Top 200 Vocabulary for Secondary 3 Mathematics (MOE G3 Syllabus) | E-Math Algebra, Graphs and Word Problems

Need the most useful Secondary 3 E-Math vocabulary? Here are 200 mathematics terms explained in plain English for algebra, quadratic equations, graphs, geometry, trigonometry, statistics and word problems. Use the list as a reference beside school notes and practice questions: knowing what a question means is often the first step towards knowing which method to use.

Under the 2027 Singapore-Cambridge Secondary Education Certificate (SEC), G3 Mathematics is identified as K310, corresponding to the earlier 4052 code. This is a learning companion for Secondary 3 Mathematics, commonly called E-Math, not an official 200-word MOE list. Different schools may cover upper-secondary topics in different sequences, and the correct syllabus for the student’s subject level and exam year takes priority.

• First: identify the topic from the question’s command words and mathematical nouns.
• Next: choose the valid operation or relationship instead of memorising a “move it across” slogan.
• Then: show working, units and assumptions where necessary.
• Finally: check the answer in the original context.
• Use this glossary: ten groups of 20 terms, with a mini-practice prompt after each group.
• Do not confuse: E-Math with Additional Mathematics, or a vocabulary resource with the full SEAB syllabus.

Top 200 Secondary 3 Mathematics vocabulary words and terms

The terms below deliberately include words as well as standard multiword expressions. In mathematics, understanding “axis of symmetry” as a single concept can matter more than memorising the separate dictionary definitions of “axis” and “symmetry”. Not every term is taught for the first time in Secondary 3; earlier foundations remain necessary in upper-secondary questions.

1. Numbers, precision and notation

Numerical vocabulary protects accuracy. “Exact” and “rounded” are not competing stylistic choices: they describe different answers. Likewise, the index in 10³ tells us something different from the coefficient in 3x. Students can check whether they know a term by explaining what changes when its value changes.

1. integer — a whole number that may be positive negative or zero.
2. rational number — a number expressible as a ratio of integers.
3. irrational number — a real number not expressible as an integer ratio.
4. real number — a number located on the number line.
5. positive number — a quantity greater than zero.
6. negative number — a quantity less than zero.
7. absolute value — a number’s distance from zero.
8. exponent — the raised number indicating a power.
9. index — another name for an exponent.
10. base — the quantity repeatedly multiplied in a power.
11. standard form — writing a number as A times ten to an integer power.
12. significant figures — digits that carry meaningful measurement precision.
13. decimal places — the count of digits after the decimal point.
14. estimate — a sensible approximate value.
15. exact value — a result expressed without rounding.
16. approximation — a value close to but not exactly equal to another.
17. rounding — replacing a number with a nearby simpler value.
18. reciprocal — one divided by a nonzero number.
19. square root — a value whose square gives the original number.
20. cube root — a value whose cube gives the original number.

Mini-check: Check: Explain the difference between 3.14 and an exact expression involving π. State when rounding is appropriate.

2. Algebraic expressions and relationships

Algebra gives a short way to represent relationships. For example, the expression 3(x+4) is equivalent to 3x+12 because multiplication distributes over addition. The equals sign records a relationship; it does not tell us to move a symbol arbitrarily from one side to another.

21. variable — a symbol standing for a number that may change.
22. constant — a fixed value.
23. coefficient — the number multiplying a variable or term.
24. term — a separate part of an algebraic expression.
25. expression — a combination of mathematical quantities without an equality claim.
26. equation — a statement that two expressions are equal.
27. identity — an equality true for all permitted variable values.
28. formula — a rule connecting related quantities.
29. substitution — replacing a symbol with its known value.
30. expand — remove brackets using valid multiplication rules.
31. factorise — rewrite an expression as a product of factors.
32. simplify — express a quantity in an equivalent clearer form.
33. like terms — terms with matching variable factors and powers.
34. distributive law — the rule a(b+c)=ab+ac.
35. commutative law — order can change for addition or multiplication.
36. associative law — grouping can change for addition or multiplication.
37. linear — having first-degree variable terms in the relevant expression.
38. quadratic — having highest variable power two.
39. polynomial — a finite sum of nonnegative integer powers of a variable.
40. algebraic fraction — a fraction containing algebraic expressions.

Mini-check: Check: Expand 2(x−3), then factorise 2x−6. Explain why both forms describe the same quantity.

3. Equations, inequalities and checking

Solving is more than reaching an attractive number. When squaring or multiplying by an expression involving an unknown, a later answer may violate the original condition. Check every candidate against the first equation and respect restrictions such as a denominator not being zero.

