Secondary 1 Mathematics vocabulary helps Singapore students understand what a question asks before they attempt the calculation. This guide provides 200 mathematical words and phrases with plain-English meanings covering numbers, fractions, ratio, algebra, geometry, graphs, data and real-life problem solving. The complete list appears first, followed by worked examples and a four-week study plan.
Mathematics is not only about knowing methods. Words such as factor, multiple, coefficient, estimate and at most tell students which relationships a solution must preserve. This is an independent learning glossary informed by the Singapore mathematics curriculum. It is not an official MOE list of 200 examinable Secondary 1 terms; G1, G2 and G3 syllabuses and individual school sequences are not identical.
- Find all 200 definitions, grouped into 10 practical learning themes
- Read six guided examples showing how mathematical language changes the method
- Use the error checklist, four-week parent plan and official MOE links to decide what to practise
Top 200 Secondary 1 Mathematics vocabulary: the complete list
1. Number systems and relationships — 1–20
- integer — a whole number that may be negative, zero or positive.
- natural number — a counting number such as 1, 2 or 3.
- whole number — zero or a positive counting number.
- rational number — a number expressible as a ratio of integers.
- irrational number — a real number not expressible as an integer ratio.
- real number — any number represented on the ordinary number line.
- positive — greater than zero.
- negative — less than zero.
- zero — the number separating positive and negative values.
- absolute value — distance from zero on a number line.
- opposite — a number equally far from zero on the other side.
- reciprocal — a number that multiplies with the original to give one.
- prime — an integer greater than one with exactly two positive factors.
- composite — an integer greater than one with more than two positive factors.
- factor — a number that divides another exactly.
- multiple — a number formed by multiplying by an integer.
- divisibility — whether one integer can be divided by another exactly.
- remainder — what is left over after a non-exact division.
- quotient — the result obtained by division.
- magnitude — the size or extent of a numerical quantity.
2. Operations, powers and accuracy — 21–40
- sum — the result of addition.
- difference — the result of subtraction.
- product — the result of multiplication.
- dividend — the number being divided.
- divisor — the number by which another is divided.
- exponent — the small raised number indicating a power.
- base — the number or expression being raised to a power.
- power — a compact way of writing repeated multiplication.
- square — a number multiplied by itself, as in five squared.
- cube — a number multiplied by itself three times.
- square root — a number whose square gives the stated value.
- cube root — a number whose cube gives the stated value.
- order of operations — agreed rules determining which calculations come first.
- bracket — a grouping symbol controlling an expression.
- equivalent — equal in value despite different appearance.
- approximation — a value close to but not necessarily exactly equal.
- rounding — replacing a value with a nearby value at given precision.
- estimation — finding a sensible approximate value.
- significant figure — a digit counted in the precision of a number.
- decimal place — a position to the right of a decimal point.
3. Fractions, ratio, rates and percentages — 41–60
- numerator — the top number showing selected fractional parts.
- denominator — the bottom number giving equal parts in a whole.
- proper fraction — a positive fraction smaller than one.
- improper fraction — a fraction whose numerator is at least its denominator.
- mixed number — a whole-number part together with a proper fraction.
- simplest form — a fraction or ratio with no common integer factor remaining.
- common denominator — a shared denominator used for comparing fractions.
- unit fraction — a fraction with numerator one.
- fraction bar — the line separating numerator and denominator.
- proportion — a relationship between quantities that stay in a fixed ratio.
- ratio — a comparison of quantities by division.
- equivalent ratio — a ratio representing the same comparison.
- rate — a quantity measured in relation to another unit.
- unit rate — a rate expressed per one unit.
- percentage — a proportion expressed out of one hundred.
- percentage point — the arithmetic difference between two percentages.
- percentage increase — growth expressed relative to the original value.
- percentage decrease — reduction expressed relative to the original value.
- discount — a reduction from the listed price.
- reverse percentage — working backwards from a changed amount to the original.
4. Algebra as a mathematical language — 61–80
- variable — a symbol representing a value that can change or be unknown.
