E-Math & A-Math Word-Problem Vocabulary

A Math vocabulary is not extra terminology around the subject; it tells students what mathematical or examination action the question requires. Secondary Mathematics vocabulary connects ordinary language to algebraic, graphical, geometric and trigonometric representations. This page begins with a usable vocabulary bank, then turns each term into an answer frame, representation or reasoning move so that language and subject knowledge work together.

Searches for A Math vocabulary often overlap with O-Level exam command words, E-Math word problems, A-Math vocabulary, secondary Mathematics keywords and how to answer describe/explain/compare questions. The shared difficulty is translation. A student can know a concept and still lose marks if the command, qualifier or relationship is misread.

Build E-Math and A-Math vocabulary by translating important terms into symbols, diagrams, equations or relationships. Words such as respectively, at least, gradient, factor, tangent and direct proportion control the mathematical model. Use this page with the Singapore Vocabulary Guide and the eduKate Vocabulary Learning System.

Quick Read

Algebra, graphs, geometry, trigonometry, rates and logic.
Translate terms into symbols and diagrams.
Watch inequality language such as at least/at most.
Distinguish everyday from mathematical meanings.
Practise terms inside full problems.

The short answer

72 E-Math and A-Math vocabulary items

Algebra

1. expression

For expression, write the mathematical meaning, a symbolic or diagram representation and one typical word-problem sentence. Then create a near-term that would be wrong in that context. The word should trigger a precise mathematical object, relationship or action rather than a vague association.

2. equation

For equation, write the mathematical meaning, a symbolic or diagram representation and one typical word-problem sentence. Then create a near-term that would be wrong in that context. The word should trigger a precise mathematical object, relationship or action rather than a vague association.

3. identity

For identity, write the mathematical meaning, a symbolic or diagram representation and one typical word-problem sentence. Then create a near-term that would be wrong in that context. The word should trigger a precise mathematical object, relationship or action rather than a vague association.

4. coefficient

For coefficient, write the mathematical meaning, a symbolic or diagram representation and one typical word-problem sentence. Then create a near-term that would be wrong in that context. The word should trigger a precise mathematical object, relationship or action rather than a vague association.

5. constant

For constant, write the mathematical meaning, a symbolic or diagram representation and one typical word-problem sentence. Then create a near-term that would be wrong in that context. The word should trigger a precise mathematical object, relationship or action rather than a vague association.

6. variable

For variable, write the mathematical meaning, a symbolic or diagram representation and one typical word-problem sentence. Then create a near-term that would be wrong in that context. The word should trigger a precise mathematical object, relationship or action rather than a vague association.

7. term

For term, write the mathematical meaning, a symbolic or diagram representation and one typical word-problem sentence. Then create a near-term that would be wrong in that context. The word should trigger a precise mathematical object, relationship or action rather than a vague association.

8. factor

For factor, write the mathematical meaning, a symbolic or diagram representation and one typical word-problem sentence. Then create a near-term that would be wrong in that context. The word should trigger a precise mathematical object, relationship or action rather than a vague association.

9. expand

For expand, write the mathematical meaning, a symbolic or diagram representation and one typical word-problem sentence. Then create a near-term that would be wrong in that context. The word should trigger a precise mathematical object, relationship or action rather than a vague association.

10. factorise

For factorise, write the mathematical meaning, a symbolic or diagram representation and one typical word-problem sentence. Then create a near-term that would be wrong in that context. The word should trigger a precise mathematical object, relationship or action rather than a vague association.

11. substitute

For substitute, write the mathematical meaning, a symbolic or diagram representation and one typical word-problem sentence. Then create a near-term that would be wrong in that context. The word should trigger a precise mathematical object, relationship or action rather than a vague association.

12. simplify

For simplify, write the mathematical meaning, a symbolic or diagram representation and one typical word-problem sentence. Then create a near-term that would be wrong in that context. The word should trigger a precise mathematical object, relationship or action rather than a vague association.

