Top 200 Secondary 4 Mathematics Vocabulary

Secondary 4 Mathematics vocabulary means understanding the exact meaning of words in mathematical questions. This guide provides 200 key terms with short definitions, arranged from numbers and algebra through graphs, geometry, statistics, probability and real-world problem-solving. Learn the words with the operations that make them true; do not memorise definitions without working examples.

For the 2026 GCE O-Level, Mathematics is listed as 4052. For the first 2027 Singapore-Cambridge SEC at G3, the Mathematics code is K310. The subject level and examination year matter. This 200-term glossary is an independently prepared learning guide, not an official SEAB prescribed list, and selected extension terms are included to build interpretation beyond minimum requirements.

Start here:

Find the meaning of 200 mathematical words, symbols and question commands.
Study worked examples that show why a missing definition causes a wrong method.
Use the four-week vocabulary-to-problem-solving schedule.
Check real-life examples involving money, measurement and data.
Confirm the correct official syllabus using the links below.

Top 200 Secondary 4 Mathematics Vocabulary Words and Definitions

The 200 entries are numbered so students can revise small sets. Technical phrases are treated as single entries where that is how the mathematical idea is normally named.

1. Number vocabulary: know what kind of number is being used — terms 1–20

Many errors start before calculation: the student reads a number type incorrectly. Always ask whether a value can be negative, zero or fractional.

integer — A whole number that may be positive, negative or zero.
natural number — A counting number; conventions differ on whether zero is included.
rational number — A number expressible as a ratio of two integers with nonzero denominator.
irrational number — A real number that cannot be expressed as such a ratio.
real number — A number represented on the continuous number line.
prime number — An integer greater than one with exactly two positive factors.
composite number — A positive integer greater than one that is not prime.
factor — A number or expression that divides another exactly.
multiple — A number obtained by multiplying by an integer.
highest common factor — The greatest positive integer dividing given integers.
lowest common multiple — The smallest positive common multiple of given integers.
exponent — The small raised number indicating a power.
base — The number or expression being raised to a power.
index — Another name for an exponent in index notation.
radical — A root expression represented by a radical symbol.
square root — A number whose square is a given number.
cube root — A number whose cube is a given number.
reciprocal — A number whose product with the original is one.
absolute value — The nonnegative distance from zero on the number line.
order of operations — The agreed sequence for evaluating mixed operations.

2. Algebra: equations are relationships, not tricks — terms 21–40

In algebra, an equals sign asserts a relationship. You cannot change one side of an equation without maintaining equality.

variable — A symbol representing a quantity that can change or be unknown.
constant — A value that does not change in the given context.
coefficient — A numerical or symbolic multiplier of a term.
term — One part of an expression separated by addition or subtraction.
expression — A mathematical phrase without an equals or inequality relation.
equation — A statement that two expressions have equal values.
identity — An equality true for every permitted variable value.
formula — A rule expressing a relationship among quantities.
substitution — Replacing a variable with a given value or expression.
simplification — Rewriting an expression into an equivalent simpler form.
expansion — Removing brackets using valid algebraic operations.
factorisation — Rewriting an expression as a product of factors.
linear — Of first degree when referring to a polynomial in one variable.
quadratic — Of second degree when referring to a polynomial in one variable.
polynomial — A finite sum of terms with nonnegative integer variable powers.
simultaneous equations — Two or more equations considered together for common solutions.
inequality — A statement comparing values using unequal relations.
solution set — All values that satisfy the given conditions.
rearrangement — Rewriting a formula to isolate the required variable.
subject of formula — The variable expressed alone on one side of a formula.

3. Graphs, functions and coordinates — terms 41–60

Before using a formula, read the graph: check axes, scales, units and whether the relationship is linear or curved.

relation — A collection of ordered pairs linking quantities.
function — A relation assigning exactly one output to each allowed input.
domain — The set of permitted input values of a function.
range — The set of actual output values.
mapping — An assignment from elements of one set to another.
independent variable — The input whose value is selected or controlled.
dependent variable — The output determined by an input relationship.
Cartesian plane — A plane defined by two perpendicular coordinate axes.
origin — The point where the coordinate axes meet.
coordinate — A number locating a point along an axis.
gradient — The change in vertical value divided by change in horizontal value.
intercept — Where a graph meets an axis.
x-intercept — Where a graph crosses or touches the horizontal axis.
y-intercept — Where a graph crosses or touches the vertical axis.
linear graph — The graph of a first-degree equation in two variables.
quadratic graph — The graph of a second-degree function in one variable.
parabola — The curved shape formed by a quadratic-function graph.
axis of symmetry — A line dividing a figure into mirror-image halves.
vertex — The point where the arms of an angle meet; also a graph turning point in context.
turning point — A point where a graph changes from increasing to decreasing or conversely.

