G3 Additional Mathematics vocabulary is the language that tells you what an algebraic instruction actually requires. If “solve”, “prove”, “simplify” and “show that” all sound the same, a student may carry out correct algebra but answer the wrong question. If “domain”, “root”, “gradient” and “stationary point” are unclear, graphs and calculus become a collection of procedures. Here are 200 A-Math terms explained for Singapore’s 2027 SEC G3 Additional Mathematics, SEAB subject code K341.

The official K341 syllabus (older reference code 4049) is organised into Algebra, Geometry and Trigonometry, and Calculus, assuming prior G3 Mathematics knowledge. These 200 definitions are an eduKate teaching selection, not an official prescribed word list. Some entries such as graph-transformation terminology and advanced labels support understanding but should be prioritised according to the child’s actual chapter and the 2027 official syllabus, not treated as additional exam promises.

Quick answers:

• Read the question’s command word before beginning a solution.
• Associate each term with a formula, graph, worked example or counterexample.
• Mark the first incorrect line of working rather than only the final answer.
• Keep domain restrictions and exact values visible when manipulating equations.
• Review the same term in several topics to build transfer rather than rote recall.

1–10: Algebra essentials

1. variable — A symbol representing a value that may change.
2. constant — A fixed value within the problem.
3. coefficient — Numerical or symbolic factor multiplying a term.
4. algebraic expression — Numbers and symbols combined without necessarily stating equality.
5. equation — Mathematical statement that two expressions are equal.
6. identity — Equality true for all permitted values of the variable.
7. factorisation — Writing an expression as a product of factors.
8. expansion — Multiplying brackets to write an expression without them.
9. substitution — Replacing a symbol with a known value or expression.
10. simplification — Rewriting an expression into an equivalent clearer form.

Mini-check: Write one example that uses the term correctly.

11–20: Quadratic functions

11. quadratic function — Function of the form ax² + bx + c with a not zero.
12. quadratic equation — Equation whose highest power of the unknown is two.
13. parabola — Curve forming the graph of a quadratic function.
14. axis of symmetry — Vertical line dividing a standard quadratic graph into mirror halves.
15. turning point — Point where a curve changes from rising to falling or vice versa.
16. vertex — The maximum or minimum point of a non-degenerate parabola.
17. completing the square — Rewriting a quadratic expression in squared-bracket form.
18. discriminant — Expression b² − 4ac determining the types of roots.
19. real root — Solution represented by a real number.
20. repeated root — Root occurring twice when the quadratic discriminant is zero.

Mini-check: Give a counterexample to a plausible misunderstanding.

21–30: Equations and inequalities

21. quadratic formula — Formula giving roots of ax² + bx + c = 0.
22. zero-product property — Rule that a product is zero when at least one factor is zero.
23. x-intercept — Point where a graph meets the horizontal axis.
24. simultaneous equations — Equations whose unknowns must satisfy all statements at once.
25. substitution method — Solving equations by replacing one variable using another equation.
26. quadratic inequality — Comparison involving a quadratic expression and a boundary value.
27. inequality symbol — Sign showing greater than or less than a value.
28. interval notation — Notation representing a continuous set of real-number values.
29. critical value — Boundary at which an expression becomes zero or changes behaviour.
30. solution set — All values satisfying the given equation or inequality.

Mini-check: Sketch or transform a graph illustrating the idea where applicable.

31–40: Surds and exact answers

31. surd — Irrational root written exactly in radical form.
32. radicand — Expression placed under a radical sign.
33. principal square root — Non-negative square root selected by the √ notation.
34. rationalising the denominator — Rewriting a fraction to remove a radical from its denominator.
35. conjugate expression — Partner expression with the opposite sign between paired terms.
36. square root — Number which gives the original value when squared.
37. exact value — Value written without rounding or approximation.
38. irrational number — Real number not expressible as a ratio of integers.
39. equivalent surd — Radical expression with the same numerical value as another.
40. simplified radical — Radical expression reduced by removing perfect-power factors.

Mini-check: Explain how this term changes the method used in a question.