- unknown — a value that needs to be found.
- constant — a fixed number within an expression.
- coefficient — a number multiplying a variable.
- term — a part of an expression separated by addition or subtraction.
- like terms — terms with the same variable parts and powers.
- unlike terms — terms that cannot be combined directly by addition.
- expression — a combination of numbers, variables and operations.
- equation — a statement that two expressions are equal.
- inequality — a comparison using signs such as less than.
- algebraic notation — agreed symbols for expressing mathematical relationships.
- substitution — replacing a variable with a known value.
- simplification — rewriting an expression in an equivalent clearer form.
- expansion — removing brackets through a valid multiplication rule.
- factorisation — rewriting an expression as a product of factors.
- linear equation — an equation in which the unknown has first power.
- solution — a value satisfying a stated equation or condition.
- identity — an equality true for all permitted variable values.
- formula — a rule relating quantities using symbols.
- subject of formula — the variable isolated on one side of a formula.
5. Equations, inequalities and checking — 81–100
- equality — the condition that two quantities have the same value.
- balance — the idea that equal sides stay equal under matching operations.
- inverse operation — an operation reversing another, such as division for multiplication.
- addition property — adding the same value to both sides preserves equality.
- multiplication property — multiplying both sides by the same nonzero value preserves equality.
- isolate — rearrange until the wanted variable stands alone.
- transpose — rearrange an equation using valid equal operations.
- verify — check that a proposed answer satisfies the original problem.
- test — try a value against a condition or equation.
- valid step — a transformation that preserves the required relationship.
- equality sign — the symbol indicating the two sides have equal value.
- inequality sign — a symbol comparing unequal or potentially unequal values.
- less than — a comparison meaning smaller in value.
- at most — a bound meaning less than or equal to.
- greater than — a comparison meaning larger in value.
- at least — a bound meaning greater than or equal to.
- consecutive — following one another without a gap.
- even number — an integer divisible by two.
- odd number — an integer not divisible by two.
- algebraic model — an expression or equation representing a real situation.
6. Geometry language and angle facts — 101–120
- point — an exact location without size.
- line — a straight path extending without end in both directions.
- line segment — a straight part between two endpoints.
- ray — a straight path starting at a point and extending one way.
- angle — the turning between two rays with a common endpoint.
- acute angle — an angle greater than zero and below 90 degrees.
- right angle — an angle of exactly 90 degrees.
- obtuse angle — an angle between 90 and 180 degrees.
- reflex angle — an angle between 180 and 360 degrees.
- straight angle — an angle of 180 degrees.
- vertically opposite — the equal angles opposite at intersecting lines.
- adjacent angles — angles sharing a vertex and one arm.
- parallel — lines in one plane that never meet.
- perpendicular — lines meeting at a right angle.
- transversal — a line crossing two or more other lines.
- corresponding angles — angles in matching relative positions at intersections.
- alternate angles — angles on opposite sides of a transversal.
- co-interior angles — interior angles on one side of a transversal.
- polygon — a closed plane shape made of straight sides.
- vertex — a corner where sides or rays meet.
7. Shapes, measurement and space — 121–140
- triangle — a polygon with three sides.
- quadrilateral — a polygon with four sides.
- parallelogram — a quadrilateral with both pairs of opposite sides parallel.
- rectangle — a quadrilateral with four right angles.
- rhombus — a quadrilateral with four equal-length sides.
- trapezium — a quadrilateral with one pair of parallel sides.
- regular polygon — a polygon whose sides and interior angles are equal.
- circle — a plane curve whose points are equally far from the centre.
- circumference — the distance around a circle.
- diameter — a line segment through a circle’s centre joining its boundary.
- radius — the distance from a circle’s centre to its boundary.
- chord — a straight segment joining points on a circle.
- arc — part of a circle’s circumference.
- perimeter — the total distance around a plane shape.
- area — the amount of surface enclosed by a plane region.
- volume — the three-dimensional space occupied by an object.