4. Angles, shapes and transformations — terms 61–80

Angle words often encode relationships. Draw a small diagram and mark which lines are parallel before invoking an angle rule.

point — An exact location with no size.
line segment — A straight part of a line with two endpoints.
ray — A straight path with one endpoint continuing indefinitely.
parallel — Lines in the same plane that never meet.
perpendicular — Lines meeting at a right angle.
transversal — A line cutting across two or more other lines.
alternate angles — Angle pairs formed on alternate sides of a transversal.
corresponding angles — Angles in matching relative positions at line intersections.
interior angles — Angles lying inside a geometric figure.
exterior angles — Angles formed outside a figure by extending a side.
complementary angles — Two angles whose measures add to 90 degrees.
supplementary angles — Two angles whose measures add to 180 degrees.
polygon — A closed plane figure made from straight line segments.
regular polygon — A polygon with equal sides and equal interior angles.
congruence — Equality of shape and size.
similarity — Matching shape with possibly different size.
scale factor — A multiplier connecting corresponding lengths.
reflection — A transformation mirroring a shape across a line.
rotation — A transformation turning a shape about a fixed centre.
translation — A transformation sliding every point by the same vector.

5. Measurement, circles and trigonometric language — terms 81–100

Measurement language tells you which quantity to calculate. Do not mistake area (square units) for perimeter (length units).

perimeter — Total distance around a plane figure.
area — Amount of space inside a two-dimensional region.
surface area — Sum of areas of a solid’s outer faces or surfaces.
volume — Space occupied by a three-dimensional object.
circumference — Distance all the way around a circle.
diameter — A chord of a circle through its centre.
radius — Distance from the centre of a circle to its circumference.
chord — A line segment joining two points on a circle.
arc — A connected portion of a circle’s circumference.
sector — A region bounded by two radii and the included arc.
circular segment — A region enclosed by a chord and its corresponding arc.
central angle — An angle with its vertex at a circle’s centre.
tangent line — A straight line meeting a circle at exactly one point.
sine — In a right triangle, opposite side divided by hypotenuse.
cosine — In a right triangle, adjacent side divided by hypotenuse.
tangent ratio — In a right triangle, opposite side divided by adjacent side.
hypotenuse — The side opposite the right angle of a right triangle.
bearing — A direction measured clockwise from north.
angle of elevation — An angle measured upward from the horizontal.
angle of depression — An angle measured downward from the horizontal.

6. Statistics: what data summaries actually say — terms 101–120

Statistics is more than drawing a graph. Think about who was measured, the shape of the distribution and whether an outlier changes the mean.

population — The entire group about which a study asks.
sample — A selected part of a population.
census — Collection of information from every member of a population.
random sampling — Selection using chance rather than a chosen preference.
frequency — The number of observations in a category.
relative frequency — A category frequency divided by the total frequency.
cumulative frequency — The running total of frequencies up to a value.
class interval — A range used to group continuous measurements.
class midpoint — The value halfway between a class interval’s boundaries.
mean — The total of values divided by their number.
median — The middle value after observations are ordered.
mode — The most frequently occurring value.
interquartile range — The difference between the upper and lower quartiles.
lower quartile — A value marking roughly the lower quarter of ordered data.
upper quartile — A value marking roughly the upper three-quarters of ordered data.
outlier — An observation unusually far from much of the data.
histogram — A graph using adjoining bars to show frequency density.
box plot — A display summarising median, quartiles and spread.
scatter plot — A display of paired data as points.
correlation — The tendency of two measured variables to vary together.

7. Probability and sets — terms 121–140

In probability, the denominator must describe the correct sample space. Check whether events overlap or one event changes the next.

experiment — A repeatable process whose outcome may be uncertain.
outcome — One possible result of an experiment.
event — A specified collection of possible outcomes.
sample space — The set of all possible outcomes.
equally likely — Having the same probability as another outcome.
probability — A numerical measure of how likely an event is.
complement — The outcomes not included in a specified event.
mutually exclusive — Events that cannot occur at the same time.
independent events — Events where one occurrence does not change the other’s probability.
dependent events — Events where one occurrence changes another’s probability.
union — All elements belonging to either or both of two sets.
intersection — The elements shared by two sets.
universal set — The complete collection under discussion.
subset — A set whose elements all belong to another set.
element — A member of a set.
empty set — A set containing no elements.
Venn diagram — Overlapping closed curves representing relationships among sets.
tree diagram — A branching display of possible successive outcomes.
favourable outcomes — Outcomes that satisfy the event being measured.
conditional probability — Probability of an event given that another event occurred.

