Secondary 2 Mathematics vocabulary is the language that makes algebra, graphs, geometry, statistics and word problems understandable. This guide gives students 200 practical mathematical terms with short definitions, then shows how to turn those words into reliable working and checked answers. Start with the numbered list rather than guessing what an unfamiliar instruction means.
These are 200 eduKateSG-selected terms, not a prescribed MOE or SEAB examination vocabulary list. Students in Singapore may take Mathematics at G1, G2 or G3 under Full Subject-Based Banding. The exact sequence and depth of topics depend on the subject level and school. Some vocabulary here bridges Secondary 1 and 2 and introduces language useful for upper secondary; it should not be mistaken for a promise that every topic appears in every Secondary 2 assessment.
Quick route:
- Words 1–80 explain number sense, algebra, equations and rates;
- words 81–140 clarify graphs, geometry and mensuration;
- words 141–200 support statistics, reasoning and everyday applications;
- worked examples below show the difference between knowing a definition and solving a question;
- the four-week plan helps diagnose errors before adding more practice.
Top 200 Secondary 2 Mathematics vocabulary words and meanings
1. Numbers, operations and numerical structure — words 1–20
Check each definition against one simple example. A mathematical word is useful when it tells the student what an object is, how it behaves, or what operation is permitted.
- integer — A whole number, including zero and negative whole numbers.
- rational number — A number expressible as a fraction of two integers with non-zero denominator.
- irrational number — A real number that cannot be expressed as a ratio of integers.
- real number — A number represented by a point on the number line.
- negative number — A number less than zero, such as negative four.
- absolute value — A number’s distance from zero, ignoring direction.
- magnitude — The size of a quantity without considering its sign.
- reciprocal — The multiplicative inverse; three has reciprocal one-third.
- prime factor — A factor that is also a prime number.
- prime factorisation — Writing an integer as a product of prime numbers.
- highest common factor — The largest positive factor shared by given integers.
- lowest common multiple — The smallest positive multiple shared by given integers.
- square — The product of a number multiplied by itself.
- cube — The product of a number multiplied by itself twice.
- square root — A value that gives the original number when squared.
- cube root — A value that gives the original number when cubed.
- index notation — Compact notation representing repeated multiplication by a base.
- exponent — The raised number that tells how many factors are multiplied.
- base — The number being raised to a power in an exponent expression.
- order of operations — The conventions for deciding which calculation to carry out first.
2. Algebra, symbols and expressions — words 21–40
Check each definition against one simple example. A mathematical word is useful when it tells the student what an object is, how it behaves, or what operation is permitted.
- variable — A symbol used to represent a value that may vary.
- constant — A fixed value in a particular calculation or expression.
- coefficient — A number multiplying a variable or algebraic term.
- term — A part of an expression separated by plus or minus signs.
- like terms — Terms with matching variable factors and matching powers.
- unlike terms — Terms that cannot be combined directly by addition.
- expression — A mathematical phrase without an equals sign stating an equation.
- algebraic expression — An expression that combines numbers, variables and operations.
- substitution — Replacing a variable with a given numerical value or expression.
- simplification — Rewriting an expression in a clearer equivalent form.
- expansion — Removing brackets correctly using multiplication.
- factor — A number or expression multiplied to produce a product.
- bracket — A grouping symbol that controls how parts are treated.
- distributive property — The rule linking multiplication of a sum to separate products.
- associative property — The rule allowing regrouping for addition or multiplication.
- commutative property — The rule allowing order to change for addition or multiplication.
- identity — An equality true for all permitted values of its variables.
- equivalent expression — A differently written expression with the same value for permitted inputs.
- formula — A rule expressing a relationship using mathematical symbols.
- subject of a formula — The variable written alone on one side of an equation.
3. Equations, unknowns and inequalities — words 41–60
Check each definition against one simple example. A mathematical word is useful when it tells the student what an object is, how it behaves, or what operation is permitted.
- equation — A statement that two expressions are equal.
- linear equation — An equation where the unknown has power one in the relevant form.
- solution — A value that makes an equation or problem condition true.