41. solution — a permitted value making a mathematical statement true.
42. root — a value where an equation or function equals zero.
43. inequality — a comparison such as less than or greater than.
44. boundary — a limiting value separating possible cases.
45. interval — a continuous range of numbers.
46. domain — the set of permitted input values.
47. constraint — a restriction the answer must obey.
48. simultaneous equations — two or more equations to satisfy together.
49. elimination — removing a variable by combining equations.
50. substitution method — replacing one variable using another relationship.
51. balance principle — performing equivalent operations on both equation sides.
52. inverse operation — an operation that undoes another.
53. rearrangement — changing a formula’s subject through equivalent steps.
54. quadratic formula — the standard formula for roots of ax²+bx+c=0.
55. discriminant — b² minus 4ac in a quadratic equation.
56. completing the square — rewriting a quadratic using a squared bracket.
57. cross-multiplication — a shortcut for equivalent ratios under valid conditions.
58. extraneous solution — an obtained answer invalid in the original problem.
59. verify — check a result against the original requirements.
60. satisfy — meet every condition in a mathematical statement.

Mini-check: Check: Solve 2x+5=17. Substitute your answer back into the original statement rather than relying only on the last line.

4. Coordinates, functions and graphs

Graphs provide a visual language for the same mathematical relationship. A line can show a constant rate of change. A quadratic parabola has a turning point. Always identify what the axes represent and how they are scaled before describing a trend.

61. coordinate — a number specifying a position along an axis.
62. origin — the point where coordinate axes meet.
63. x-axis — the horizontal reference axis on a Cartesian graph.
64. y-axis — the vertical reference axis on a Cartesian graph.
65. ordered pair — two coordinates written in a fixed order.
66. gradient — the steepness and direction of a line.
67. intercept — the point where a graph crosses an axis.
68. slope — another word for a line’s gradient.
69. linear graph — the straight-line graph of a linear relationship.
70. curve — a graph that does not remain straight.
71. parabola — the familiar U-shaped or inverted quadratic graph.
72. vertex — the turning point on a quadratic parabola.
73. axis of symmetry — a line dividing a symmetrical graph into matching halves.
74. turning point — a point where a graph changes increasing or decreasing direction.
75. tangent — a straight line touching a curve with matching local direction.
76. rate of change — how quickly one quantity varies with another.
77. rise over run — vertical change divided by horizontal change.
78. graph scale — how distances on axes represent numerical values.
79. plot — mark a point accurately on a graph.
80. sketch — show the main graph features without exact plotting throughout.

Mini-check: Check: For y=2x+1, identify the gradient and y-intercept. Sketch where the line crosses the axes and why.

5. Ratio, percentage and everyday applications

Everyday percentages become clearer when the reference amount is identified. A rise from 50 to 60 is a 20% increase because 10 is 20% of 50. A drop from 60 to 50 is not the reverse 20%; 10 is one-sixth of 60, approximately 16.7%.

81. ratio — a comparison of quantities by division.
82. proportion — a relationship between corresponding ratios.
83. direct proportion — two quantities changing by a constant multiplier.
84. inverse proportion — a relationship whose product remains constant.
85. rate — a quantity measured per unit of another.
86. unit rate — a rate stated for exactly one unit.
87. percentage — a quantity measured in hundredths.
88. percentage point — an absolute difference between two percentages.
89. percentage change — the change relative to the original amount.
90. simple interest — interest calculated on the starting principal only.
91. compound interest — interest calculated on principal and accumulated interest.
92. principal — the initial amount invested or borrowed.
93. multiplier — a factor used to model repeated change.
94. discount — a reduction from an original price.
95. markup — an increase applied to a cost or price.
96. exchange rate — a comparison of values between currencies.
97. speed — distance travelled per unit time.
98. distance — the length between locations or along a route.
99. time — the duration of an event.
100. conversion — changing a measurement or amount into equivalent units.

Mini-check: Check: A $50 item rises by 20% and then falls by 20%. Use multipliers to find the final $48 price, not the tempting $50.

6. Geometric relationships and angle language

Geometry questions reward precise conditions. Parallel lines alone do not make every angle equal; the location of a transversal and which angles are compared matter. Similar triangles preserve angles and proportional sides; congruent triangles preserve size as well.

