G2 Mathematics K210 verification is strongest when the final answer is put back into the original problem. Solving moves from conditions to an answer; forward substitution moves from the candidate answer back through the conditions to see whether it actually satisfies them.
This one-hundred-and-fourteenth Learner’s Guide develops forward-substitution verification. It complements Vol 0102 Work-Backward Reconstruction and Vol 0072 Verification Asymmetry.
The forward-substitution protocol
Take the candidate answer, insert it into the earliest original relation available, and recompute the observable condition. Check equality, units, domain and context. Whenever possible, verify against the original problem rather than the transformed equation where an extraneous solution may have entered.
1. linear equation
For linear equation, identify the original condition that the candidate must satisfy. Substitute the candidate and evaluate that condition without repeating the entire solving route.
If the candidate fails, locate the earliest transformation capable of producing the mismatch. If it passes algebraically but fails domain, unit or context, reject it anyway. Verification tests the whole answer, not just arithmetic consistency.
For practice, include one deliberately wrong candidate that is numerically close to the correct answer. Forward substitution should reject it for a specific reason: equality fails, constraint fails, unit fails or the reconstructed quantity does not match the given data.
2. simultaneous equations
For simultaneous equations, identify the original condition that the candidate must satisfy. Substitute the candidate and evaluate that condition without repeating the entire solving route.
If the candidate fails, locate the earliest transformation capable of producing the mismatch. If it passes algebraically but fails domain, unit or context, reject it anyway. Verification tests the whole answer, not just arithmetic consistency.
For practice, include one deliberately wrong candidate that is numerically close to the correct answer. Forward substitution should reject it for a specific reason: equality fails, constraint fails, unit fails or the reconstructed quantity does not match the given data.
3. quadratic root
For quadratic root, identify the original condition that the candidate must satisfy. Substitute the candidate and evaluate that condition without repeating the entire solving route.
If the candidate fails, locate the earliest transformation capable of producing the mismatch. If it passes algebraically but fails domain, unit or context, reject it anyway. Verification tests the whole answer, not just arithmetic consistency.
For practice, include one deliberately wrong candidate that is numerically close to the correct answer. Forward substitution should reject it for a specific reason: equality fails, constraint fails, unit fails or the reconstructed quantity does not match the given data.
4. factorised equation
For factorised equation, identify the original condition that the candidate must satisfy. Substitute the candidate and evaluate that condition without repeating the entire solving route.
If the candidate fails, locate the earliest transformation capable of producing the mismatch. If it passes algebraically but fails domain, unit or context, reject it anyway. Verification tests the whole answer, not just arithmetic consistency.
For practice, include one deliberately wrong candidate that is numerically close to the correct answer. Forward substitution should reject it for a specific reason: equality fails, constraint fails, unit fails or the reconstructed quantity does not match the given data.
5. fractional equation
For fractional equation, identify the original condition that the candidate must satisfy. Substitute the candidate and evaluate that condition without repeating the entire solving route.
If the candidate fails, locate the earliest transformation capable of producing the mismatch. If it passes algebraically but fails domain, unit or context, reject it anyway. Verification tests the whole answer, not just arithmetic consistency.
For practice, include one deliberately wrong candidate that is numerically close to the correct answer. Forward substitution should reject it for a specific reason: equality fails, constraint fails, unit fails or the reconstructed quantity does not match the given data.
6. formula rearrangement
For formula rearrangement, identify the original condition that the candidate must satisfy. Substitute the candidate and evaluate that condition without repeating the entire solving route.
If the candidate fails, locate the earliest transformation capable of producing the mismatch. If it passes algebraically but fails domain, unit or context, reject it anyway. Verification tests the whole answer, not just arithmetic consistency.
For practice, include one deliberately wrong candidate that is numerically close to the correct answer. Forward substitution should reject it for a specific reason: equality fails, constraint fails, unit fails or the reconstructed quantity does not match the given data.
7. percentage original
For percentage original, identify the original condition that the candidate must satisfy. Substitute the candidate and evaluate that condition without repeating the entire solving route.
If the candidate fails, locate the earliest transformation capable of producing the mismatch. If it passes algebraically but fails domain, unit or context, reject it anyway. Verification tests the whole answer, not just arithmetic consistency.
For practice, include one deliberately wrong candidate that is numerically close to the correct answer. Forward substitution should reject it for a specific reason: equality fails, constraint fails, unit fails or the reconstructed quantity does not match the given data.
8. percentage final
For percentage final, identify the original condition that the candidate must satisfy. Substitute the candidate and evaluate that condition without repeating the entire solving route.
If the candidate fails, locate the earliest transformation capable of producing the mismatch. If it passes algebraically but fails domain, unit or context, reject it anyway. Verification tests the whole answer, not just arithmetic consistency.
For practice, include one deliberately wrong candidate that is numerically close to the correct answer. Forward substitution should reject it for a specific reason: equality fails, constraint fails, unit fails or the reconstructed quantity does not match the given data.
9. ratio part
For ratio part, identify the original condition that the candidate must satisfy. Substitute the candidate and evaluate that condition without repeating the entire solving route.
If the candidate fails, locate the earliest transformation capable of producing the mismatch. If it passes algebraically but fails domain, unit or context, reject it anyway. Verification tests the whole answer, not just arithmetic consistency.
For practice, include one deliberately wrong candidate that is numerically close to the correct answer. Forward substitution should reject it for a specific reason: equality fails, constraint fails, unit fails or the reconstructed quantity does not match the given data.
10. ratio total
For ratio total, identify the original condition that the candidate must satisfy. Substitute the candidate and evaluate that condition without repeating the entire solving route.
If the candidate fails, locate the earliest transformation capable of producing the mismatch. If it passes algebraically but fails domain, unit or context, reject it anyway. Verification tests the whole answer, not just arithmetic consistency.