- root — A solution of an equation, often where an expression equals zero.
- balance principle — Applying equal valid operations to both sides preserves equality.
- inverse operation — An operation that reverses another operation.
- elimination — Removing an unknown by combining equations or expressions appropriately.
- rearrangement — Changing a formula’s form while keeping its relationship valid.
- inequality — A comparison stating that quantities are not equal in a specified direction.
- number line — A line representing ordered numerical values and intervals.
- interval — A connected set of numerical values between boundaries.
- strict inequality — A comparison using less-than or greater-than without equality.
- inclusive inequality — A comparison allowing equality at a boundary.
- simultaneous equations — Equations that must hold together for the same unknown values.
- linear relationship — A relationship that gives a straight-line graph.
- unknown — A value that must be determined from the information given.
- checking by substitution — Putting a proposed answer into the original equation to verify it.
- consistency — Agreement among the conditions or equations of a problem.
- restriction — A rule limiting which values are permitted.
- boundary — An edge value separating permitted from excluded cases.
4. Ratio, rate, percentage and financial arithmetic — words 61–80
Check each definition against one simple example. A mathematical word is useful when it tells the student what an object is, how it behaves, or what operation is permitted.
- ratio — A comparison of quantities by division.
- proportion — A relationship stating that two ratios are equal.
- direct proportion — A relationship in which one quantity is a constant multiple of another.
- inverse proportion — A relationship where the product of two varying quantities is constant.
- unit rate — A rate expressed per one unit of the comparison quantity.
- rate — The amount of change or activity relative to another quantity.
- average speed — Total distance divided by total time for a journey.
- distance — How far something travels or the separation between points.
- elapsed time — The time that passes between two events.
- conversion factor — A multiplier used to change units without changing the underlying quantity.
- percentage — A way of expressing a ratio in parts per hundred.
- percentage point — A difference between two percentage figures, not a relative percent change.
- percentage increase — How much a value rises relative to its original value.
- percentage decrease — How much a value falls relative to its original value.
- reverse percentage — Finding the original value when a final value and percentage change are known.
- discount — A reduction from the stated selling price.
- markup — An amount added to cost to obtain a selling price.
- interest — A charge for borrowing or return on money, depending on context.
- commission — Payment calculated as a portion of sales or transactions.
- scale factor — A multiplier describing enlargement, reduction or a scale relationship.
5. Coordinates, straight lines and data graphs — words 81–100
Check each definition against one simple example. A mathematical word is useful when it tells the student what an object is, how it behaves, or what operation is permitted.
- Cartesian plane — A grid using two perpendicular number axes.
- coordinate — A numerical position along an axis or within a system.
- ordered pair — Two numbers written in an order, usually x then y.
- origin — The point where both coordinate axes meet, usually zero-zero.
- x-axis — The horizontal axis of a usual Cartesian graph.
- y-axis — The vertical axis of a usual Cartesian graph.
- gradient — How steeply a line rises or falls, expressed as change in y over change in x.
- y-intercept — The point where a graph meets the vertical axis.
- x-intercept — The point where a graph meets the horizontal axis.
- horizontal line — A line with constant y-coordinate.
- vertical line — A line with constant x-coordinate.
- slope — Another name for a line’s gradient.
- equation of a line — A symbolic rule describing points on a line.
- table of values — Paired inputs and outputs used to describe a relationship.
- plot — Place a point or graph accurately on axes.
- line graph — A display connecting data points to show change or relationship.
- linear graph — A graph that forms a straight line.
- intersection — A point where two graphs or shapes meet.
- interpolation — Estimating a value inside the range of observed data.
- extrapolation — Estimating beyond observed data; it requires extra caution.
6. Angles and geometrical relationships — words 101–120
Check each definition against one simple example. A mathematical word is useful when it tells the student what an object is, how it behaves, or what operation is permitted.
- acute angle — An angle greater than zero and less than ninety degrees.
- obtuse angle — An angle greater than ninety and less than one hundred eighty degrees.
- right angle — An angle measuring exactly ninety degrees.
- straight angle — An angle measuring exactly one hundred eighty degrees.