- surface area — the combined area of a solid’s exterior faces.
- prism — a solid with parallel congruent polygonal end faces.
- composite shape — a figure formed by joining simpler shapes.
- symmetry — a balanced correspondence after reflection or rotation.
8. Coordinates, graphs and changing quantities — 141–160
- horizontal axis — the left-to-right reference line on a graph.
- vertical axis — the up-and-down reference line on a graph.
- origin — the point where coordinate axes meet.
- coordinate — a number helping locate a point.
- ordered pair — two values specifying a point in a given order.
- Cartesian plane — a plane organised using perpendicular numbered axes.
- x-coordinate — a point’s horizontal position in Cartesian coordinates.
- y-coordinate — a point’s vertical position in Cartesian coordinates.
- quadrant — one of four regions made by coordinate axes.
- scale — the relationship between a diagram unit and represented quantity.
- interval — the gap between successive labelled values.
- gradient — the steepness of a line.
- intercept — a point where a graph crosses an axis.
- plot — mark a point or relationship on a graph.
- graph — a visual representation of numerical relationships.
- linear relationship — a relationship represented by a straight-line graph.
- table of values — paired values used to describe a relationship.
- dependent variable — a value influenced by another variable.
- independent variable — a value deliberately selected or varied.
- trend — a general direction shown by values or data.
9. Statistics, representations and chance — 161–180
- data — recorded information used for analysis.
- dataset — a collection of related observations.
- frequency — the number of times something occurs.
- tally — marks used to count occurrences.
- bar graph — separate bars showing comparisons between categories.
- line graph — connected points showing change or relationships.
- pie chart — a circle divided into sectors showing parts of a whole.
- histogram — adjoining bars representing grouped numerical data.
- pictogram — symbols used to show quantities.
- mean — the total divided by the number of values.
- median — the middle value of ordered data.
- mode — the value appearing most often.
- range — the highest value minus the lowest.
- outlier — a value noticeably different from the others.
- sample — a selected part of a larger group.
- population — the complete group of interest in a study.
- sampling bias — a distortion caused by an unrepresentative selection.
- misleading scale — axis labelling that distorts visual comparisons.
- probability — the mathematical description of how likely an event is.
- outcome — one possible result of a process or experiment.
10. Real-world problem language — 181–200
- quantity — an amount that can be counted or measured.
- unit — an agreed standard used to express a measurement.
- conversion — changing a measure into an equivalent unit.
- distance — the length between positions or along a route.
- time — the duration or instant involved in a problem.
- speed — distance travelled per unit of time.
- average speed — total distance divided by total travel time.
- constant speed — movement at an unchanging speed.
- cost price — the amount paid to obtain an item.
- selling price — the amount for which an item is sold.
- profit — a positive difference between selling price and cost.
- loss — a negative difference between selling price and cost.
- budget — a plan for spending limited resources.
- capacity — the amount a container can hold.
- mass — a measurement of the amount of matter.
- density — mass per unit volume.
- scale drawing — an image showing actual lengths by a fixed ratio.
- unitary method — finding the value of one unit before scaling.
- proportional reasoning — reasoning through equivalent multiplicative relationships.
- reasonableness — whether an answer makes sense in its context.
What changes between Primary 6 and Secondary 1 Mathematics?
A student arriving from Primary 6 may recognise most operations but still find a Secondary 1 question difficult. The new work expects them to recognise mathematical structures from words and notation. Instead of only calculating ‘three times seven’, they may see 3x = 21 and must understand that x is an unknown, 3 is a coefficient, the equal sign expresses balance and the solution should satisfy the original equation. No single trick replaces that understanding.
When a student says that a number ‘moves to the other side’, ask what operation preserves equality. From 3x = 21, divide both sides by 3 to obtain x = 7. Check 3 × 7 = 21. This small explanation is more useful than a memorised movement rule that breaks down with negatives, brackets or fractions.