For practice, include one deliberately wrong candidate that is numerically close to the correct answer. Forward substitution should reject it for a specific reason: equality fails, constraint fails, unit fails or the reconstructed quantity does not match the given data.
11. rate equation
For rate equation, identify the original condition that the candidate must satisfy. Substitute the candidate and evaluate that condition without repeating the entire solving route.
If the candidate fails, locate the earliest transformation capable of producing the mismatch. If it passes algebraically but fails domain, unit or context, reject it anyway. Verification tests the whole answer, not just arithmetic consistency.
For practice, include one deliberately wrong candidate that is numerically close to the correct answer. Forward substitution should reject it for a specific reason: equality fails, constraint fails, unit fails or the reconstructed quantity does not match the given data.
12. speed-distance-time
For speed-distance-time, identify the original condition that the candidate must satisfy. Substitute the candidate and evaluate that condition without repeating the entire solving route.
If the candidate fails, locate the earliest transformation capable of producing the mismatch. If it passes algebraically but fails domain, unit or context, reject it anyway. Verification tests the whole answer, not just arithmetic consistency.
For practice, include one deliberately wrong candidate that is numerically close to the correct answer. Forward substitution should reject it for a specific reason: equality fails, constraint fails, unit fails or the reconstructed quantity does not match the given data.
13. density relation
For density relation, identify the original condition that the candidate must satisfy. Substitute the candidate and evaluate that condition without repeating the entire solving route.
If the candidate fails, locate the earliest transformation capable of producing the mismatch. If it passes algebraically but fails domain, unit or context, reject it anyway. Verification tests the whole answer, not just arithmetic consistency.
For practice, include one deliberately wrong candidate that is numerically close to the correct answer. Forward substitution should reject it for a specific reason: equality fails, constraint fails, unit fails or the reconstructed quantity does not match the given data.
14. mean reconstruction
For mean reconstruction, identify the original condition that the candidate must satisfy. Substitute the candidate and evaluate that condition without repeating the entire solving route.
If the candidate fails, locate the earliest transformation capable of producing the mismatch. If it passes algebraically but fails domain, unit or context, reject it anyway. Verification tests the whole answer, not just arithmetic consistency.
For practice, include one deliberately wrong candidate that is numerically close to the correct answer. Forward substitution should reject it for a specific reason: equality fails, constraint fails, unit fails or the reconstructed quantity does not match the given data.
15. weighted mean
For weighted mean, identify the original condition that the candidate must satisfy. Substitute the candidate and evaluate that condition without repeating the entire solving route.
If the candidate fails, locate the earliest transformation capable of producing the mismatch. If it passes algebraically but fails domain, unit or context, reject it anyway. Verification tests the whole answer, not just arithmetic consistency.
For practice, include one deliberately wrong candidate that is numerically close to the correct answer. Forward substitution should reject it for a specific reason: equality fails, constraint fails, unit fails or the reconstructed quantity does not match the given data.
16. probability complement
For probability complement, identify the original condition that the candidate must satisfy. Substitute the candidate and evaluate that condition without repeating the entire solving route.
If the candidate fails, locate the earliest transformation capable of producing the mismatch. If it passes algebraically but fails domain, unit or context, reject it anyway. Verification tests the whole answer, not just arithmetic consistency.
For practice, include one deliberately wrong candidate that is numerically close to the correct answer. Forward substitution should reject it for a specific reason: equality fails, constraint fails, unit fails or the reconstructed quantity does not match the given data.
17. probability tree path
For probability tree path, identify the original condition that the candidate must satisfy. Substitute the candidate and evaluate that condition without repeating the entire solving route.
If the candidate fails, locate the earliest transformation capable of producing the mismatch. If it passes algebraically but fails domain, unit or context, reject it anyway. Verification tests the whole answer, not just arithmetic consistency.
For practice, include one deliberately wrong candidate that is numerically close to the correct answer. Forward substitution should reject it for a specific reason: equality fails, constraint fails, unit fails or the reconstructed quantity does not match the given data.
18. direct proportion
For direct proportion, identify the original condition that the candidate must satisfy. Substitute the candidate and evaluate that condition without repeating the entire solving route.
If the candidate fails, locate the earliest transformation capable of producing the mismatch. If it passes algebraically but fails domain, unit or context, reject it anyway. Verification tests the whole answer, not just arithmetic consistency.
For practice, include one deliberately wrong candidate that is numerically close to the correct answer. Forward substitution should reject it for a specific reason: equality fails, constraint fails, unit fails or the reconstructed quantity does not match the given data.
19. inverse proportion
For inverse proportion, identify the original condition that the candidate must satisfy. Substitute the candidate and evaluate that condition without repeating the entire solving route.
If the candidate fails, locate the earliest transformation capable of producing the mismatch. If it passes algebraically but fails domain, unit or context, reject it anyway. Verification tests the whole answer, not just arithmetic consistency.
For practice, include one deliberately wrong candidate that is numerically close to the correct answer. Forward substitution should reject it for a specific reason: equality fails, constraint fails, unit fails or the reconstructed quantity does not match the given data.
20. arithmetic sequence
For arithmetic sequence, identify the original condition that the candidate must satisfy. Substitute the candidate and evaluate that condition without repeating the entire solving route.
If the candidate fails, locate the earliest transformation capable of producing the mismatch. If it passes algebraically but fails domain, unit or context, reject it anyway. Verification tests the whole answer, not just arithmetic consistency.
For practice, include one deliberately wrong candidate that is numerically close to the correct answer. Forward substitution should reject it for a specific reason: equality fails, constraint fails, unit fails or the reconstructed quantity does not match the given data.
21. geometric sequence
For geometric sequence, identify the original condition that the candidate must satisfy. Substitute the candidate and evaluate that condition without repeating the entire solving route.