Functions and graphs

13. function

For function, write the mathematical meaning, a symbolic or diagram representation and one typical word-problem sentence. Then create a near-term that would be wrong in that context. The word should trigger a precise mathematical object, relationship or action rather than a vague association.

14. domain

For domain, write the mathematical meaning, a symbolic or diagram representation and one typical word-problem sentence. Then create a near-term that would be wrong in that context. The word should trigger a precise mathematical object, relationship or action rather than a vague association.

15. range

For range, write the mathematical meaning, a symbolic or diagram representation and one typical word-problem sentence. Then create a near-term that would be wrong in that context. The word should trigger a precise mathematical object, relationship or action rather than a vague association.

16. gradient

For gradient, write the mathematical meaning, a symbolic or diagram representation and one typical word-problem sentence. Then create a near-term that would be wrong in that context. The word should trigger a precise mathematical object, relationship or action rather than a vague association.

17. intercept

For intercept, write the mathematical meaning, a symbolic or diagram representation and one typical word-problem sentence. Then create a near-term that would be wrong in that context. The word should trigger a precise mathematical object, relationship or action rather than a vague association.

18. turning point

For turning point, write the mathematical meaning, a symbolic or diagram representation and one typical word-problem sentence. Then create a near-term that would be wrong in that context. The word should trigger a precise mathematical object, relationship or action rather than a vague association.

19. increasing

For increasing, write the mathematical meaning, a symbolic or diagram representation and one typical word-problem sentence. Then create a near-term that would be wrong in that context. The word should trigger a precise mathematical object, relationship or action rather than a vague association.

20. decreasing

For decreasing, write the mathematical meaning, a symbolic or diagram representation and one typical word-problem sentence. Then create a near-term that would be wrong in that context. The word should trigger a precise mathematical object, relationship or action rather than a vague association.

21. maximum

For maximum, write the mathematical meaning, a symbolic or diagram representation and one typical word-problem sentence. Then create a near-term that would be wrong in that context. The word should trigger a precise mathematical object, relationship or action rather than a vague association.

22. minimum

For minimum, write the mathematical meaning, a symbolic or diagram representation and one typical word-problem sentence. Then create a near-term that would be wrong in that context. The word should trigger a precise mathematical object, relationship or action rather than a vague association.

23. linear

For linear, write the mathematical meaning, a symbolic or diagram representation and one typical word-problem sentence. Then create a near-term that would be wrong in that context. The word should trigger a precise mathematical object, relationship or action rather than a vague association.

24. quadratic

For quadratic, write the mathematical meaning, a symbolic or diagram representation and one typical word-problem sentence. Then create a near-term that would be wrong in that context. The word should trigger a precise mathematical object, relationship or action rather than a vague association.

Geometry

25. parallel

For parallel, write the mathematical meaning, a symbolic or diagram representation and one typical word-problem sentence. Then create a near-term that would be wrong in that context. The word should trigger a precise mathematical object, relationship or action rather than a vague association.

26. perpendicular

For perpendicular, write the mathematical meaning, a symbolic or diagram representation and one typical word-problem sentence. Then create a near-term that would be wrong in that context. The word should trigger a precise mathematical object, relationship or action rather than a vague association.

27. tangent

For tangent, write the mathematical meaning, a symbolic or diagram representation and one typical word-problem sentence. Then create a near-term that would be wrong in that context. The word should trigger a precise mathematical object, relationship or action rather than a vague association.

28. radius

For radius, write the mathematical meaning, a symbolic or diagram representation and one typical word-problem sentence. Then create a near-term that would be wrong in that context. The word should trigger a precise mathematical object, relationship or action rather than a vague association.

29. diameter

For diameter, write the mathematical meaning, a symbolic or diagram representation and one typical word-problem sentence. Then create a near-term that would be wrong in that context. The word should trigger a precise mathematical object, relationship or action rather than a vague association.

30. chord

For chord, write the mathematical meaning, a symbolic or diagram representation and one typical word-problem sentence. Then create a near-term that would be wrong in that context. The word should trigger a precise mathematical object, relationship or action rather than a vague association.