A second change concerns the wording of word problems. ‘At least’ includes the stated boundary; ‘greater than’ excludes it. ‘Percentage point’ is different from ‘percentage increase’. Mathematical vocabulary is not decoration: the definition is part of the reasoning.
Six worked examples that connect vocabulary to mathematical steps
1. Factor versus multiple
For 18, the number 6 is a factor because 18 ÷ 6 = 3 exactly. The number 36 is a multiple of 18 because 18 × 2 = 36. Factors divide a number; multiples are generated by multiplication. Many incorrect HCF and LCM answers start with confusing these two directions.
2. Integer and absolute value
The integers −4 and +4 are opposites. Their absolute values are both 4 because each is four units from zero on the number line. However, −4 + 4 = 0. Absolute value is a distance, not an instruction to ignore negative signs in every calculation.
3. Simplification versus solving
Simplify 3x + 2x and obtain 5x: there was no equation to solve. Solve 3x + 2x = 20 and obtain x = 4 after simplifying to 5x = 20 and dividing both sides by 5. Read the instruction first. The required answer form changes the working.
4. Ratio and equivalent relationships
A recipe uses rice and water in the ratio 2:3. Doubling both quantities gives 4:6, an equivalent ratio. Increasing only one quantity to produce 2:6 changes the relationship. Ratio questions are multiplicative comparisons, not invitations to add the same number to both sides.
5. Percentage increase versus percentage points
A club’s participation rises from 40% to 50%. The change is 10 percentage points. Relative to the original 40%, the percentage increase is (50 − 40) ÷ 40 × 100% = 25%. The phrases sound similar, but they answer different questions.
6. Average speed and units
A traveller covers 60 km in two hours, then 30 km in one hour. Total distance is 90 km and total time is three hours; average speed = 30 km/h. Always divide total distance by total time. Do not average two speeds without checking the journey durations. State units so the result is interpretable.
How to read a Mathematics question without losing the meaning
First underline the exact requested quantity. If a question asks for the number of remaining seats, the answer must be a non-negative count. If it asks for the distance between two points, negative distance would not make sense in that context. Next separate known quantities from unknown quantities, write the relationship and choose operations that preserve it. Finish by checking that the numerical result is of the right order and has the correct unit.
Take an everyday problem: A bus card contains $25. Each trip costs $1.80. A student wants at least $7 remaining. Write 25 − 1.8n ≥ 7, where n is the number of trips. Rearranging gives n ≤ 10; n must be a whole number. The meaningful answer is up to ten trips, including ten. The key word ‘at least’ determines the inequality direction and the real-world interpretation. This is an original illustration, not an official school examination question.
Geometry language must connect a named fact to a diagram
Students sometimes can recite ‘alternate angles are equal’ but fail to notice whether the lines are parallel. Start by identifying the diagram conditions, the transversal and the pair of angles. Say the fact in a complete sentence: ‘The alternate interior angles are equal because the two marked lines are parallel.’ A reasoning statement is safer than writing two numbers with no explanation. Different angle facts are not interchangeable.
For mensuration, separate perimeter from area. A rectangle measuring 8 cm by 3 cm has perimeter 2(8 + 3) = 22 cm and area 8 × 3 = 24 cm². Different calculations and different units. A useful self-check is to ask whether the problem is measuring a boundary or a surface.
Graphs, data and questions outside the textbook
Graphs translate quantities into a visual story. On a distance–time graph, increasing vertical position means the total distance shown is increasing; how steeply it changes can convey a rate, depending on the axes. If the vertical axis begins at 90 instead of zero, a small difference may look dramatic. Students should inspect axis labels and scales before describing a trend.
Statistics words can also help a teenager read sports results, transport reports or school surveys. The mean responds strongly to an extreme value, while the median may better represent the centre of skewed data. Not every data word in this collection is necessarily taught during Secondary 1 at every subject level; extension terms are included to make new graphs and general reading easier to understand.