If the candidate fails, locate the earliest transformation capable of producing the mismatch. If it passes algebraically but fails domain, unit or context, reject it anyway. Verification tests the whole answer, not just arithmetic consistency.
For practice, include one deliberately wrong candidate that is numerically close to the correct answer. Forward substitution should reject it for a specific reason: equality fails, constraint fails, unit fails or the reconstructed quantity does not match the given data.
22. coordinate midpoint
For coordinate midpoint, identify the original condition that the candidate must satisfy. Substitute the candidate and evaluate that condition without repeating the entire solving route.
If the candidate fails, locate the earliest transformation capable of producing the mismatch. If it passes algebraically but fails domain, unit or context, reject it anyway. Verification tests the whole answer, not just arithmetic consistency.
For practice, include one deliberately wrong candidate that is numerically close to the correct answer. Forward substitution should reject it for a specific reason: equality fails, constraint fails, unit fails or the reconstructed quantity does not match the given data.
23. gradient equation
For gradient equation, identify the original condition that the candidate must satisfy. Substitute the candidate and evaluate that condition without repeating the entire solving route.
If the candidate fails, locate the earliest transformation capable of producing the mismatch. If it passes algebraically but fails domain, unit or context, reject it anyway. Verification tests the whole answer, not just arithmetic consistency.
For practice, include one deliberately wrong candidate that is numerically close to the correct answer. Forward substitution should reject it for a specific reason: equality fails, constraint fails, unit fails or the reconstructed quantity does not match the given data.
24. line equation
For line equation, identify the original condition that the candidate must satisfy. Substitute the candidate and evaluate that condition without repeating the entire solving route.
If the candidate fails, locate the earliest transformation capable of producing the mismatch. If it passes algebraically but fails domain, unit or context, reject it anyway. Verification tests the whole answer, not just arithmetic consistency.
For practice, include one deliberately wrong candidate that is numerically close to the correct answer. Forward substitution should reject it for a specific reason: equality fails, constraint fails, unit fails or the reconstructed quantity does not match the given data.
25. Pythagoras
For Pythagoras, identify the original condition that the candidate must satisfy. Substitute the candidate and evaluate that condition without repeating the entire solving route.
If the candidate fails, locate the earliest transformation capable of producing the mismatch. If it passes algebraically but fails domain, unit or context, reject it anyway. Verification tests the whole answer, not just arithmetic consistency.
For practice, include one deliberately wrong candidate that is numerically close to the correct answer. Forward substitution should reject it for a specific reason: equality fails, constraint fails, unit fails or the reconstructed quantity does not match the given data.
26. similarity length
For similarity length, identify the original condition that the candidate must satisfy. Substitute the candidate and evaluate that condition without repeating the entire solving route.
If the candidate fails, locate the earliest transformation capable of producing the mismatch. If it passes algebraically but fails domain, unit or context, reject it anyway. Verification tests the whole answer, not just arithmetic consistency.
For practice, include one deliberately wrong candidate that is numerically close to the correct answer. Forward substitution should reject it for a specific reason: equality fails, constraint fails, unit fails or the reconstructed quantity does not match the given data.
27. similarity area
For similarity area, identify the original condition that the candidate must satisfy. Substitute the candidate and evaluate that condition without repeating the entire solving route.
If the candidate fails, locate the earliest transformation capable of producing the mismatch. If it passes algebraically but fails domain, unit or context, reject it anyway. Verification tests the whole answer, not just arithmetic consistency.
For practice, include one deliberately wrong candidate that is numerically close to the correct answer. Forward substitution should reject it for a specific reason: equality fails, constraint fails, unit fails or the reconstructed quantity does not match the given data.
28. similarity volume
For similarity volume, identify the original condition that the candidate must satisfy. Substitute the candidate and evaluate that condition without repeating the entire solving route.
If the candidate fails, locate the earliest transformation capable of producing the mismatch. If it passes algebraically but fails domain, unit or context, reject it anyway. Verification tests the whole answer, not just arithmetic consistency.
For practice, include one deliberately wrong candidate that is numerically close to the correct answer. Forward substitution should reject it for a specific reason: equality fails, constraint fails, unit fails or the reconstructed quantity does not match the given data.
29. circle circumference
For circle circumference, identify the original condition that the candidate must satisfy. Substitute the candidate and evaluate that condition without repeating the entire solving route.
If the candidate fails, locate the earliest transformation capable of producing the mismatch. If it passes algebraically but fails domain, unit or context, reject it anyway. Verification tests the whole answer, not just arithmetic consistency.
For practice, include one deliberately wrong candidate that is numerically close to the correct answer. Forward substitution should reject it for a specific reason: equality fails, constraint fails, unit fails or the reconstructed quantity does not match the given data.
30. circle area
For circle area, identify the original condition that the candidate must satisfy. Substitute the candidate and evaluate that condition without repeating the entire solving route.
If the candidate fails, locate the earliest transformation capable of producing the mismatch. If it passes algebraically but fails domain, unit or context, reject it anyway. Verification tests the whole answer, not just arithmetic consistency.
For practice, include one deliberately wrong candidate that is numerically close to the correct answer. Forward substitution should reject it for a specific reason: equality fails, constraint fails, unit fails or the reconstructed quantity does not match the given data.
31. rectangle area
For rectangle area, identify the original condition that the candidate must satisfy. Substitute the candidate and evaluate that condition without repeating the entire solving route.
If the candidate fails, locate the earliest transformation capable of producing the mismatch. If it passes algebraically but fails domain, unit or context, reject it anyway. Verification tests the whole answer, not just arithmetic consistency.
For practice, include one deliberately wrong candidate that is numerically close to the correct answer. Forward substitution should reject it for a specific reason: equality fails, constraint fails, unit fails or the reconstructed quantity does not match the given data.