8. Money, ratios, change and everyday applications — terms 141–160

Real-world mathematics involves assumptions, fees, time, units and rounding. A correct percentage can still answer the wrong practical question.

ratio — A comparison of quantities by division.
proportion — An equality between two ratios.
direct proportion — A relationship where one quantity scales by the same factor as another.
inverse proportion — A relationship where the product of two quantities stays constant.
rate — A comparison of quantities with different units.
speed — Distance travelled per unit time.
distance — The length travelled or separation between points.
time interval — The duration between two instants.
percentage — A proportion expressed out of one hundred.
discount — A reduction from the original selling price.
tax — A compulsory charge imposed under applicable rules.
simple interest — Interest calculated on the original principal only.
compound interest — Interest calculated on a changing accumulated amount.
growth factor — The multiplier describing an increase in a period.
decay factor — The multiplier describing a decrease in a period.
currency conversion — Changing an amount from one currency into another.
unit cost — The cost per single standard unit.
exchange rate — The value of one currency in terms of another.
scale drawing — A drawing whose lengths correspond by a fixed scale.
estimation — A sensible approximation when an exact calculation is unnecessary.

9. What examination verbs are asking you to do — terms 161–180

Command verbs require different responses: state may need a short result, while prove and justify require a chain of reasons.

calculate — Find a value through mathematical operations.
determine — Find an answer using available information.
deduce — Reach a result from established facts.
justify — Explain with valid mathematical reasons.
prove — Demonstrate that a mathematical claim must be true.
show that — Supply working that establishes a given result.
hence — Use the result already obtained to take the next step.
solve — Find the value or values satisfying the conditions.
construct — Produce an accurate geometric figure using specified tools.
sketch — Draw an approximately correct shape showing its main features.
plot — Mark data points or a graph on axes.
label — Write the required names or values beside a diagram.
approximate — Replace a value with one sufficiently close for the purpose.
round — Replace a number with a specified simpler representation.
significant figures — Digits that communicate a value’s stated precision.
decimal places — The number of digits written after the decimal point.
exact value — A value kept without rounding error.
verify — Check that a proposed result satisfies requirements.
state — Provide the requested answer concisely.
explain — Describe the mathematical reason or relationship.

10. Modelling, accuracy and error diagnosis — terms 181–200

Reliable work includes a reasonableness check: what would the answer mean for a person buying something, travelling or reading a graph?

assumption — A simplifying condition accepted for a model.
mathematical model — A representation of real conditions using mathematical relationships.
constraint — A restriction on permitted values or choices.
boundary — A limit separating permitted and non-permitted values.
maximum — The greatest value within the relevant domain.
minimum — The least value within the relevant domain.
optimum — The best permitted result under a chosen criterion.
feasible solution — A solution satisfying all stated restrictions.
interval — A continuous set of values between endpoints.
upper bound — A stated limit above which the value cannot lie.
lower bound — A stated limit below which the value cannot lie.
tolerance — An acceptable range around a target measurement.
accuracy — How close a measurement or estimate is to a true value.
precision — The fineness or consistency of measurements, not necessarily correctness.
units — Standard labels showing what a quantity measures.
dimension — A basic physical quantity type such as length or time.
inverse operation — An operation that undoes another operation.
substitution check — Putting a found answer back into the original condition.
reasonableness — Whether a result makes sense in context and magnitude.
counterexample — One valid case disproving a universal mathematical claim.

Five Worked Examples: The Word That Determines the Method

Example 1: Factorise, expand and solve are different tasks

Consider 3(x − 2) = 12. To expand, write 3x − 6 = 12. To solve, add 6 to both sides and divide by 3, giving x = 6. To verify, substitute x = 6 into the original equation: 3(6 − 2) = 12. The three verbs lead to different mathematical actions.

Common error: Students see “solve” and stop at 3x − 6 = 12. Their algebra may be correct, but the question is unanswered. Read the instruction before beginning the working.

Example 2: Gradient and intercept reveal a story

A taxi-style example uses the simplified relationship C = 2d + 3, where C is a hypothetical fare in dollars and d is distance in kilometres. The gradient 2 means the model adds $2 for every additional kilometre; the y-intercept 3 represents the starting charge when distance is zero. These figures are illustrative, not a real taxi tariff.

Two questions follow. What is the fare at 4 km? The model gives C = 2(4) + 3 = $11. Is it sensible to extrapolate to any distance? Not necessarily: actual services may add waiting fees, surcharges, minimums or different rate bands. The graph models only the assumptions it includes.

Example 3: Percentage increase versus percentage points

If a survey response rises from 40% to 50%, that is a change of 10 percentage points. Relative to the original 40%, the percentage increase is (50 − 40) ÷ 40 × 100% = 25%. Confusing these two types of change leads to misleading statements in financial, political and scientific reporting.

