Sequence. An ordered list of numbers following a stated rule.
- Series. The sum of the terms in a sequence.
- Term. One entry in a sequence, identified by its position.
- General term. A formula giving the nth term directly.
- Arithmetic progression. A sequence with a fixed difference between consecutive terms.
- Common difference. The constant added to reach the next arithmetic term.
- Geometric progression. A sequence with a fixed ratio between successive terms.
- Common ratio. The multiplier joining consecutive geometric terms.
- Partial sum. The total of the first n terms of a series.
- Summation notation. The sigma symbol and indices used to specify addition.
- Recurrence relation. A rule defining terms from one or more preceding terms.
- Finite series. A sum ending after a specified number of terms.
- Infinite series. A sum extending indefinitely and studied through partial sums.
- Convergence. Approaching a definite finite limit.
- Divergence. Failure to settle at a finite limit.
- Sum to infinity. The finite limiting value of partial sums for a convergent series.
- Exponential growth. Multiplicative increase by equal proportions across equal intervals.
- Exponential decay. Multiplicative decrease by equal proportions across equal intervals.
- Compound interest. Interest accumulating on both the initial amount and past interest.
- Induction. A proof approach using a base case and a step from n to n+1.
5. Vectors and three-dimensional geometry (words 81–100)
A point describes position. A vector describes displacement or direction. Keeping them separate prevents many geometry errors.
- Vector. A quantity with both magnitude and direction.
- Scalar. A magnitude-only quantity or a numerical multiplier of a vector.
- Position vector. A vector from the origin to a specified point.
- Displacement vector. A vector from an initial position to a final position.
- Direction vector. A non-zero vector parallel to a line.
- Magnitude. The length or size of a vector.
- Unit vector. A vector whose length equals one.
- Parallel vectors. Vectors related by a scalar multiple.
- Collinear points. Points lying on a single straight line.
- Coplanar vectors. Vectors that lie in the same plane.
- Scalar product. A vector product yielding a number, equal to |a||b|cos θ.
- Dot product. Another name for scalar product.
- Vector product. A three-dimensional product returning a perpendicular vector.
- Cross product. Another name for vector product.
- Angle between vectors. The smaller angle between two non-zero directed vectors.
- Normal vector. A vector perpendicular to a plane or line.
- Vector equation of line. A position vector plus a parameter times a direction vector.
- Cartesian equation of plane. An equation ax + by + cz = d in three-dimensional space.
- Shortest distance. The minimum separation between geometric objects.
- Projection. The component of one vector in a chosen direction.
6. Complex numbers (words 101–120)
Complex-number questions become more intelligible when you picture a point in the Argand plane alongside the algebra.
- Complex number. A value of the form a + bi where i² = −1.
- Real part. The real coefficient a in z = a + bi.
- Imaginary part. The real coefficient b in z = a + bi.
- Imaginary unit. The symbol i, defined by i² = −1.
- Complex conjugate. The number a − bi associated with a + bi.
- Modulus of complex number. The distance of a complex number from the origin.
- Argument. The directed angle made with the positive real axis.
- Principal argument. The representative angle selected from a stated principal interval.
- Argand diagram. A plane showing real components horizontally and imaginary components vertically.
- Cartesian form. The representation a + bi of a complex number.
- Polar form. A representation using modulus and argument.
- Euler form. The representation re^(iθ) of a non-zero complex number.
- Complex root. A possibly non-real solution of an equation.
- Conjugate pair. Two numbers with equal real parts and opposite imaginary parts.
- De Moivre’s theorem. A relationship between integer powers and multiples of complex arguments.
- Locus. All points or complex numbers satisfying a stated condition.
- Rotation in Argand plane. The change in direction produced by multiplying by a unit complex number.
- Complex multiplication. An operation multiplying moduli and adding arguments in polar form.
- Real coefficient. A polynomial coefficient drawn from the real numbers.
- Quadratic factor. A degree-two polynomial factor, sometimes formed by conjugate roots.
7. Limits and differentiation (words 121–140)
A derivative is not merely a differentiated expression. It answers a change question and may have physical units.
- Limit. A value approached by a function near a specified input.
- Continuity. A function agreeing with its limiting behaviour at a point.