32. perimeter
For perimeter, identify the original condition that the candidate must satisfy. Substitute the candidate and evaluate that condition without repeating the entire solving route.
If the candidate fails, locate the earliest transformation capable of producing the mismatch. If it passes algebraically but fails domain, unit or context, reject it anyway. Verification tests the whole answer, not just arithmetic consistency.
For practice, include one deliberately wrong candidate that is numerically close to the correct answer. Forward substitution should reject it for a specific reason: equality fails, constraint fails, unit fails or the reconstructed quantity does not match the given data.
33. angle sum
For angle sum, identify the original condition that the candidate must satisfy. Substitute the candidate and evaluate that condition without repeating the entire solving route.
If the candidate fails, locate the earliest transformation capable of producing the mismatch. If it passes algebraically but fails domain, unit or context, reject it anyway. Verification tests the whole answer, not just arithmetic consistency.
For practice, include one deliberately wrong candidate that is numerically close to the correct answer. Forward substitution should reject it for a specific reason: equality fails, constraint fails, unit fails or the reconstructed quantity does not match the given data.
34. parallel-line angle
For parallel-line angle, identify the original condition that the candidate must satisfy. Substitute the candidate and evaluate that condition without repeating the entire solving route.
If the candidate fails, locate the earliest transformation capable of producing the mismatch. If it passes algebraically but fails domain, unit or context, reject it anyway. Verification tests the whole answer, not just arithmetic consistency.
For practice, include one deliberately wrong candidate that is numerically close to the correct answer. Forward substitution should reject it for a specific reason: equality fails, constraint fails, unit fails or the reconstructed quantity does not match the given data.
35. scale drawing
For scale drawing, identify the original condition that the candidate must satisfy. Substitute the candidate and evaluate that condition without repeating the entire solving route.
If the candidate fails, locate the earliest transformation capable of producing the mismatch. If it passes algebraically but fails domain, unit or context, reject it anyway. Verification tests the whole answer, not just arithmetic consistency.
For practice, include one deliberately wrong candidate that is numerically close to the correct answer. Forward substitution should reject it for a specific reason: equality fails, constraint fails, unit fails or the reconstructed quantity does not match the given data.
36. currency conversion
For currency conversion, identify the original condition that the candidate must satisfy. Substitute the candidate and evaluate that condition without repeating the entire solving route.
If the candidate fails, locate the earliest transformation capable of producing the mismatch. If it passes algebraically but fails domain, unit or context, reject it anyway. Verification tests the whole answer, not just arithmetic consistency.
For practice, include one deliberately wrong candidate that is numerically close to the correct answer. Forward substitution should reject it for a specific reason: equality fails, constraint fails, unit fails or the reconstructed quantity does not match the given data.
37. unit conversion
For unit conversion, identify the original condition that the candidate must satisfy. Substitute the candidate and evaluate that condition without repeating the entire solving route.
If the candidate fails, locate the earliest transformation capable of producing the mismatch. If it passes algebraically but fails domain, unit or context, reject it anyway. Verification tests the whole answer, not just arithmetic consistency.
For practice, include one deliberately wrong candidate that is numerically close to the correct answer. Forward substitution should reject it for a specific reason: equality fails, constraint fails, unit fails or the reconstructed quantity does not match the given data.
38. compound growth
For compound growth, identify the original condition that the candidate must satisfy. Substitute the candidate and evaluate that condition without repeating the entire solving route.
If the candidate fails, locate the earliest transformation capable of producing the mismatch. If it passes algebraically but fails domain, unit or context, reject it anyway. Verification tests the whole answer, not just arithmetic consistency.
For practice, include one deliberately wrong candidate that is numerically close to the correct answer. Forward substitution should reject it for a specific reason: equality fails, constraint fails, unit fails or the reconstructed quantity does not match the given data.
39. depreciation
For depreciation, identify the original condition that the candidate must satisfy. Substitute the candidate and evaluate that condition without repeating the entire solving route.
If the candidate fails, locate the earliest transformation capable of producing the mismatch. If it passes algebraically but fails domain, unit or context, reject it anyway. Verification tests the whole answer, not just arithmetic consistency.
For practice, include one deliberately wrong candidate that is numerically close to the correct answer. Forward substitution should reject it for a specific reason: equality fails, constraint fails, unit fails or the reconstructed quantity does not match the given data.
40. simple interest
For simple interest, identify the original condition that the candidate must satisfy. Substitute the candidate and evaluate that condition without repeating the entire solving route.
If the candidate fails, locate the earliest transformation capable of producing the mismatch. If it passes algebraically but fails domain, unit or context, reject it anyway. Verification tests the whole answer, not just arithmetic consistency.
For practice, include one deliberately wrong candidate that is numerically close to the correct answer. Forward substitution should reject it for a specific reason: equality fails, constraint fails, unit fails or the reconstructed quantity does not match the given data.
41. profit relation
For profit relation, identify the original condition that the candidate must satisfy. Substitute the candidate and evaluate that condition without repeating the entire solving route.
If the candidate fails, locate the earliest transformation capable of producing the mismatch. If it passes algebraically but fails domain, unit or context, reject it anyway. Verification tests the whole answer, not just arithmetic consistency.
For practice, include one deliberately wrong candidate that is numerically close to the correct answer. Forward substitution should reject it for a specific reason: equality fails, constraint fails, unit fails or the reconstructed quantity does not match the given data.
42. margin relation
For margin relation, identify the original condition that the candidate must satisfy. Substitute the candidate and evaluate that condition without repeating the entire solving route.
If the candidate fails, locate the earliest transformation capable of producing the mismatch. If it passes algebraically but fails domain, unit or context, reject it anyway. Verification tests the whole answer, not just arithmetic consistency.