How G1, G2 and G3 affect the choice of words
Under Full Subject-Based Banding, students may take Mathematics at G1, G2 or G3 subject levels. These are learning levels, not labels of personal worth. MOE publishes separate G1 Mathematics and G2/G3 Mathematics syllabus documents. Parents should match practice to the child’s actual level and school sequence. For a learner rebuilding number sense, words such as factor, negative and equivalent may be more urgent than gradient or factorisation. For a confident learner, the challenge may be explaining why a solution is valid and when a formula applies.
A vocabulary list is an invitation to understand, not a demand to master all 200 terms in one term. Some words prepare students for later secondary work. Label those as ‘later extension’ in the student’s notebook rather than treating every word as an immediate test requirement.
Four-week revision plan for parents and students
| Week | Main focus | Simple diagnostic |
|---|---|---|
| 1 | Number signs, order of operations, factors, fractions and decimals. | Explain four sign rules and solve five problems accurately. |
| 2 | Ratio, percentages, variables, terms and the balance principle. | Translate three sentences into equations; check each solution. |
| 3 | Angles, geometry language, area and perimeter. | Label a diagram and explain why the chosen fact applies. |
| 4 | Graphs, data, rates and mixed word problems. | Show the meaning of the answer, not just the number. |
Use four short sessions per week: read five words; explain them aloud without the glossary; solve one related problem; and revisit the definitions after a day. Keep a small error map with three columns: word misread, incorrect step, corrected meaning. Relearning a single weak link is more valuable than completing a page of questions that repeat the same error.
Parent checklist: diagnose the first weak link
- Calculation error: does the student know the number operation but lose a sign? Repair directed-number basics.
- Translation error: does ‘at most’, ‘of’, ‘per’, ‘difference’ or ‘remaining’ lead to the wrong expression? Rephrase the sentence with a concrete example.
- Notation error: can the student explain the difference between 3x, x³ and 3 + x?
- Method error: is an equation being simplified instead of solved, or a fraction being added without a common denominator?
- Diagram error: does the learner claim an angle property without identifying the required parallel or intersecting lines?
- Answer error: is the numerical output inconsistent with units, scale, whole-number restrictions or context?
Frequently asked questions
Does every Secondary 1 student learn all 200 terms?
No. This is an independent cross-topic glossary. Students follow their G1, G2 or G3 syllabus and the order their school teaches.
Is this the official MOE Secondary 1 Mathematics vocabulary list?
No. MOE publishes syllabuses and expected mathematical learning, but this 200-entry format and its definitions are eduKate’s study aid.
What are the most important words for algebra?
Start with variable, term, coefficient, expression, equation, substitution, simplify, solve, and verify. Apply each to actual workings.
What is the difference between expression and equation?
An expression has no required equals statement, such as 2x + 5. An equation states equality, such as 2x + 5 = 17.
How do I choose a G1, G2 or G3 practice resource?
Check the student’s current subject level, current school chapter and teacher feedback, then select a closely matched resource.
Is Further Mathematics or Additional Mathematics part of this Secondary 1 guide?
No. This is a Secondary 1 foundation reference. It is not a guide to upper-secondary Additional Mathematics.
How do we know the vocabulary has been learned?
Ask for a plain-English explanation, a correct example, a contrasting non-example and an accurate response to a fresh problem.
When should Mathematics tuition begin?
Only after the student’s starting position is clear. Identify whether the gap is meaning, number sense, algebraic structure, reasoning or accuracy before deciding.
Official syllabuses and connected eduKate guides
MOE reference: G1 Mathematics syllabus; G2 and G3 Mathematics syllabuses; MOE secondary education guidance. These primary sources describe curriculum requirements; the school confirms the current teaching sequence.
For the next step see eduKate vocabulary master guide, the school vocabulary hub, How Mathematics Works and Secondary 1 Mathematics support. The Secondary 1 Mathematics Clementi guide provides a separate explanation of the transition to algebra and small-group learning.
Reviewed November 2026. All worked scenarios are original teaching examples, not official examination items. This resource does not override MOE or a student’s school syllabus.