41–50: Polynomials and factors

41. polynomial — Sum of terms with non-negative integer powers of a variable.
42. polynomial degree — Highest exponent occurring in a non-zero polynomial.
43. leading coefficient — Coefficient of a polynomial’s highest-degree term.
44. remainder theorem — Remainder when f(x) is divided by x−a equals f(a).
45. factor theorem — If f(a)=0 then x−a is a factor of f(x).
46. cubic equation — Polynomial equation of degree three.
47. polynomial division — Finding quotient and remainder from division of polynomials.
48. long division — Written algorithm for division using successive leading terms.
49. cubic factorisation — Expressing a cubic polynomial as a product of lower-degree factors.
50. linear factor — Factor of degree one in a polynomial.

Mini-check: Write one example that uses the term correctly.

51–60: Partial fractions

51. rational expression — Quotient of two polynomials with non-zero denominator.
52. proper rational fraction — Rational expression with numerator degree less than denominator degree.
53. improper rational fraction — Rational expression with numerator degree at least denominator degree.
54. partial fraction — One simpler fraction in a sum equivalent to a rational expression.
55. distinct linear factors — Different first-degree factors of a polynomial denominator.
56. repeated linear factor — First-degree factor appearing with multiplicity greater than one.
57. irreducible quadratic — Quadratic polynomial having no real linear factors.
58. decomposition — Rewriting a rational expression as a sum of simpler fractions.
59. denominator — Expression below a fraction bar.
60. numerator — Expression above a fraction bar.

Mini-check: Give a counterexample to a plausible misunderstanding.

61–70: Binomial expansion

61. binomial — Expression containing two terms added or subtracted.
62. binomial expansion — Result of raising a binomial to a positive integer power.
63. binomial coefficient — Number of ways to select a given count from a larger set.
64. factorial — Product of consecutive positive integers down to one.
65. combination — Selection where the order of items does not matter.
66. general term — Formula representing any specified term in an expansion.
67. index — Exponent showing a power to which a base is raised.
68. positive integer — Whole number greater than zero.
69. coefficient of x — Multiplier of the x term of the specified degree.
70. exponent — Number indicating a repeated-power operation.

Mini-check: Sketch or transform a graph illustrating the idea where applicable.

71–80: Exponential and logarithmic functions

71. exponential function — Function in which the variable appears in an exponent.
72. logarithm — Exponent to which a base is raised to produce a given number.
73. logarithmic function — Function giving the logarithm of its input.
74. base — Fixed positive number other than one used in a logarithm.
75. index law — Rule for simplifying expressions with powers.
76. logarithm law — Rule converting products, quotients or powers into log expressions.
77. natural logarithm — Logarithm with base e.
78. Euler’s number — Constant e approximately 2.71828.
79. change-of-base formula — Rule expressing a logarithm using a new base.
80. exponential growth — Increase in proportion to the current amount.

Mini-check: Explain how this term changes the method used in a question.

81–90: The six trigonometric functions

81. sine — Trigonometric function describing vertical coordinate on a unit circle.
82. cosine — Trigonometric function describing horizontal coordinate on a unit circle.
83. tangent — Ratio of sine to cosine where cosine is non-zero.
84. cosecant — Reciprocal of sine where sine is non-zero.
85. secant — Reciprocal of cosine where cosine is non-zero.
86. cotangent — Reciprocal of tangent where defined, equal to cosine over sine.
87. radian — Angle unit based on arc length divided by radius.
88. degree — Angle unit giving 360 degrees to a full revolution.
89. unit circle — Circle centred at the origin with radius one.
90. reference angle — Smallest positive angle to the horizontal axis used for trig signs.

Mini-check: Write one example that uses the term correctly.

91–100: Trigonometric identities and graphs

91. trigonometric identity — Trig equation true for all permitted angles.
92. double-angle formula — Identity relating trig functions of 2A to those of A.
93. angle-addition formula — Identity expressing trig function of a sum of angles.
94. angle-subtraction formula — Identity expressing trig function of an angle difference.
95. reciprocal identity — Relation between a trig function and its reciprocal.
96. Pythagorean identity — Identity such as sin²x + cos²x = 1.
97. amplitude — Maximum vertical distance from a sinusoidal midline.
98. periodicity — Property of a function repeating after a regular interval.
99. phase shift — Horizontal movement of a periodic graph.
100. midline — Central horizontal reference level of an oscillating graph.