101. point — an exact position without size.
102. line segment — a part of a straight line between endpoints.
103. ray — a line extending without end in one direction.
104. parallel — lines in a plane that never meet.
105. perpendicular — meeting at a right angle.
106. transversal — a line intersecting other lines.
107. corresponding angles — angles in matching positions at a transversal.
108. alternate angles — angles on opposite sides of a transversal in matching regions.
109. co-interior angles — interior angles on the same side of a transversal.
110. supplementary — angles whose measures add to 180 degrees.
111. complementary — angles whose measures add to 90 degrees.
112. adjacent — next to another angle sharing a vertex and one arm.
113. vertically opposite — the opposing angles formed by intersecting lines.
114. polygon — a closed flat shape made of straight sides.
115. regular polygon — a polygon with equal sides and equal interior angles.
116. exterior angle — the angle formed outside a polygon at a vertex.
117. interior angle sum — the total of all angles inside a polygon.
118. congruent — identical in shape and size.
119. similar — same shape but possibly different size.
120. symmetry — a transformation leaving a figure matching itself.

Mini-check: Check: Draw two parallel lines cut by a transversal. Mark one pair of alternate angles and explain the equality condition.

7. Measurement, circles and three-dimensional shapes

Students often confuse different dimensions. Perimeter is measured in units of length, area in square units and volume in cubic units. Memorising a formula is not enough if the selected radius, diameter or perpendicular height is incorrect.

121. perimeter — the total distance around a flat shape.
122. area — the two-dimensional space within a boundary.
123. volume — the amount of three-dimensional space occupied.
124. surface area — the sum of all exposed surface areas.
125. circumference — the length around a circle.
126. diameter — a chord passing through the centre of a circle.
127. radius — the distance from centre to circle boundary.
128. arc — a portion of a circle’s circumference.
129. sector — a region bounded by two radii and an arc.
130. chord — a segment joining two circle boundary points.
131. secant — a line cutting a curve at two points.
132. prism — a solid with matching parallel cross-sections.
133. cylinder — a solid with two matching parallel circular bases.
134. cone — a solid tapering from a circular base to one vertex.
135. sphere — a solid whose surface points share one distance from its centre.
136. pyramid — a solid with one polygon base and triangular faces meeting at a vertex.
137. height — a perpendicular distance from base to top.
138. slant height — a measured side distance along a cone or pyramid face.
139. cross-section — the shape seen when a solid is cut.
140. capacity — how much a container can hold.

Mini-check: Check: Explain why doubling every length of a cube multiplies its surface area by four and its volume by eight.

8. Trigonometry, bearings and scale

Trigonometric words describe positions relative to a chosen angle. The opposite side changes when the reference angle changes, but the hypotenuse of a right triangle does not. A bearing starts at north and turns clockwise, so a compass sketch is often worth the effort.

141. right angle — an angle of exactly 90 degrees.
142. hypotenuse — the longest side opposite the right angle in a right triangle.
143. opposite side — the side across from the selected angle.
144. adjacent side — the non-hypotenuse side beside the selected angle.
145. sine — opposite side divided by hypotenuse in a right triangle.
146. cosine — adjacent side divided by hypotenuse in a right triangle.
147. tangent ratio — opposite side divided by adjacent side in a right triangle.
148. angle of elevation — an angle measured above the horizontal.
149. angle of depression — an angle measured below the horizontal.
150. bearing — a direction measured clockwise from north.
151. three-figure bearing — a bearing written using three digits.
152. Pythagoras’ theorem — a²+b²=c² for the sides of a right triangle.
153. trigonometric ratio — a side relationship connected to an angle.
154. angle measure — the numerical size of an angle.
155. degree — a unit measuring angles with 360 in a full turn.
156. construction — drawing geometric objects using specified tools and rules.
157. angle bisector — a ray dividing an angle into two equal parts.
158. perpendicular bisector — a line crossing a segment at its midpoint at 90 degrees.
159. scale drawing — a drawing using a fixed ratio to actual measurements.
160. map scale — the rule relating map distance to actual distance.

Mini-check: Check: From a 30° angle in a right triangle, label opposite, adjacent and hypotenuse before selecting a ratio.

9. Data, statistics and uncertainty

Statistics turns observations into descriptions, not automatic explanations. A large outlier can shift the mean while leaving the median less affected. A graph with a broken scale may exaggerate the visual impression. Read the data and state the limits of the conclusion.

161. data — observations or measurements collected for analysis.
162. categorical data — observations described using groups or labels.
163. numerical data — observations expressed as numbers.
164. frequency — the number of times an observation occurs.
165. frequency table — an organised count of observations.
166. class interval — a continuous range used to group data.
167. histogram — adjoining bars representing grouped numerical data.
168. mean — the arithmetic average of observed values.
169. median — the middle value after ordering the observations.
170. mode — the most frequently observed value.
171. range — maximum value minus minimum value.
172. quartile — a point dividing ordered data into four parts.
173. interquartile range — upper quartile minus lower quartile.
174. cumulative frequency — running total of observations up to a value.
175. standard deviation — a measure of spread around the mean.
176. outlier — an observation unusually far from others.
177. sample — a selected subset of a larger population.
178. population — the full group of interest in a study.
179. probability — a measure of how likely an event is.
180. relative frequency — frequency expressed as a fraction of total trials.