31. arc

For arc, write the mathematical meaning, a symbolic or diagram representation and one typical word-problem sentence. Then create a near-term that would be wrong in that context. The word should trigger a precise mathematical object, relationship or action rather than a vague association.

32. sector

For sector, write the mathematical meaning, a symbolic or diagram representation and one typical word-problem sentence. Then create a near-term that would be wrong in that context. The word should trigger a precise mathematical object, relationship or action rather than a vague association.

33. similar

For similar, write the mathematical meaning, a symbolic or diagram representation and one typical word-problem sentence. Then create a near-term that would be wrong in that context. The word should trigger a precise mathematical object, relationship or action rather than a vague association.

34. congruent

For congruent, write the mathematical meaning, a symbolic or diagram representation and one typical word-problem sentence. Then create a near-term that would be wrong in that context. The word should trigger a precise mathematical object, relationship or action rather than a vague association.

35. angle

For angle, write the mathematical meaning, a symbolic or diagram representation and one typical word-problem sentence. Then create a near-term that would be wrong in that context. The word should trigger a precise mathematical object, relationship or action rather than a vague association.

36. bearing

For bearing, write the mathematical meaning, a symbolic or diagram representation and one typical word-problem sentence. Then create a near-term that would be wrong in that context. The word should trigger a precise mathematical object, relationship or action rather than a vague association.

Trigonometry

37. sine

For sine, write the mathematical meaning, a symbolic or diagram representation and one typical word-problem sentence. Then create a near-term that would be wrong in that context. The word should trigger a precise mathematical object, relationship or action rather than a vague association.

38. cosine

For cosine, write the mathematical meaning, a symbolic or diagram representation and one typical word-problem sentence. Then create a near-term that would be wrong in that context. The word should trigger a precise mathematical object, relationship or action rather than a vague association.

39. tangent ratio

For tangent ratio, write the mathematical meaning, a symbolic or diagram representation and one typical word-problem sentence. Then create a near-term that would be wrong in that context. The word should trigger a precise mathematical object, relationship or action rather than a vague association.

40. opposite

For opposite, write the mathematical meaning, a symbolic or diagram representation and one typical word-problem sentence. Then create a near-term that would be wrong in that context. The word should trigger a precise mathematical object, relationship or action rather than a vague association.

41. adjacent

For adjacent, write the mathematical meaning, a symbolic or diagram representation and one typical word-problem sentence. Then create a near-term that would be wrong in that context. The word should trigger a precise mathematical object, relationship or action rather than a vague association.

42. hypotenuse

For hypotenuse, write the mathematical meaning, a symbolic or diagram representation and one typical word-problem sentence. Then create a near-term that would be wrong in that context. The word should trigger a precise mathematical object, relationship or action rather than a vague association.

43. angle of elevation

For angle of elevation, write the mathematical meaning, a symbolic or diagram representation and one typical word-problem sentence. Then create a near-term that would be wrong in that context. The word should trigger a precise mathematical object, relationship or action rather than a vague association.

44. angle of depression

For angle of depression, write the mathematical meaning, a symbolic or diagram representation and one typical word-problem sentence. Then create a near-term that would be wrong in that context. The word should trigger a precise mathematical object, relationship or action rather than a vague association.

45. radian

For radian, write the mathematical meaning, a symbolic or diagram representation and one typical word-problem sentence. Then create a near-term that would be wrong in that context. The word should trigger a precise mathematical object, relationship or action rather than a vague association.

46. amplitude

For amplitude, write the mathematical meaning, a symbolic or diagram representation and one typical word-problem sentence. Then create a near-term that would be wrong in that context. The word should trigger a precise mathematical object, relationship or action rather than a vague association.

47. period

For period, write the mathematical meaning, a symbolic or diagram representation and one typical word-problem sentence. Then create a near-term that would be wrong in that context. The word should trigger a precise mathematical object, relationship or action rather than a vague association.

48. identity

Rates and proportion

49. direct proportion

For direct proportion, write the mathematical meaning, a symbolic or diagram representation and one typical word-problem sentence. Then create a near-term that would be wrong in that context. The word should trigger a precise mathematical object, relationship or action rather than a vague association.