For practice, include one deliberately wrong candidate that is numerically close to the correct answer. Forward substitution should reject it for a specific reason: equality fails, constraint fails, unit fails or the reconstructed quantity does not match the given data.
43. markup relation
For markup relation, identify the original condition that the candidate must satisfy. Substitute the candidate and evaluate that condition without repeating the entire solving route.
If the candidate fails, locate the earliest transformation capable of producing the mismatch. If it passes algebraically but fails domain, unit or context, reject it anyway. Verification tests the whole answer, not just arithmetic consistency.
For practice, include one deliberately wrong candidate that is numerically close to the correct answer. Forward substitution should reject it for a specific reason: equality fails, constraint fails, unit fails or the reconstructed quantity does not match the given data.
44. capacity utilisation
For capacity utilisation, identify the original condition that the candidate must satisfy. Substitute the candidate and evaluate that condition without repeating the entire solving route.
If the candidate fails, locate the earliest transformation capable of producing the mismatch. If it passes algebraically but fails domain, unit or context, reject it anyway. Verification tests the whole answer, not just arithmetic consistency.
For practice, include one deliberately wrong candidate that is numerically close to the correct answer. Forward substitution should reject it for a specific reason: equality fails, constraint fails, unit fails or the reconstructed quantity does not match the given data.
45. population density
For population density, identify the original condition that the candidate must satisfy. Substitute the candidate and evaluate that condition without repeating the entire solving route.
If the candidate fails, locate the earliest transformation capable of producing the mismatch. If it passes algebraically but fails domain, unit or context, reject it anyway. Verification tests the whole answer, not just arithmetic consistency.
For practice, include one deliberately wrong candidate that is numerically close to the correct answer. Forward substitution should reject it for a specific reason: equality fails, constraint fails, unit fails or the reconstructed quantity does not match the given data.
46. flow rate
For flow rate, identify the original condition that the candidate must satisfy. Substitute the candidate and evaluate that condition without repeating the entire solving route.
If the candidate fails, locate the earliest transformation capable of producing the mismatch. If it passes algebraically but fails domain, unit or context, reject it anyway. Verification tests the whole answer, not just arithmetic consistency.
For practice, include one deliberately wrong candidate that is numerically close to the correct answer. Forward substitution should reject it for a specific reason: equality fails, constraint fails, unit fails or the reconstructed quantity does not match the given data.
47. work rate
For work rate, identify the original condition that the candidate must satisfy. Substitute the candidate and evaluate that condition without repeating the entire solving route.
If the candidate fails, locate the earliest transformation capable of producing the mismatch. If it passes algebraically but fails domain, unit or context, reject it anyway. Verification tests the whole answer, not just arithmetic consistency.
For practice, include one deliberately wrong candidate that is numerically close to the correct answer. Forward substitution should reject it for a specific reason: equality fails, constraint fails, unit fails or the reconstructed quantity does not match the given data.
48. data rate
For data rate, identify the original condition that the candidate must satisfy. Substitute the candidate and evaluate that condition without repeating the entire solving route.
If the candidate fails, locate the earliest transformation capable of producing the mismatch. If it passes algebraically but fails domain, unit or context, reject it anyway. Verification tests the whole answer, not just arithmetic consistency.
For practice, include one deliberately wrong candidate that is numerically close to the correct answer. Forward substitution should reject it for a specific reason: equality fails, constraint fails, unit fails or the reconstructed quantity does not match the given data.
49. runway
For runway, identify the original condition that the candidate must satisfy. Substitute the candidate and evaluate that condition without repeating the entire solving route.
If the candidate fails, locate the earliest transformation capable of producing the mismatch. If it passes algebraically but fails domain, unit or context, reject it anyway. Verification tests the whole answer, not just arithmetic consistency.
For practice, include one deliberately wrong candidate that is numerically close to the correct answer. Forward substitution should reject it for a specific reason: equality fails, constraint fails, unit fails or the reconstructed quantity does not match the given data.
50. upper/lower bound candidate
For upper/lower bound candidate, identify the original condition that the candidate must satisfy. Substitute the candidate and evaluate that condition without repeating the entire solving route.
If the candidate fails, locate the earliest transformation capable of producing the mismatch. If it passes algebraically but fails domain, unit or context, reject it anyway. Verification tests the whole answer, not just arithmetic consistency.
For practice, include one deliberately wrong candidate that is numerically close to the correct answer. Forward substitution should reject it for a specific reason: equality fails, constraint fails, unit fails or the reconstructed quantity does not match the given data.
51. integer minimum
For integer minimum, identify the original condition that the candidate must satisfy. Substitute the candidate and evaluate that condition without repeating the entire solving route.
If the candidate fails, locate the earliest transformation capable of producing the mismatch. If it passes algebraically but fails domain, unit or context, reject it anyway. Verification tests the whole answer, not just arithmetic consistency.
For practice, include one deliberately wrong candidate that is numerically close to the correct answer. Forward substitution should reject it for a specific reason: equality fails, constraint fails, unit fails or the reconstructed quantity does not match the given data.
52. integer maximum
For integer maximum, identify the original condition that the candidate must satisfy. Substitute the candidate and evaluate that condition without repeating the entire solving route.
If the candidate fails, locate the earliest transformation capable of producing the mismatch. If it passes algebraically but fails domain, unit or context, reject it anyway. Verification tests the whole answer, not just arithmetic consistency.
For practice, include one deliberately wrong candidate that is numerically close to the correct answer. Forward substitution should reject it for a specific reason: equality fails, constraint fails, unit fails or the reconstructed quantity does not match the given data.
53. case split candidate
For case split candidate, identify the original condition that the candidate must satisfy. Substitute the candidate and evaluate that condition without repeating the entire solving route.
If the candidate fails, locate the earliest transformation capable of producing the mismatch. If it passes algebraically but fails domain, unit or context, reject it anyway. Verification tests the whole answer, not just arithmetic consistency.