Mini-check: Check: Compare mean and median for 2, 3, 4, 5, 36. Which better represents a typical value in this set and why?

10. Reading and answering word problems

Word problems connect all the preceding tools. Begin with the quantity being asked for, choose a representation, write the relevant relationships and check whether the solution makes physical sense. A calculated negative number of buses is evidence that interpretation has failed.

181. unknown — the quantity to be determined.
182. given — information supplied in a problem.
183. required — what the question specifically asks for.
184. representation — a way to express a situation mathematically.
185. model — a simplified mathematical description of reality.
186. diagram — a drawing used to organise relationships.
187. assumption — a condition accepted to build a model.
188. reasonable — consistent with the situation and its limitations.
189. units — standard labels describing measured quantities.
190. dimension — a physical measurement such as length or time.
191. method — an organised series of valid steps.
192. justify — explain why a statement or step is valid.
193. prove — establish a statement through mathematical reasoning.
194. counterexample — an example showing a general claim is false.
195. working — the recorded steps leading to an answer.
196. accuracy — how close a result is to the correct value.
197. check — an independent test of the proposed result.
198. interpretation — what a calculated result means in its setting.
199. conclusion — a final statement answering the problem.
200. revision — review and correction of earlier learning.

Mini-check: Check: Estimate the answer to a rate question first. Then solve and inspect whether the units match the question.

Three worked mathematical language examples

Example 1: the meaning of a quadratic solution

Question: Solve x² − 5x + 6 = 0. First, recognise that “quadratic” means the highest power is two. “Solve” asks for the permitted value or values of x that make the equality true. It does not ask for the name of the curve or for the value of an expression at an arbitrary x.

Method: Factorise x² − 5x + 6 into (x − 2)(x − 3). For a product to be zero, at least one factor must be zero. Hence x − 2 = 0 or x − 3 = 0, giving x = 2 or x = 3. Check: 2² − 5(2) + 6 = 0; 3² − 5(3) + 6 = 0.

What the vocabulary teaches: “Factorise” changes the form of an expression without changing its value. “Roots” are the x-values where the associated function becomes zero. “Verify” sends the proposed answers back to the original question. A student who remembers only a procedure may miss why two answers are possible.

Example 2: why successive percentages do not cancel

Question: A bag costs $80. The price rises by 25%, then a promotion reduces the new price by 20%. What is the final price and is it the same as the original?

Method: After the rise, $80 × 1.25 = $100. The later discount uses $100 as its reference, so $100 × 0.80 = $80. In this case the two particular factors multiply to one: 1.25 × 0.80 = 1. However, equal percentage increases and decreases usually do not cancel. A 20% rise followed by a 20% fall gives a multiplier of 1.20 × 0.80 = 0.96.

What the vocabulary teaches: The “base” of a percentage comparison is the reference amount. “Percentage change” describes a relative difference; “percentage point” compares percentage figures directly. Without identifying the reference amount, a correct-looking shortcut may be wrong.

Example 3: reading a graph in a real situation

Situation: A delivery service charges a $4 fixed fee and $2 per kilometre. Let d represent distance in kilometres and C represent cost in dollars. Then C = 2d + 4 for distances in the service’s permitted domain.

The gradient is 2 dollars per kilometre; the C-axis intercept is 4 dollars; and the domain must respect the real rule, including nonnegative distance. If the question asks the cost for 3 km, substitute d = 3: C = 2(3)+4 = $10. A negative-distance answer might satisfy a manipulated equation but does not fit the physical context.

What the vocabulary teaches: A graph is a model with units and restrictions. Words such as gradient, intercept, variable and domain each carry a precise role. Translate a result back into a sentence: “The charge for three kilometres is ten dollars.”

Why a student can know the formula and still lose marks

Language misunderstanding: Confusing “factorise” with “solve”, “estimate” with “calculate”, or “prove” with “show one example”. The remedy is to explain what the command requests before beginning. A correct algebraic expression is not always an answer to the question asked.

Concept misunderstanding: Knowing that a gradient is “rise over run” but not understanding what the rise and run mean on scaled axes. The remedy is to connect notation, diagram, verbal explanation and a real example. Students should be able to teach the meaning, not only repeat a rule.