50. inverse proportion

For inverse proportion, write the mathematical meaning, a symbolic or diagram representation and one typical word-problem sentence. Then create a near-term that would be wrong in that context. The word should trigger a precise mathematical object, relationship or action rather than a vague association.

51. rate

For rate, write the mathematical meaning, a symbolic or diagram representation and one typical word-problem sentence. Then create a near-term that would be wrong in that context. The word should trigger a precise mathematical object, relationship or action rather than a vague association.

52. speed

For speed, write the mathematical meaning, a symbolic or diagram representation and one typical word-problem sentence. Then create a near-term that would be wrong in that context. The word should trigger a precise mathematical object, relationship or action rather than a vague association.

53. density

For density, write the mathematical meaning, a symbolic or diagram representation and one typical word-problem sentence. Then create a near-term that would be wrong in that context. The word should trigger a precise mathematical object, relationship or action rather than a vague association.

54. average

For average, write the mathematical meaning, a symbolic or diagram representation and one typical word-problem sentence. Then create a near-term that would be wrong in that context. The word should trigger a precise mathematical object, relationship or action rather than a vague association.

55. constant of proportionality

For constant of proportionality, write the mathematical meaning, a symbolic or diagram representation and one typical word-problem sentence. Then create a near-term that would be wrong in that context. The word should trigger a precise mathematical object, relationship or action rather than a vague association.

56. percentage change

For percentage change, write the mathematical meaning, a symbolic or diagram representation and one typical word-problem sentence. Then create a near-term that would be wrong in that context. The word should trigger a precise mathematical object, relationship or action rather than a vague association.

57. ratio

For ratio, write the mathematical meaning, a symbolic or diagram representation and one typical word-problem sentence. Then create a near-term that would be wrong in that context. The word should trigger a precise mathematical object, relationship or action rather than a vague association.

58. scale

For scale, write the mathematical meaning, a symbolic or diagram representation and one typical word-problem sentence. Then create a near-term that would be wrong in that context. The word should trigger a precise mathematical object, relationship or action rather than a vague association.

59. unit rate

For unit rate, write the mathematical meaning, a symbolic or diagram representation and one typical word-problem sentence. Then create a near-term that would be wrong in that context. The word should trigger a precise mathematical object, relationship or action rather than a vague association.

60. compound change

For compound change, write the mathematical meaning, a symbolic or diagram representation and one typical word-problem sentence. Then create a near-term that would be wrong in that context. The word should trigger a precise mathematical object, relationship or action rather than a vague association.

Word-problem logic

61. at least

For at least, write the mathematical meaning, a symbolic or diagram representation and one typical word-problem sentence. Then create a near-term that would be wrong in that context. The word should trigger a precise mathematical object, relationship or action rather than a vague association.

62. at most

For at most, write the mathematical meaning, a symbolic or diagram representation and one typical word-problem sentence. Then create a near-term that would be wrong in that context. The word should trigger a precise mathematical object, relationship or action rather than a vague association.

63. no more than

For no more than, write the mathematical meaning, a symbolic or diagram representation and one typical word-problem sentence. Then create a near-term that would be wrong in that context. The word should trigger a precise mathematical object, relationship or action rather than a vague association.

64. no less than

For no less than, write the mathematical meaning, a symbolic or diagram representation and one typical word-problem sentence. Then create a near-term that would be wrong in that context. The word should trigger a precise mathematical object, relationship or action rather than a vague association.

65. respectively

For respectively, write the mathematical meaning, a symbolic or diagram representation and one typical word-problem sentence. Then create a near-term that would be wrong in that context. The word should trigger a precise mathematical object, relationship or action rather than a vague association.

66. consecutive

For consecutive, write the mathematical meaning, a symbolic or diagram representation and one typical word-problem sentence. Then create a near-term that would be wrong in that context. The word should trigger a precise mathematical object, relationship or action rather than a vague association.