For practice, include one deliberately wrong candidate that is numerically close to the correct answer. Forward substitution should reject it for a specific reason: equality fails, constraint fails, unit fails or the reconstructed quantity does not match the given data.
54. absolute-value candidate
For absolute-value candidate, identify the original condition that the candidate must satisfy. Substitute the candidate and evaluate that condition without repeating the entire solving route.
If the candidate fails, locate the earliest transformation capable of producing the mismatch. If it passes algebraically but fails domain, unit or context, reject it anyway. Verification tests the whole answer, not just arithmetic consistency.
For practice, include one deliberately wrong candidate that is numerically close to the correct answer. Forward substitution should reject it for a specific reason: equality fails, constraint fails, unit fails or the reconstructed quantity does not match the given data.
55. square-root candidate
For square-root candidate, identify the original condition that the candidate must satisfy. Substitute the candidate and evaluate that condition without repeating the entire solving route.
If the candidate fails, locate the earliest transformation capable of producing the mismatch. If it passes algebraically but fails domain, unit or context, reject it anyway. Verification tests the whole answer, not just arithmetic consistency.
For practice, include one deliberately wrong candidate that is numerically close to the correct answer. Forward substitution should reject it for a specific reason: equality fails, constraint fails, unit fails or the reconstructed quantity does not match the given data.
56. graph intersection
For graph intersection, identify the original condition that the candidate must satisfy. Substitute the candidate and evaluate that condition without repeating the entire solving route.
If the candidate fails, locate the earliest transformation capable of producing the mismatch. If it passes algebraically but fails domain, unit or context, reject it anyway. Verification tests the whole answer, not just arithmetic consistency.
For practice, include one deliberately wrong candidate that is numerically close to the correct answer. Forward substitution should reject it for a specific reason: equality fails, constraint fails, unit fails or the reconstructed quantity does not match the given data.
57. table-derived parameter
For table-derived parameter, identify the original condition that the candidate must satisfy. Substitute the candidate and evaluate that condition without repeating the entire solving route.
If the candidate fails, locate the earliest transformation capable of producing the mismatch. If it passes algebraically but fails domain, unit or context, reject it anyway. Verification tests the whole answer, not just arithmetic consistency.
For practice, include one deliberately wrong candidate that is numerically close to the correct answer. Forward substitution should reject it for a specific reason: equality fails, constraint fails, unit fails or the reconstructed quantity does not match the given data.
58. MCQ numeric option
For MCQ numeric option, identify the original condition that the candidate must satisfy. Substitute the candidate and evaluate that condition without repeating the entire solving route.
If the candidate fails, locate the earliest transformation capable of producing the mismatch. If it passes algebraically but fails domain, unit or context, reject it anyway. Verification tests the whole answer, not just arithmetic consistency.
For practice, include one deliberately wrong candidate that is numerically close to the correct answer. Forward substitution should reject it for a specific reason: equality fails, constraint fails, unit fails or the reconstructed quantity does not match the given data.
59. calculator result
For calculator result, identify the original condition that the candidate must satisfy. Substitute the candidate and evaluate that condition without repeating the entire solving route.
If the candidate fails, locate the earliest transformation capable of producing the mismatch. If it passes algebraically but fails domain, unit or context, reject it anyway. Verification tests the whole answer, not just arithmetic consistency.
For practice, include one deliberately wrong candidate that is numerically close to the correct answer. Forward substitution should reject it for a specific reason: equality fails, constraint fails, unit fails or the reconstructed quantity does not match the given data.
60. rounded answer
For rounded answer, identify the original condition that the candidate must satisfy. Substitute the candidate and evaluate that condition without repeating the entire solving route.
If the candidate fails, locate the earliest transformation capable of producing the mismatch. If it passes algebraically but fails domain, unit or context, reject it anyway. Verification tests the whole answer, not just arithmetic consistency.
For practice, include one deliberately wrong candidate that is numerically close to the correct answer. Forward substitution should reject it for a specific reason: equality fails, constraint fails, unit fails or the reconstructed quantity does not match the given data.
61. exact answer
For exact answer, identify the original condition that the candidate must satisfy. Substitute the candidate and evaluate that condition without repeating the entire solving route.
If the candidate fails, locate the earliest transformation capable of producing the mismatch. If it passes algebraically but fails domain, unit or context, reject it anyway. Verification tests the whole answer, not just arithmetic consistency.
For practice, include one deliberately wrong candidate that is numerically close to the correct answer. Forward substitution should reject it for a specific reason: equality fails, constraint fails, unit fails or the reconstructed quantity does not match the given data.
62. negative root
For negative root, identify the original condition that the candidate must satisfy. Substitute the candidate and evaluate that condition without repeating the entire solving route.
If the candidate fails, locate the earliest transformation capable of producing the mismatch. If it passes algebraically but fails domain, unit or context, reject it anyway. Verification tests the whole answer, not just arithmetic consistency.
For practice, include one deliberately wrong candidate that is numerically close to the correct answer. Forward substitution should reject it for a specific reason: equality fails, constraint fails, unit fails or the reconstructed quantity does not match the given data.
63. extraneous root
For extraneous root, identify the original condition that the candidate must satisfy. Substitute the candidate and evaluate that condition without repeating the entire solving route.
If the candidate fails, locate the earliest transformation capable of producing the mismatch. If it passes algebraically but fails domain, unit or context, reject it anyway. Verification tests the whole answer, not just arithmetic consistency.
For practice, include one deliberately wrong candidate that is numerically close to the correct answer. Forward substitution should reject it for a specific reason: equality fails, constraint fails, unit fails or the reconstructed quantity does not match the given data.
64. domain-restricted root
For domain-restricted root, identify the original condition that the candidate must satisfy. Substitute the candidate and evaluate that condition without repeating the entire solving route.