Mini-check: Give a counterexample to a plausible misunderstanding.

101–110: Trigonometric equations and inverses

101. principal value — Selected angle returned by an inverse trig function.
102. inverse sine — Function returning an angle whose sine is a stated value.
103. inverse cosine — Function returning an angle whose cosine is a stated value.
104. inverse tangent — Function returning an angle whose tangent is a stated value.
105. trigonometric equation — Equation containing one or more trig functions.
106. domain restriction — Limit on permitted values of an expression or function.
107. periodic symmetry — Repeated and reflected relationships in trig values.
108. exact trigonometric value — Exact sine, cosine or tangent at a special angle.
109. degree mode — Calculator mode interpreting trigonometric angles in degrees.
110. radian mode — Calculator mode interpreting trigonometric angles in radians.

Mini-check: Sketch or transform a graph illustrating the idea where applicable.

111–120: Coordinate geometry

111. Cartesian plane — Two-dimensional plane with perpendicular coordinate axes.
112. ordered pair — Two coordinates written in a fixed order.
113. line gradient — Slope representing vertical change per unit horizontal change.
114. midpoint — Point halfway between two ends of a segment.
115. straight-line equation — Algebraic relation representing a line.
116. perpendicular lines — Lines meeting at a right angle.
117. parallel lines — Lines in a plane with the same direction and no intersection.
118. y-intercept — Point where a graph crosses the vertical axis.
119. equation of a circle — Relation such as (x−a)²+(y−b)²=r².
120. radius — Distance from a circle’s centre to its boundary.

Mini-check: Explain how this term changes the method used in a question.

121–130: Plane geometry and proofs

121. theorem — Mathematical statement established by valid proof.
122. proof — Chain of reasoning demonstrating a mathematical statement.
123. congruence — Equality of shape and size between figures.
124. similarity — Same shape with possibly different sizes.
125. tangent-chord theorem — Relation between tangent–chord angle and angle in the alternate segment.
126. midpoint theorem — Triangle result relating midpoints of two sides to the third.
127. cyclic quadrilateral — Quadrilateral with all vertices on one circle.
128. transversal — Line intersecting two or more other lines.
129. corresponding angle — Angle in the same relative position at two intersections.
130. alternate angle — Angle formed on alternating sides of a transversal.

Mini-check: Write one example that uses the term correctly.

131–140: Graphs and functional language

131. function — Rule assigning exactly one output to each permitted input.
132. domain — Set of inputs for which a function is defined.
133. range — Set of outputs a function can produce.
134. independent variable — Input whose values are selected or varied.
135. dependent variable — Output whose value depends on an input.
136. graph transformation — Change to the position or shape of a graph.
137. translation — Shift of a graph without changing its shape.
138. reflection — Flipping a graph across a selected line.
139. asymptote — Line a curve approaches in a specified limit without necessarily meeting.
140. origin — Point with coordinates (0,0).

Mini-check: Give a counterexample to a plausible misunderstanding.

141–150: Differentiation foundations

141. calculus — Mathematics of continuous change and accumulated quantities.
142. derivative — Instantaneous rate of change of a function.
143. differentiation — Process of finding a derivative.
144. first derivative — Derivative measuring local slope or instantaneous change.
145. instantaneous rate of change — Rate measured at a specified instant or point.
146. tangent line — Line touching a differentiable curve with matching local gradient.
147. normal line — Line perpendicular to the tangent at a curve point.
148. gradient function — Function giving slope at each differentiable point.
149. power rule for differentiation — Rule for deriving powers of x.
150. derivative notation — Symbols such as dy/dx or f′(x) for a derivative.

Mini-check: Sketch or transform a graph illustrating the idea where applicable.

151–160: Rules and stationary points

151. chain rule — Rule for differentiating compositions of functions.
152. product rule — Rule for differentiating a product of two functions.
153. quotient rule — Rule for differentiating a quotient of functions.
154. composite function — Function made by applying one function after another.
155. constant multiple rule — Rule allowing a constant multiplier to stay outside differentiation.
156. sum rule — Rule for differentiating sums term by term.
157. stationary point — Point where the first derivative equals zero.
158. local maximum — Function value greater than nearby values.
159. local minimum — Function value smaller than nearby values.
160. stationary inflexion — Stationary point where concavity changes without local extremum.