- reflex angle — An angle greater than one hundred eighty and less than three hundred sixty degrees.
- complementary angles — Angles whose measures add to ninety degrees.
- supplementary angles — Angles whose measures add to one hundred eighty degrees.
- vertically opposite angles — Opposite angles formed by crossing lines; they are equal.
- corresponding angles — Angles in matching positions when a transversal crosses two lines.
- alternate angles — Angles on opposite sides of a transversal in relevant matching positions.
- co-interior angles — Interior angles on one side of a transversal; supplementary for parallel lines.
- transversal — A line crossing two or more other lines.
- parallel lines — Lines in one plane that never meet.
- perpendicular lines — Lines meeting at a right angle.
- triangle — A polygon with three sides and three interior angles.
- quadrilateral — A polygon with four sides.
- polygon — A closed two-dimensional figure formed by straight segments.
- regular polygon — A polygon whose sides and interior angles are all equal.
- line symmetry — A reflection that leaves a shape unchanged.
- congruence — The relation between shapes having matching size and shape.
7. Mensuration, shapes, units and accuracy — words 121–140
Check each definition against one simple example. A mathematical word is useful when it tells the student what an object is, how it behaves, or what operation is permitted.
- perimeter — The total length around a two-dimensional figure.
- area — The size of a two-dimensional region.
- volume — The three-dimensional space occupied by an object.
- surface area — The total area of the exterior faces or surfaces of a solid.
- capacity — The amount a container can hold.
- radius — A line segment from the centre of a circle to its boundary.
- diameter — A chord passing through the centre of a circle.
- circumference — The distance around a circle.
- pi — The constant ratio of a circle’s circumference to its diameter.
- chord — A straight segment joining two points on a circle.
- arc — A part of the curved boundary of a circle.
- sector — A region enclosed by two radii and an arc.
- net — A flat arrangement of faces that folds into a three-dimensional solid.
- prism — A solid with a uniform polygonal cross-section along its length.
- cylinder — A solid with two parallel congruent circular bases.
- square unit — An area unit such as a square centimetre.
- cubic unit — A volume unit such as a cubic centimetre.
- precision — The degree of detail expressed by a measurement or calculation.
- significant figures — Digits used to communicate the precision of a number.
- rounding — Replacing a value with a nearby value at a stated precision.
8. Statistics, charts and chance — words 141–160
Check each definition against one simple example. A mathematical word is useful when it tells the student what an object is, how it behaves, or what operation is permitted.
- data set — A collection of observations or recorded values.
- frequency — The number of times a value or category occurs.
- tally — A simple counting record using marks.
- frequency table — A table showing categories or values and their counts.
- bar chart — A chart representing categories with separate bars.
- pie chart — A circular display showing each category as a fraction of a whole.
- histogram — A chart of numerical intervals using adjoining bars, usually with frequency density when widths differ.
- dot plot — A display showing observations as dots over a scale.
- mean — The arithmetic average: total divided by number of values.
- median — The middle value after data are sorted, or mean of two middles.
- mode — The most frequent value or category.
- range — The largest value minus the smallest value.
- outlier — An observation notably distant from the others.
- distribution — How values are spread and occur within a data set.
- sample — A selected part of a larger population.
- population — The full group about which a study asks a question.
- survey — A method of collecting information by asking people questions.
- random — Not governed by a predictable choice pattern in the relevant model.
- probability — A numerical measure of how likely an event is.
- outcome — One possible result of a random process.
9. Reasoning, patterns and mathematical proof — words 161–180
Check each definition against one simple example. A mathematical word is useful when it tells the student what an object is, how it behaves, or what operation is permitted.
- estimate — Find a useful approximate result from limited information.
- approximate — Close to an exact value but not necessarily identical.
- exact value — A value expressed without rounding error.
- verify — Check by calculation or a valid method that a result works.
- validate — Check whether a model or conclusion fits its intended real situation.
- justify — Give a logical reason for a mathematical step.
- prove — Establish a statement through a logically valid argument.
- counterexample — A single valid example that disproves a universal claim.