If the candidate fails, locate the earliest transformation capable of producing the mismatch. If it passes algebraically but fails domain, unit or context, reject it anyway. Verification tests the whole answer, not just arithmetic consistency.
For practice, include one deliberately wrong candidate that is numerically close to the correct answer. Forward substitution should reject it for a specific reason: equality fails, constraint fails, unit fails or the reconstructed quantity does not match the given data.
65. transformation coordinate
For transformation coordinate, identify the original condition that the candidate must satisfy. Substitute the candidate and evaluate that condition without repeating the entire solving route.
If the candidate fails, locate the earliest transformation capable of producing the mismatch. If it passes algebraically but fails domain, unit or context, reject it anyway. Verification tests the whole answer, not just arithmetic consistency.
For practice, include one deliberately wrong candidate that is numerically close to the correct answer. Forward substitution should reject it for a specific reason: equality fails, constraint fails, unit fails or the reconstructed quantity does not match the given data.
66. translation vector
For translation vector, identify the original condition that the candidate must satisfy. Substitute the candidate and evaluate that condition without repeating the entire solving route.
If the candidate fails, locate the earliest transformation capable of producing the mismatch. If it passes algebraically but fails domain, unit or context, reject it anyway. Verification tests the whole answer, not just arithmetic consistency.
For practice, include one deliberately wrong candidate that is numerically close to the correct answer. Forward substitution should reject it for a specific reason: equality fails, constraint fails, unit fails or the reconstructed quantity does not match the given data.
67. reflection point
For reflection point, identify the original condition that the candidate must satisfy. Substitute the candidate and evaluate that condition without repeating the entire solving route.
If the candidate fails, locate the earliest transformation capable of producing the mismatch. If it passes algebraically but fails domain, unit or context, reject it anyway. Verification tests the whole answer, not just arithmetic consistency.
For practice, include one deliberately wrong candidate that is numerically close to the correct answer. Forward substitution should reject it for a specific reason: equality fails, constraint fails, unit fails or the reconstructed quantity does not match the given data.
68. rotation point
For rotation point, identify the original condition that the candidate must satisfy. Substitute the candidate and evaluate that condition without repeating the entire solving route.
If the candidate fails, locate the earliest transformation capable of producing the mismatch. If it passes algebraically but fails domain, unit or context, reject it anyway. Verification tests the whole answer, not just arithmetic consistency.
For practice, include one deliberately wrong candidate that is numerically close to the correct answer. Forward substitution should reject it for a specific reason: equality fails, constraint fails, unit fails or the reconstructed quantity does not match the given data.
69. enlargement point
For enlargement point, identify the original condition that the candidate must satisfy. Substitute the candidate and evaluate that condition without repeating the entire solving route.
If the candidate fails, locate the earliest transformation capable of producing the mismatch. If it passes algebraically but fails domain, unit or context, reject it anyway. Verification tests the whole answer, not just arithmetic consistency.
For practice, include one deliberately wrong candidate that is numerically close to the correct answer. Forward substitution should reject it for a specific reason: equality fails, constraint fails, unit fails or the reconstructed quantity does not match the given data.
70. frequency total
For frequency total, identify the original condition that the candidate must satisfy. Substitute the candidate and evaluate that condition without repeating the entire solving route.
If the candidate fails, locate the earliest transformation capable of producing the mismatch. If it passes algebraically but fails domain, unit or context, reject it anyway. Verification tests the whole answer, not just arithmetic consistency.
For practice, include one deliberately wrong candidate that is numerically close to the correct answer. Forward substitution should reject it for a specific reason: equality fails, constraint fails, unit fails or the reconstructed quantity does not match the given data.
71. relative frequency
For relative frequency, identify the original condition that the candidate must satisfy. Substitute the candidate and evaluate that condition without repeating the entire solving route.
If the candidate fails, locate the earliest transformation capable of producing the mismatch. If it passes algebraically but fails domain, unit or context, reject it anyway. Verification tests the whole answer, not just arithmetic consistency.
For practice, include one deliberately wrong candidate that is numerically close to the correct answer. Forward substitution should reject it for a specific reason: equality fails, constraint fails, unit fails or the reconstructed quantity does not match the given data.
72. percentage-point change
For percentage-point change, identify the original condition that the candidate must satisfy. Substitute the candidate and evaluate that condition without repeating the entire solving route.
If the candidate fails, locate the earliest transformation capable of producing the mismatch. If it passes algebraically but fails domain, unit or context, reject it anyway. Verification tests the whole answer, not just arithmetic consistency.
For practice, include one deliberately wrong candidate that is numerically close to the correct answer. Forward substitution should reject it for a specific reason: equality fails, constraint fails, unit fails or the reconstructed quantity does not match the given data.
73. index number
For index number, identify the original condition that the candidate must satisfy. Substitute the candidate and evaluate that condition without repeating the entire solving route.
If the candidate fails, locate the earliest transformation capable of producing the mismatch. If it passes algebraically but fails domain, unit or context, reject it anyway. Verification tests the whole answer, not just arithmetic consistency.
For practice, include one deliberately wrong candidate that is numerically close to the correct answer. Forward substitution should reject it for a specific reason: equality fails, constraint fails, unit fails or the reconstructed quantity does not match the given data.
74. normalised share
For normalised share, identify the original condition that the candidate must satisfy. Substitute the candidate and evaluate that condition without repeating the entire solving route.
If the candidate fails, locate the earliest transformation capable of producing the mismatch. If it passes algebraically but fails domain, unit or context, reject it anyway. Verification tests the whole answer, not just arithmetic consistency.
For practice, include one deliberately wrong candidate that is numerically close to the correct answer. Forward substitution should reject it for a specific reason: equality fails, constraint fails, unit fails or the reconstructed quantity does not match the given data.