Mini-check: Explain how this term changes the method used in a question.

161–170: Using differentiation

161. rate of change — How fast one quantity changes relative to another.
162. increasing function — Function rising as input increases on a given interval.
163. decreasing function — Function falling as input increases on a given interval.
164. second derivative — Derivative of the first derivative.
165. second derivative test — Method using curvature near a stationary point to classify it.
166. optimisation — Finding a permitted maximum or minimum value.
167. gradient at a point — Instantaneous slope evaluated at a chosen input.
168. perpendicular gradient — Slope of a line perpendicular to another non-vertical line.
169. connected rates — Relating simultaneous changes in linked quantities.
170. local extremum — Maximum or minimum relative to nearby values.

Mini-check: Write one example that uses the term correctly.

171–180: Integration fundamentals

171. integration — Operation recovering accumulated change or an antiderivative.
172. antiderivative — Function whose derivative equals the given function.
173. indefinite integral — Family of antiderivatives containing an arbitrary constant.
174. constant of integration — Arbitrary additive constant in indefinite integration.
175. definite integral — Integral evaluated between stated bounds.
176. upper limit — Final bound of a definite integral.
177. lower limit — Initial bound of a definite integral.
178. integrand — Function being integrated.
179. power rule for integration — Rule finding antiderivative of most powers of x.
180. integral notation — Symbol ∫ and accompanying expression used for integration.

Mini-check: Give a counterexample to a plausible misunderstanding.

181–190: Integration in applications

181. bounded region — Area enclosed by specified curves or lines.
182. area under a curve — Geometric region between graph and reference axis where appropriate.
183. signed area — Integral contribution positive above and negative below a horizontal axis.
184. integration limits — Input values defining the interval of a definite integral.
185. displacement from velocity — Net position change obtained by integrating velocity over time.
186. velocity from acceleration — Change in velocity obtained by integrating acceleration over time.
187. region below the x-axis — Graph region whose definite integral has negative sign.
188. net change — Final quantity minus initial quantity over an interval.
189. total distance — Length travelled regardless of direction or signed displacement.
190. reverse differentiation — Using antiderivatives to undo a derivative up to a constant.

Mini-check: Sketch or transform a graph illustrating the idea where applicable.

191–200: Examination wording and accuracy

191. hence — Use the result just established to reach the next result.
192. deduce — Infer the answer logically from given or proved information.
193. show that — Demonstrate the specified result with valid working.
194. prove — Establish a statement by logically sound argument.
195. solve — Find all values satisfying stated conditions.
196. approximate — Express a value close to, but not necessarily equal to, the exact one.
197. significant figure — A meaningful digit counted from the first non-zero digit.
198. exact form — Answer retained in symbols rather than rounded decimal form.
199. sketch — Draw key shape and features without exact plotting every point.
200. interpret — Explain what a mathematical result means in context.

Mini-check: Explain how this term changes the method used in a question.

Six worked examples that connect mathematical vocabulary to results

1. Discriminant: why roots can disappear

For x² − 4x + 4 = 0, the discriminant is (−4)² − 4(1)(4) = 0. This means the quadratic has a repeated real root, x = 2. The parabola touches the horizontal axis at one point. If a student confuses the discriminant with the turning point’s coordinates, the graph interpretation will be wrong even if the quadratic formula is recalled.

2. Completing the square: see the turning point immediately

The function f(x) = x² − 6x + 11 can be rewritten as (x − 3)² + 2. Its minimum is 2 at x = 3. The form reveals the vertex and symmetry without needing many substituted points. This is a useful comparison between algebraic rewriting and graph understanding.

3. Remainder theorem: one substitution replaces a long calculation

Let f(x) = x³ − 2x + 5. Dividing by x − 2 leaves remainder f(2) = 8 − 4 + 5 = 9. A zero remainder would show x−2 is a factor; here it is not. “Factor” and “remainder” are linked but not interchangeable.

4. Logarithm: an exponent written the other way around

2³ = 8 is equivalent to log₂ 8 = 3. The base is 2, the result is 8 and the logarithm tells us the exponent 3. The arguments must remain positive in the real-number domain and the base must be positive and not one.