- Derivative. The instantaneous rate of change or tangent gradient.
- Differentiation. The process of calculating derivatives.
- First derivative. A function describing gradient and instantaneous change.
- Second derivative. The derivative of the first derivative, indicating how gradient changes.
- Gradient. The slope of a line or a curve’s tangent.
- Tangent. A line sharing a curve’s local direction at a point.
- Normal line. A line perpendicular to a tangent at the contact point.
- Chain rule. A rule for differentiating a composite function.
- Product rule. A rule for differentiating the product of functions.
- Quotient rule. A rule for differentiating a quotient with non-zero denominator.
- Implicit differentiation. Differentiating a relationship without explicitly isolating y.
- Parametric differentiation. Computing dy/dx using derivatives with respect to a shared parameter.
- Rate of change. The change in a quantity per unit change in another.
- Related rates. A technique linking rates of quantities connected by an equation.
- Optimisation. Finding the largest or smallest permitted value.
- Critical value. An input at which a derivative is zero or undefined.
- Increasing function. Outputs become larger as inputs increase on a stated interval.
- Decreasing function. Outputs become smaller as inputs increase on a stated interval.
8. Integration and differential equations (words 141–160)
An indefinite integral needs a constant; a definite integral evaluates an accumulation over limits. Remember signed area.
- Antiderivative. A function whose derivative is a given expression.
- Indefinite integral. A family of antiderivatives containing an arbitrary constant.
- Constant of integration. An additive constant included after indefinite integration.
- Definite integral. A signed accumulation between stated bounds.
- Fundamental theorem of calculus. A key connection between differentiation and definite integration.
- Integrand. The expression being integrated.
- Variable of integration. The variable named after the differential symbol.
- Integration by substitution. A method changing variables to simplify an integral.
- Integration by parts. An integration rule derived from the differentiation product rule.
- Area under curve. Geometric area bounded by a curve and a chosen axis.
- Signed area. An integral counting contributions below the axis negatively.
- Area between curves. The integrated difference between upper and lower functions.
- Volume of revolution. The volume obtained by rotating a region around an axis.
- Differential equation. An equation involving a function and its derivatives.
- Order of differential equation. The highest derivative order present in the equation.
- Separable differential equation. A differential equation rearrangeable into separate variable expressions.
- Initial condition. A given value selecting a particular solution.
- General solution. A family of possible solutions, often containing constants.
- Particular solution. One member of a solution family meeting the stated conditions.
- Mathematical model. A representation of a real process using assumptions and mathematical relationships.
9. Probability and distributions (words 161–180)
Probability starts with a clearly defined event and a model of dependence. Equations without those assumptions can mislead.
- Random experiment. A process with an uncertain outcome.
- Sample space. All possible outcomes of a random experiment.
- Event. A specified collection of outcomes.
- Complement. The event that a specified event does not occur.
- Mutually exclusive events. Events that cannot occur together.
- Independent events. Events whose probabilities do not influence one another.
- Conditional probability. The probability of an event given another has occurred.
- Addition rule. A relation for finding the probability of a union of events.
- Multiplication rule. A relation linking joint and conditional probabilities.
- Bayes’ theorem. A method of updating conditional probabilities using new information.
- Random variable. A numerical quantity determined by a random outcome.
- Discrete variable. A variable taking separated countable values.
- Continuous variable. A variable taking possible values across intervals.
- Probability distribution. A model assigning probabilities to possible random-variable values.
- Expected value. The probability-weighted average of possible values.
- Variance. The average squared deviation from the mean under a distribution.
- Standard deviation. The square root of variance, measuring spread in original units.
- Binomial distribution. A model counting successes in fixed independent Bernoulli trials.
- Normal distribution. A symmetrical bell-shaped continuous probability model.
- Standardisation. Converting a value to a common scale, often a z-score.
10. Statistics, inference and communication (words 181–200)
Statistical evidence is not proof. Explain hypotheses, assumptions and uncertainty as carefully as you give a computed answer.
- Population. The complete group a study aims to describe.
- Sample. A selected subset used to study a larger population.
- Sampling distribution. The distribution of a statistic across repeated samples.
- Sample mean. The average of the observed sample values.