75. comparison rate
For comparison rate, identify the original condition that the candidate must satisfy. Substitute the candidate and evaluate that condition without repeating the entire solving route.
If the candidate fails, locate the earliest transformation capable of producing the mismatch. If it passes algebraically but fails domain, unit or context, reject it anyway. Verification tests the whole answer, not just arithmetic consistency.
For practice, include one deliberately wrong candidate that is numerically close to the correct answer. Forward substitution should reject it for a specific reason: equality fails, constraint fails, unit fails or the reconstructed quantity does not match the given data.
76. unit rate
For unit rate, identify the original condition that the candidate must satisfy. Substitute the candidate and evaluate that condition without repeating the entire solving route.
If the candidate fails, locate the earliest transformation capable of producing the mismatch. If it passes algebraically but fails domain, unit or context, reject it anyway. Verification tests the whole answer, not just arithmetic consistency.
For practice, include one deliberately wrong candidate that is numerically close to the correct answer. Forward substitution should reject it for a specific reason: equality fails, constraint fails, unit fails or the reconstructed quantity does not match the given data.
77. reciprocal rate
For reciprocal rate, identify the original condition that the candidate must satisfy. Substitute the candidate and evaluate that condition without repeating the entire solving route.
If the candidate fails, locate the earliest transformation capable of producing the mismatch. If it passes algebraically but fails domain, unit or context, reject it anyway. Verification tests the whole answer, not just arithmetic consistency.
For practice, include one deliberately wrong candidate that is numerically close to the correct answer. Forward substitution should reject it for a specific reason: equality fails, constraint fails, unit fails or the reconstructed quantity does not match the given data.
78. reverse-engineered value
For reverse-engineered value, identify the original condition that the candidate must satisfy. Substitute the candidate and evaluate that condition without repeating the entire solving route.
If the candidate fails, locate the earliest transformation capable of producing the mismatch. If it passes algebraically but fails domain, unit or context, reject it anyway. Verification tests the whole answer, not just arithmetic consistency.
For practice, include one deliberately wrong candidate that is numerically close to the correct answer. Forward substitution should reject it for a specific reason: equality fails, constraint fails, unit fails or the reconstructed quantity does not match the given data.
79. work-backward chain
For work-backward chain, identify the original condition that the candidate must satisfy. Substitute the candidate and evaluate that condition without repeating the entire solving route.
If the candidate fails, locate the earliest transformation capable of producing the mismatch. If it passes algebraically but fails domain, unit or context, reject it anyway. Verification tests the whole answer, not just arithmetic consistency.
For practice, include one deliberately wrong candidate that is numerically close to the correct answer. Forward substitution should reject it for a specific reason: equality fails, constraint fails, unit fails or the reconstructed quantity does not match the given data.
80. dependency intermediate
For dependency intermediate, identify the original condition that the candidate must satisfy. Substitute the candidate and evaluate that condition without repeating the entire solving route.
If the candidate fails, locate the earliest transformation capable of producing the mismatch. If it passes algebraically but fails domain, unit or context, reject it anyway. Verification tests the whole answer, not just arithmetic consistency.
For practice, include one deliberately wrong candidate that is numerically close to the correct answer. Forward substitution should reject it for a specific reason: equality fails, constraint fails, unit fails or the reconstructed quantity does not match the given data.
81. sensitivity case
For sensitivity case, identify the original condition that the candidate must satisfy. Substitute the candidate and evaluate that condition without repeating the entire solving route.
If the candidate fails, locate the earliest transformation capable of producing the mismatch. If it passes algebraically but fails domain, unit or context, reject it anyway. Verification tests the whole answer, not just arithmetic consistency.
For practice, include one deliberately wrong candidate that is numerically close to the correct answer. Forward substitution should reject it for a specific reason: equality fails, constraint fails, unit fails or the reconstructed quantity does not match the given data.
82. bound estimate
For bound estimate, identify the original condition that the candidate must satisfy. Substitute the candidate and evaluate that condition without repeating the entire solving route.
If the candidate fails, locate the earliest transformation capable of producing the mismatch. If it passes algebraically but fails domain, unit or context, reject it anyway. Verification tests the whole answer, not just arithmetic consistency.
For practice, include one deliberately wrong candidate that is numerically close to the correct answer. Forward substitution should reject it for a specific reason: equality fails, constraint fails, unit fails or the reconstructed quantity does not match the given data.
83. final substitution rule
For final substitution rule, identify the original condition that the candidate must satisfy. Substitute the candidate and evaluate that condition without repeating the entire solving route.
If the candidate fails, locate the earliest transformation capable of producing the mismatch. If it passes algebraically but fails domain, unit or context, reject it anyway. Verification tests the whole answer, not just arithmetic consistency.
For practice, include one deliberately wrong candidate that is numerically close to the correct answer. Forward substitution should reject it for a specific reason: equality fails, constraint fails, unit fails or the reconstructed quantity does not match the given data.
Substitution is especially valuable after non-reversible moves
Squaring, clearing denominators, rounding, taking roots and splitting cases can change or enlarge the candidate set. Substitution into the original condition is therefore more informative than checking only the final transformed expression.
Links
Use the Mathematics Hub, Vol 0110 Comparison-Measure Choice, Vol 0098 Case Splitting, the Examination Craft hub and the PSLE Learner’s Guide.
Official-source discipline
For the current 2027 SEC G2 school-candidate framework, use the official SEAB G2 syllabus directory and linked K210 Mathematics syllabus. Forward-substitution verification is an eduKateSengkang checking framework, not an additional SEAB syllabus topic.
Final rule
Do not ask only whether the working looks familiar. Put the answer back into the original condition. A candidate that cannot reproduce the givens, satisfy the domain and preserve the units is not finished.