67. integer

For integer, write the mathematical meaning, a symbolic or diagram representation and one typical word-problem sentence. Then create a near-term that would be wrong in that context. The word should trigger a precise mathematical object, relationship or action rather than a vague association.

68. remainder

For remainder, write the mathematical meaning, a symbolic or diagram representation and one typical word-problem sentence. Then create a near-term that would be wrong in that context. The word should trigger a precise mathematical object, relationship or action rather than a vague association.

69. difference

For difference, write the mathematical meaning, a symbolic or diagram representation and one typical word-problem sentence. Then create a near-term that would be wrong in that context. The word should trigger a precise mathematical object, relationship or action rather than a vague association.

70. product

For product, write the mathematical meaning, a symbolic or diagram representation and one typical word-problem sentence. Then create a near-term that would be wrong in that context. The word should trigger a precise mathematical object, relationship or action rather than a vague association.

71. sum

For sum, write the mathematical meaning, a symbolic or diagram representation and one typical word-problem sentence. Then create a near-term that would be wrong in that context. The word should trigger a precise mathematical object, relationship or action rather than a vague association.

72. in terms of

For in terms of, write the mathematical meaning, a symbolic or diagram representation and one typical word-problem sentence. Then create a near-term that would be wrong in that context. The word should trigger a precise mathematical object, relationship or action rather than a vague association.

Language controls the answer shape

Underline the command, relationship or qualifier before solving. Convert it into a mental frame: describe what changes, explain why, compare A with B, show working, identify a value, or justify a choice. This prevents correct knowledge from being poured into the wrong response shape.

Apply this directly to A Math vocabulary: choose three terms from the bank, build a question for each, represent the meaning and create one plausible but wrong interpretation. Explain the boundary before solving.

Represent the meaning

Translate important words into an equation, graph feature, diagram, inequality or answer structure. Then translate the representation back into words. Bidirectional translation reveals whether the student truly understands the term.

The Fencing Method

Place near-terms side by side and state the boundary. State/describe/explain; factor/term/coefficient; at least/at most; tangent/chord; increase by/increase to. Minimal pairs reveal the exact word that changes the mathematical or response requirement.

Units and conditions

Words such as respectively, constant, exact, approximate, per, no more than and integer constrain the answer. They are not minor details. Annotate them before calculation so the model respects every condition.

Worked reasoning

For each term, create one question where it is central and one near-miss question where a related term would change the method. Solve both. Contrastive problems make vocabulary differences memorable because they change what the student does.

Retrieval

Close the page and retrieve from a representation. Show a graph and ask for gradient, intercept, turning point or increasing. Give an instruction and ask which command word would produce it. Reverse practice creates stronger access.

Error diagnosis

Separate vocabulary misunderstanding from mathematical or subject error. If the student built the wrong equation from correct arithmetic, repair language-to-model translation. If the model was correct but execution failed, repair the mathematical process.

Transfer

Move the vocabulary across textbook questions, unfamiliar contexts and timed practice. A term is mastered when it triggers the correct reasoning even when the surface story changes.

30 translation drills

Drill 1

Choose one term from this page. Write a question that makes the term essential, convert it to a representation or answer frame, and solve or answer it. Then change one word so a different method or depth is required. Compare the two versions.

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Frequently asked questions

Should students memorise definitions?

Definitions are a start; the term must also trigger the correct representation or answer action.

Why do command words matter?

They specify the response shape and often the depth of reasoning expected.

Are keyword tricks reliable in Mathematics?

No single word should override the full relationship and conditions.

How should parents help?

Ask the student to explain the wording before calculating.

How should teachers diagnose errors?

Separate language interpretation, representation and execution.

Can one term have an everyday and mathematical meaning?

Yes. Context decides which technical meaning applies.

How should vocabulary be revised?

Inside real subject questions, not only as isolated flashcards.

What shows mastery?

The student can translate accurately from wording to reasoning and back again.

Continue through the Singapore Vocabulary Guide.

eduKate SG

E-Math and A-Math Word-Problem Vocabulary