- conjecture — A proposed mathematical statement that still needs proof.
- generalise — Extend an observed relationship to a wider class with justification.
- pattern — A repeated or predictable mathematical arrangement.
- sequence — A list of terms arranged by a rule or order.
- term number — A position in an ordered sequence.
- common difference — The fixed change between successive terms of an arithmetic sequence.
- rule — A description of how values or objects are related.
- relation — A pairing or connection between values in a specified set.
- logical step — A move justified by a rule, fact or earlier result.
- representation — A diagram, table, formula or model showing a mathematical idea.
- diagram — A visual drawing used to display or reason about a problem.
- model — A simplified mathematical representation of a real situation.
10. Mathematics beyond the classroom — words 181–200
Check each definition against one simple example. A mathematical word is useful when it tells the student what an object is, how it behaves, or what operation is permitted.
- budget — A plan for money available and how it may be spent.
- revenue — Money received from sales or other business activity.
- expense — Money spent to obtain goods, services or resources.
- profit — Revenue left after relevant costs are deducted.
- loss — A situation where costs exceed the relevant revenue.
- tax — A compulsory payment imposed by a government.
- exchange rate — A rate comparing the values of two currencies.
- distance-time graph — A graph showing how distance changes with time.
- speed-time graph — A graph showing how speed changes with time.
- scale drawing — A drawing using a consistent ratio to represent real dimensions.
- map scale — A relationship between map distance and ground distance.
- bearing — A clockwise angle from north used to describe direction.
- tariff — A schedule of charges for use of a service.
- consumption — How much of a resource or product is used.
- savings — Money kept rather than spent.
- fixed cost — A cost that stays unchanged over a specified activity range.
- variable cost — A cost that changes with the quantity of activity.
- break-even — The point where revenue equals costs.
- constraint — A restriction that limits possible solutions.
- unit cost — The cost associated with one unit of a product or service.
Why Mathematics vocabulary makes a difference to marks
A student can carry out multiplication accurately and still lose marks because the question is misread. “Find the percentage increase” is not the same as “Find the percentage point increase”. “State the gradient” is not the same as “Give the y-intercept”. “Explain why the angles are equal” asks for a property, not a new measurement. In each case the mathematics and language work together. The exact words determine which calculation or explanation is relevant.
Think of the transition from arithmetic to algebra. In primary school, a student may see three bags each containing seven objects and calculate twenty-one. In secondary Mathematics the same structure becomes 3x = 21. Now the student needs to recognise that x is an unknown, 3 is its coefficient and equality must be preserved. The symbol is not an unfamiliar decoration; it represents a relationship that the student must manage carefully.
The objective of vocabulary learning is not to give a memorised definition in isolation. A student must connect the word with a representation, an example, a non-example and a decision about the correct operation. For instance, the phrase like terms allows 3x + 5x to become 8x. It does not allow 3x + 5y to become 8xy. That is a concrete test of whether the meaning has been understood.
Worked example 1 — Expression, equation and identity
Compare three statements. “4x + 3” is an expression; it describes a mathematical quantity but makes no equality claim. “4x + 3 = 19” is an equation; its solution is x = 4. “2(x + 3) = 2x + 6” is an identity; it is true for every permitted value of x. These words cannot be interchanged. Recognising the difference tells the student whether to simplify, solve or explain a rule.
When solving 4x + 3 = 19, subtract 3 from both sides and divide both sides by 4. The answer x = 4 should be checked in the original equation: 4(4) + 3 = 19. That check is not merely an additional line of work. It demonstrates what solution means: a value that makes the original statement true.
Worked example 2 — A percentage is not a percentage point
Suppose a club’s attendance rate rises from 40% to 50%. The difference is 10 percentage points. The relative percentage increase is (50 − 40) ÷ 40 × 100% = 25%. Both figures are correct answers to different questions. The vocabulary tells us which comparison is being requested. Without that distinction, a student may use an accurate subtraction and still answer the wrong question.