Example 4: Mean, median and outliers

Suppose the daily reading times in minutes are 10, 15, 20, 25 and 130. The mean is (10 + 15 + 20 + 25 + 130) ÷ 5 = 40 minutes. The median is 20 minutes. The very large value 130 pulls the mean upwards. Neither statistic is automatically wrong: the appropriate summary depends on what the question asks.

Example 5: A probability complement

A bag contains three red counters and two blue counters. With one random draw, P(red) = 3/5, so P(not red) = 1 − 3/5 = 2/5. This is the complement of the red event. With two draws without replacement, probabilities change after the first selection; do not assume independence without checking the process.

The Vocabulary-to-Working Repair Method

When a student loses marks, identify the first incorrect decision, not only the final answer. A graph answer may fail because the student misread gradient. A geometry proof may fail because the student does not know the conditions under which alternate angles are equal. A probability answer may fail because the denominator describes the wrong sample space.

Underline the command verb: What must the completed response do?
Translate the technical terms: State the meaning of each crucial quantity in ordinary language.
Choose a valid relationship: Write the equation or theorem with its necessary conditions.
Carry units and signs: A value is not fully interpreted without its direction, size and units where appropriate.
Check the original question: Substitute an answer, estimate its magnitude or compare it with the diagram and constraints.

Consider a frequent trap: “The length is at least 5 cm.” That means length ≥ 5 cm, not length > 5 cm. The phrase includes exactly 5. “More than 5 cm” excludes it. These two short expressions can completely change an inequality solution set.

Another trap occurs in reverse percentage. If a price after a 20% discount is $80, the original price is not $80 + 20% of $80. It is $80 ÷ 0.8 = $100. The base of the percentage matters.

How the 200 Terms Connect to Singapore Life

Household spending: Use unit cost and percentage correctly when comparing packs. A large discount is not automatically the cheapest option if pack sizes differ. Make the denominator comparable before concluding.

Travel: The difference between speed and distance becomes obvious when a train service is interrupted. Average speed requires total distance divided by total elapsed time, including a wait if the question asks for the overall journey.

Public data: When a graph shows a change in test scores or prices, ask whether the vertical axis begins at zero, whether the sample represents the wider population and whether two trends merely correlate.

Design: Surface area and volume behave differently when an object is scaled. Doubling every length multiplies a similar solid’s surface area by four and its volume by eight. The words name different dimensions.

Four-Week Secondary 4 Mathematics Language Plan

Week 1 — Core control: Revise entries 1–50. Every day, translate five expressions into ordinary language and solve three problems requiring different command verbs.
Week 2 — Geometry and data: Revise entries 51–100. Draw a diagram from a verbal description and explain why a theorem is applicable.
Week 3 — Probability and applications: Revise entries 101–150. Work through short everyday problems, stating assumptions and units before calculating.
Week 4 — Exam interpretation: Revise entries 151–200. Practise reading the final sentence of each question, then check whether working answers the exact request.

Use a simple error notebook with four columns: question wording, misread term, correct meaning, next successful example. Improvement is visible when the same error stops appearing across unfamiliar questions, not merely when a memorised worksheet becomes fast.

Frequently Asked Questions About Secondary 4 Mathematics Vocabulary

Are all 200 items in the G3 SEAB syllabus?

No. The glossary deliberately combines important subject vocabulary, problem-solving language and some mathematical extension terms. It is not a syllabus checklist. The official syllabus determines assessable content for each year and level.

What is the difference between Mathematics 4052 and K310?

4052 is the 2026 GCE O-Level Mathematics subject code; K310 is the 2027 SEC G3 Mathematics subject code. They refer to different examination systems and years. Use the relevant SEAB document for the details.

Is Additional Mathematics the same as Mathematics?

No. They have different syllabuses and subject codes; in 2027 G3, Additional Mathematics is K341. This page explains the broad Mathematics vocabulary, not a replacement for Additional Mathematics preparation.

Should students memorise every definition before doing questions?

No. Learn the term while solving a corresponding example. Definitions become useful when a student can recognise a situation, choose the correct operation and explain why it works.

How do we know whether a student needs more tuition or simply better reading of questions?

Inspect completed work first. If the student understands the mathematics when a term is explained, begin with language repair and independent practice. If the underlying concept is missing, a more structured teaching plan may help. Choose support only after the starting position is clear.

Are worked numerical examples actual past examination questions?

No. The examples here are original illustrations prepared to teach the language. For official assessment design and content, consult SEAB’s year-specific syllabus.

Official References and Related eduKate Guides

Editorial update: 6 November 2026. This study glossary is independent of MOE and SEAB. Follow the official syllabus and your school’s instructions for examinations.

Top 200 Vocabulary for Secondary 4 Mathematics | O-Level and SEC 2027 Formulas, Graphs and Problem-Solving Guide