Operation mistake: Distributing a multiplier across only one bracket term, cancelling across addition, using a wrong sign, or squaring the wrong quantity. The remedy is to mark the exact line where equivalence breaks. Redo the small operation correctly before tackling an entire new page of questions.

Representation mistake: Drawing a diagram with the wrong dimensions or failing to label which side is opposite the selected trigonometric angle. The remedy is to mark known and unknown quantities directly on the sketch, then confirm the chosen ratio matches the labelled relationships.

Transfer difficulty: Succeeding on a familiar worksheet but failing when the same idea appears inside a transport fare, science measurement or finance story. The remedy is mixed practice with explanation: identify the structure without being told the topic. This is why students should learn mathematical terms as concepts, not as a disconnected vocabulary test.

How E-Math fits beside Additional Mathematics

Both subjects use algebraic reasoning, but they are separate subjects with different curriculum depth and assessment requirements. Secondary 3 Additional Mathematics commonly places greater emphasis on extended manipulation of functions, equations, graphs and further trigonometric structures. A student should not assume that success in one automatically replaces studying the other.

The mathematical language overlaps; methods and assessed scope may differ. When using a term such as “discriminant”, ask whether the current school task requires calculation, graph interpretation or proof of the number of roots. The same word can be used at different levels of depth. The relevant school notes and SEAB subject document should govern scope.

A four-week plan for useful mastery

Week 1: numbers, algebra and solving

Use groups 1–3. Each day, explain eight to ten terms in your own words and complete two short questions applying them. Use a correction page divided into “word misunderstood”, “rule misunderstood” and “calculation error”. Retest a wrong question two days later with altered values.

Week 2: graphs, ratio and geometry

Use groups 4–6. Draw lines and parabolas by hand, label real axes and translate between diagrams and sentences. For ratio and percentage, identify the reference quantity before calculating. For geometry, state the condition that permits an angle relationship rather than announcing an unsupported rule.

Week 3: measurement, trigonometry and data

Use groups 7–9. Practise selecting correct units and sketching shapes. In trigonometry, label the chosen reference angle before writing SOHCAHTOA. For data, explain one feature a graph shows and one thing it cannot establish. Use a calculator only after setting up the intended relationship.

Week 4: word problems and independent transfer

Use group 10 and mixed tasks from every earlier group. Give the student an unfamiliar question without a topic heading. Ask: What is given? What is required? Which relationships connect the information? What would a reasonable answer look like? After solving, verify by substitution or another method. Keep the correction log concise and test again after a few days.

Parent checkpoint: Ask the student to explain a single previously wrong line and its repair. If they can solve a variant independently, the understanding is becoming durable. Ten unexplained repetitions provide less evidence than one correct explanation and one successful transfer.

Frequently asked questions

Are these the official 200 MOE Secondary 3 Mathematics vocabulary words?

No. This is an independently curated glossary of useful terms and concepts, some introduced before Secondary 3 and others developed in upper-secondary work. Official syllabuses specify learning outcomes and topics, not this particular 200-item list.

Does every G3 school teach these topics in the same Secondary 3 order?

No. School sequencing may vary and some material is consolidated in Secondary 4. Match your textbook, school assignment and examination year before treating a term as an immediate assessment priority.

What is the difference between G3 Mathematics and Additional Mathematics?

They are distinct subjects. G3 Mathematics (2027 SEC K310) is the core Mathematics pathway at that subject level. Additional Mathematics (2027 SEC K341) has its own syllabus and higher-depth topics. Students taking both need appropriate preparation for each.

How many words should a student learn in one lesson?

About eight to ten is a useful starting amount if the student can explain each word and apply it. The right number depends on the starting position. Do not trade understanding for list completion.

Is mathematical vocabulary important for Science?

Yes. Words such as variable, gradient, proportion, significant figures and uncertainty help students interpret experimental data and scientific relationships. However, the same word may require a discipline-specific definition.

When does extra teaching help?

When repeated mistakes reveal a specific unstable concept or method that the student cannot correct independently. Diagnose the starting position first; a smaller, well-chosen sequence of tasks can be more valuable than adding many more worksheets.

Reliable reading and next steps

For curriculum details, use the official 2027 SEC G3 syllabus page and select Mathematics K310. For a broader explanation of concept building, see The eduKate Mathematics Learning System. The Clementi small-group Mathematics guide also illustrates a foundation-first method: diagnose a misunderstanding, explain the mechanism, practise independently and check transfer.

Final practical test: Can the student read a new question, name the mathematical relationship it contains, solve it accurately and explain what the answer means? That is the purpose of learning mathematics vocabulary.