Now consider a jacket sold for $72 after a 20% discount. The selling price represents 80% of the original price. The original price is 72 ÷ 0.8 = $90. This is a reverse percentage situation: you know the final value and need the starting value. Dividing $72 by 1.2 would be wrong because a discount is a reduction, not an increase.
Worked example 3 — Direct proportion and inverse proportion
If five identical tickets cost $30, the price is $6 per ticket. For eight tickets, the price is $48. The total cost is directly proportional to the number of tickets, assuming a fixed per-ticket price. We can say cost = 6 × number of tickets. Doubling the quantity doubles the cost, and halving it halves the cost.
Inverse proportion behaves differently. Imagine a fixed amount of work that four identical machines complete in six hours. Under the simplifying assumption that all machines work at the same constant rate without interruptions, eight machines could finish in three hours. The product of machine count and time remains constant. The assumption matters: real jobs can include bottlenecks, waiting time or setup costs. A good mathematical model says where its limits are.
Worked example 4 — Gradient, intercept and a graph’s message
A school charity stall starts with $20 of fixed costs and pays $2 for every item it makes. If x is the number of items and y is the total cost, y = 2x + 20. The gradient is 2, meaning the total cost rises by $2 per additional item. The y-intercept is 20, meaning the starting cost when no item has been made. The line’s equation is useful because it explains the process rather than simply producing points on a graph.
For x = 0, the cost is $20. For x = 5, it is $30. For x = 10, it is $40. Plot these ordered pairs accurately. If a student draws an increasing line but labels the vertical axis “items”, the result communicates the wrong relationship. Mathematical vocabulary includes knowing what each axis, coordinate and unit represents.
Do not confuse interpolation with extrapolation. Estimating the cost of seven items within the known pattern is interpolation. Predicting the cost of ten thousand items may be extrapolation, but the simple fixed-rate model might stop being realistic if production, bulk prices or resource limits change.
Worked example 5 — Angle language makes geometry explainable
When a transversal crosses two parallel lines, alternate angles are equal. The word alternate helps the student locate the relevant positions; the word parallel supplies the condition that makes the rule valid. If the lines are not known to be parallel, a student must not simply assume alternate angles are equal. The diagram’s appearance is not proof.
Similarly, vertically opposite angles formed by intersecting straight lines are equal. Complementary angles sum to 90 degrees; supplementary angles sum to 180 degrees. These are different relations. A good geometry answer states the property used, makes the substitution and then solves for the unknown angle. “Because it looks like it” is not a mathematical reason.
Worked example 6 — Accuracy, rounding and units
Suppose a rectangular floor is 3.2 metres long and 2.5 metres wide. Its area is 3.2 × 2.5 = 8.0 square metres. It is not 8 metres, because an area uses square units. If the same floor needed a border, the perimeter would be 2(3.2 + 2.5) = 11.4 metres. Confusing perimeter and area is therefore not just a small arithmetic mistake; it changes the physical quantity being measured.
Rounding should usually take place at the requested stage, not carelessly in the middle of a multi-step calculation. Where practical, keep adequate working precision until the final answer. If a measurement is approximate, do not report an impossible level of certainty. A result written to four significant figures is not automatically more accurate than the measurements used to obtain it.
Worked example 7 — Mean, median and the story hidden in data
Take the numbers 2, 3, 3, 4, 18. Their mean is 6; the median is 3; the mode is 3; and the range is 16. A student who says “the average is six” may be mathematically correct if mean is requested, but this number gives a distorted impression of a typical value because of the high observation 18. The median and the outlier give essential context.
The meaning of data depends on how the sample was obtained. A survey of only the students who remain after school may not describe the views of the entire year group. The sample is not necessarily representative of the population. Mathematical reasoning therefore extends to questions of evidence, fairness and good decision-making.
Worked example 8 — A counterexample can save time
Someone claims, “Squaring any number makes it bigger.” Rather than trying twenty positive examples, choose one valid counterexample: (0.5)² = 0.25, which is smaller than 0.5. One counterexample disproves a universal assertion. This is a powerful idea that connects Mathematics with Science, debate and everyday fact-checking.