- Population mean. The true average across the entire population.
- Unbiased estimator. A statistic whose expectation equals the parameter it estimates.
- Null hypothesis. The starting statistical claim tested with data.
- Alternative hypothesis. A competing statistical claim evaluated against the null.
- Significance level. The chosen probability of rejecting a true null hypothesis.
- p-value. The probability under the null model of data at least this extreme.
- Critical region. Test results that lead to rejecting the null hypothesis.
- One-tailed test. A test whose alternative points in one direction.
- Two-tailed test. A test allowing departures on either side.
- Type I error. Rejecting a null hypothesis that is actually true.
- Type II error. Failing to reject a null hypothesis that is actually false.
- Correlation. A measure of association, not proof that one variable causes another.
- Regression. A method fitting a relationship between variables.
- Residual. The observed value minus its model-predicted value.
- Interpolation. Estimating inside the observed data range.
- Extrapolation. Predicting beyond the observed data range, with added uncertainty.
Worked example: domain, range and inverse
Let f(x) = 2x + 3 for x ≥ 0. The domain is x ≥ 0 and the range is y ≥ 3. Rearranging y = 2x + 3 gives the inverse f⁻¹(x) = (x − 3)/2. Its domain is x ≥ 3. The inverse operation has changed not only the formula but which values are accepted as inputs. This is why ‘domain’ and ‘inverse’ must be understood together.
Worked example: a stationary point is not automatically a maximum
For f(x) = x³, the derivative is f′(x) = 3x² and f′(0) = 0. The origin is stationary, but the curve is increasing on both sides of zero. By contrast, for g(x) = 4x − x², g′(x) = 4 − 2x, giving a stationary point at x = 2. Since g″(x) = −2, it is a maximum. The words stationary, turning and maximum cannot be interchanged.
Worked example: interpreting a p-value
If a test gives p = 0.03 with a preselected 5% significance level, the result is unusual enough under the null hypothesis to reject that hypothesis at the 5% level. It does not mean the null hypothesis has a 3% chance of being true. Distinguishing a result from an interpretation is part of being mathematically literate.
Four-week vocabulary-to-problem routine
- Week 1: Pick 40 terms from current lessons. Write one example and one near miss for each. Revisit domains and restrictions daily.
- Week 2: Add 40 more terms. Redo tutorial questions using correct language, showing why the technique applies.
- Week 3: Select confusing pairs: inverse versus reciprocal, tangent versus normal, maximum versus stationary, independent versus mutually exclusive. Explain both sides of each pair.
- Week 4: Use an error log from a timed assignment. For every error, identify which term or assumption you misunderstood, then solve a different question to check transfer.
FAQ: JC1 H2 Mathematics in Singapore
Does JC1 cover all 200 words?
No. The 2027 syllabus describes the full A-Level subject. Junior colleges can teach its topics in different orders, so terms from later probability, statistics or other areas are included as reference material rather than immediate JC1 requirements.
Is H2 Mathematics the same as O-Level Additional Mathematics?
No. H2 builds on O-Level Mathematics and assumes Additional Mathematics knowledge in several areas. It extends ideas into functions, calculus, vectors, complex numbers and statistical reasoning with new application requirements.
Should I memorise definitions or practise questions?
Do both in a connected way. Define a term, spot it in a question, choose a method and explain the answer. Simply reproducing a definition does not demonstrate application.
Can a graphing calculator replace working?
No. The examination uses an approved graphing calculator, but some questions call for mathematical steps or justification. A calculator answer still has to satisfy the question’s accuracy and working requirements.
How can a parent help?
Ask the student to describe one new concept, give a correct example, and explain a common mistake. This reveals understanding without requiring the parent to teach the calculation.
Official syllabus and further reading
Verify examinable scope against the SEAB 2027 H2 Mathematics syllabus (9758). For an early topic, read JC1 functions, domain and inverse. For subject choices, read H1 versus H2 Mathematics and university options. Return to eduKate Singapore when you need the next lesson.
Teaching guide
Introduce precise vocabulary only alongside a solved problem, a failed attempt or an explanation of a graph. Ask what the term means, where it applies and what would make it invalid. A learner has mastered a word when they can use it correctly in a new question, not just recite it.