5. Derivative: slope now, not merely average slope

For y = x² − 4x + 1, the derivative is dy/dx = 2x − 4. At x = 3, the tangent gradient is 2. At x = 2, the derivative is zero and the curve has a local minimum. The derivative is a function describing local rate of change; a stationary point is a position at which that rate equals zero.

6. Definite integral: signed area versus geometric area

Integrating y = x from −1 to 1 gives 0 because positive and negative signed areas cancel. The total geometric area between this line and the x-axis over the same interval is 1 square unit, found by adding the absolute areas of the two triangles. This is why “evaluate the integral” and “find the area” sometimes need different final steps.

The most useful distinctions in A-Math

Expression versus equation: x²−1 is an expression; x²−1=0 states a condition to solve. Identity versus equation: an identity holds throughout its permitted domain, while an equation may hold only for particular inputs. Approximate versus exact: √2 is exact; 1.414 is a rounded approximation. Gradient versus derivative: a straight line has a constant gradient, while a derivative gives the local gradient of a varying curve.

How to read the 2027 K341 paper

For 2027, SEAB specifies two written papers, each 2 hours 15 minutes and 50% of the assessment, with 90 marks each. Approved calculators may be used in both papers, and essential working must be shown. For non-exact answers, follow the syllabus’s accuracy instructions rather than rounding too early. The provided formulae do not remove the need to know how and when relationships apply.

A four-week connected revision plan

1. Week 1 — Algebra: use sets 1–8. Alternate solving quadratics, manipulating surds, factorising polynomials and translating exponential-logarithmic statements.
2. Week 2 — Trigonometry: use sets 9–11. Draw periodic graphs, use identities and solve restricted-domain trig equations with the correct calculator mode.
3. Week 3 — Geometry and graphs: use sets 12–14. Practise circle equations, line gradients, proofs and the meaning of domain and range.
4. Week 4 — Calculus and reasoning: use sets 15–20. Differentiate, integrate, interpret rates and areas, and write full justifications. Revisit all previously missed terms.

One correctly reasoned problem may teach five terms simultaneously. The goal is to reduce avoidable uncertainty, not make the child’s routine longer than necessary.

Common mistakes to catch before an exam

• Dividing or cancelling by an algebraic expression that might equal zero without checking the lost case.
• Ignoring positive-input restrictions for real logarithms.
• Confusing trigonometric degrees with radians in calculation.
• Claiming any stationary point must be a maximum or minimum; stationary points of inflexion exist.
• Forgetting the arbitrary additive constant after indefinite integration.
• Using signed integral output as geometric area without checking whether a region lies below the axis.

Frequently asked questions

Is this the official list of 200 K341 A-Math words?

No. This is an independently prepared glossary aligned to relevant topics. Use SEAB’s 2027 syllabus index and the full K341 document to check learning outcomes.

Is Additional Mathematics compulsory for all G3 students?

No. Subject offering and entry decisions depend on the school’s subject arrangements. Confirm the available options with the school.

What should we learn first: calculus or algebra?

Secure core algebraic manipulation and graphs first. Differentiation and integration make much more sense when functions and exponents are reliable.

Are all 200 terms equally important?

No. Some bridge different topics or clarify notation. Select those that correspond to present syllabus work and repeat problem-solving errors.

What should a Punggol parent check on an A-Math paper?

Look for precise understanding of the instruction, complete working, domain checks, signs and interpretation, rather than merely counting the number of questions attempted.

How does this help later H2 Mathematics?

It builds the language of algebra, trigonometric functions and basic calculus, which makes later mathematics easier to interpret.

Official sources and related eduKate reading

The 2027 SEAB G3 Additional Mathematics syllabus K341 confirms the three content strands and the two-paper assessment; the G3 2027 subject index confirms K341 and the earlier reference 4049. Read Can my child take Additional Mathematics in Secondary 3? and Bar models or algebra: selecting a useful model for related learning decisions. Additional Mathematics support is most useful when the starting position is clear.

eduKate Punggol educational glossary, November 2026. This is independent commentary and a learning aid, not an official SEAB word list.