Quantitative response formats: all valid values and numerical entry
| English | 中文 | Pinyin |
|---|---|---|
| rounding/ˈraʊndɪŋ/ | 舍入 | shě rù |
| candidate solution/ˈkændɪdeɪt səˈluːʃn/ | 候选解 | hòu xuǎn jiě |
A decision before an answer
- An equation may have several allowed answers; a numeric entry asks for the specific requested value, not every root.
- Your goal: Select every allowed answer without assuming a fixed number.
Read the relationship
- Read the response instruction before calculation. Select-one asks for one option; select-one-or-more can require several; Numerical Entry has no options to cue an approximate answer. Identify restrictions such as integer, positive or rounded to a stated precision. In select-all tasks, test every option against those restrictions.
- State numerical answers in the requested representation and unit.
For x²=9 and x>0, which value is allowed?
Positivity excludes -3.
Use the defining rule
- Solving a transformed equation yields candidates. A denominator restriction or a sign requirement in an unsquared radical can remove one. Substituting into the original is more reliable than recognising a familiar-looking list of roots. For inequality options, test the strict or inclusive boundary as written.
- Use estimation and substitution to verify a computed response.
The probability 0.08 equals what percent?
Multiply a probability by 100 for a percentage.
Check the conditions
- A requested fraction and a requested decimal require different entry forms. Equivalent fractions are accepted in official Numeric Entry; simplify if needed to fit the boxes. Apply rounding only at the end when instructed. Check units: a percentage answer 25 differs from a probability answer 0.25. The free local numerical drill below requests an exact terminating decimal; it is a teaching check, not a replacement for the official two-box fraction interface.
- Use estimation and substitution to verify a computed response.
Original select-all: x is real and (x−2)(x+3)=0. Choices −3, −2, 0, 2, 3. Select −3 and 2, and verify each factorisation root in the original. If the stem additionally requires x>0, only 2 remains. Original numerical entry: three of eight equally likely counters are marked; enter the probability as a decimal. P(marked)=3/8=0.375. Enter 0.375, not 37.5 (a percent value) or 3 (the count).
If 3x+2=20, x=____.
Subtract 2 and divide by 3.
For real x, select all solutions of (x−2)(x+3)=0.
Either factor may equal zero, giving −3 and 2. No other listed value satisfies the equation.
Apply the task format
- Estimate before using the on-screen General-test calculator and verify after entry. An implausible order of magnitude often reveals misplaced parentheses or a percent converted incorrectly. The GRE General mathematical level does not require calculus; sophisticated reasoning can still arise from elementary constraints and careful instructions.
- Use estimation and substitution to verify a computed response.
The number of correct select-all choices comes from the constraints, not from a guessed pattern. Numeric form is part of the task.
Which answer fits this case?
Select every allowed answer without assuming a fixed number
A select-one-or-more quantitative item must have exactly two correct choices.
Determine every valid choice from the conditions.
Three of eight equally likely counters are marked. Enter P(marked) as an exact decimal.
P(marked)=3/8=0.375. The requested form is probability, not percent.
Keep the distinctions
- candidate solution 候选解 — A value produced by a solving step that still needs checking.
- rounding 舍入 — Reporting a value at a stated precision after calculation.
- Select every allowed answer without assuming a fixed number.
- State numerical answers in the requested representation and unit.
- Use estimation and substitution to verify a computed response.
Match each term with its precise meaning in this lesson.
Keep the distinctions stated in the teaching example.
Put this lesson’s reasoning or event sequence in order.
The order follows the stated process; check each stage before the next.