A different claim may be plausible but not yet proven. For example, “the next term in the pattern will be 16” depends on what rule is intended. Many rules fit a short finite sequence. Students should distinguish between spotting a pattern, making a conjecture and giving a mathematical justification.
Three types of mathematics difficulty to diagnose
Meaning error: the word itself is misunderstood
The student sees “reverse percentage” and calculates a forward percentage change. Correction requires discussing what is known, what is unknown and what the phrase “original value” refers to. More practice of the wrong operation will simply make the mistake faster.
Process error: the word is understood but a rule is misapplied
The student knows what “expansion” means but writes 3(x + 2) = 3x + 2. Ask the student to represent the brackets as three groups of x + 2; then distribute the three to both terms. The repair is to reconnect the operation to meaning, not memorise an unexplained command.
Representation error: the working does not match the situation
The student correctly calculates a gradient but reverses the axes or leaves out a unit. Ask what each variable stands for, what the graph communicates and how the proposed answer would sound in an ordinary sentence. Diagram and language checks often reveal a mistake before the last line.
A four-week Secondary 2 Mathematics vocabulary plan
Week 1 — Number and algebra fluency
Review words 1–40 with a selection of genuine school questions. Have the student label the variable, constant, coefficient, term and operation before calculating. Pair every definition with a non-example. Spend more time on misunderstandings that lead to repeated errors than on copying glossary entries.
Week 2 — Equations, ratios and percentages
Use words 41–80 in five real-world questions. Make the learner underline what is given and box what is being asked. In each worked answer, ask which operation preserves equality or which starting quantity defines the percentage. This week should finish with a checked, explained solution, not just a numerical answer.
Week 3 — Graphs, angles and measurement
Use words 81–140 to interpret a line graph, explain an angle property and compare area with perimeter. Encourage the student to say the reason for each step. Good explanations include the condition: “alternate angles are equal because these lines are parallel”, rather than the shorter but incomplete statement “alternate angles”.
Week 4 — Data, reasoning and transfer
Use words 141–200 in a small survey, budget or transport comparison. Ask students to calculate, explain what the answer means, identify any modelling assumptions and propose how to check the conclusion. Keep a notebook of the five most persistent vocabulary errors and retest them after several days.
Frequently asked questions
Are these 200 words an official Secondary 2 MOE list?
No. This is a curated eduKateSG glossary for mathematical understanding, including useful bridging language. MOE syllabuses and schools set actual content expectations.
Is the vocabulary different for G1, G2 and G3 Mathematics?
Many foundational meanings are shared, but the depth of the methods, questions and applications differs. Match examples to the student’s offered subject level.
Will learning definitions alone improve my Mathematics grade?
No. Definitions help students read tasks, but real gains require correct methods, accurate calculations, working explanations, checking and retrieval after a delay.
Must students learn all 200 this term?
No. Start with the terms that currently block progress. Revisit them in actual questions until the language can be used independently.
Why is “solve” not the same as “simplify”?
Solving normally seeks values satisfying an equation or condition; simplifying rewrites an expression without changing its meaning. The distinction determines the expected answer.
Are these words useful outside school?
Yes. Rates, proportions, averages, percentages, scales and graph interpretation help with transport, consumer choices, budgets, surveys and news reports.
How can parents help without giving the answer?
Ask the student to define the quantity, draw a simple diagram, estimate a reasonable result, explain the operation and check the final answer in the original question.
What is the most useful revision habit?
Maintain an error log that separates language errors, conceptual errors, arithmetic errors and presentation errors; then practise the exact weakness.
Official references and further eduKateSG reading
Use MOE’s published Mathematics syllabus reference to understand mathematical goals and content structure. It predates the latest Full SBB implementation terminology, so use current MOE Full SBB information and the student’s school scope for the appropriate subject level. The SEAB SEC syllabus directory describes later national examination arrangements and is not itself a Secondary 2 vocabulary list.
For more learning routes, visit eduKateSG Vocabulary, School Vocabulary P1–JC and the mathematics transition and first-principles guide. The broader vocabulary hub builds word memory; this page handles subject-specific mathematical language and worked reasoning.