Independent dMAT preparation
General Academic Module: apply the information provided
Read a supplied model, separate assumptions from conclusions and practise an original energy-budget example with answers.
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Read an academic problem as a small working model. Identify what is given, what is permitted and what the question asks you to derive. A formula alone is not enough: units, assumptions and the allowed values of its variables can determine the answer.
The official FAQ describes application to academic problems and approximately 60 individual questions, with the actual number allowed to vary.
Read in three passes
- Model: identify the rule and meaning of each quantity. Ask which terms are fixed and which change.
- Constraints: find the range, units and assumptions. “Whole number” can matter after division.
- Question: distinguish an exact value from a maximum, a minimum or a claim that must always hold.
On a passage with several questions, retain the model but read each question’s conditions again. A new question may use a different budget or ask about a change rather than a total.
Worked original academic passage
These are original Aptitrail teaching examples. They are independent of official exercises and are not an official difficulty benchmark.
Original passage: laboratory energy budget. A laboratory makes identical batches in one session. It uses 12 energy units to start the equipment and 3 additional units for each batch. Total energy is E(n) = 12 + 3n, where n is a whole number from 0 to 8. Assume every batch is completed in the same session, the setup runs once, and there are no other energy costs. A research group needs at least 5 batches.
How much energy is needed for exactly 5 batches? Choose one: A. 15 units; B. 27 units; C. 60 units; D. 72 units.
Reveal the application and answer
B: 27 units. Substitute n = 5 into the supplied model: E(5) = 12 + 3 × 5 = 27. The 12-unit setup is charged once; the 3-unit batch cost is charged five times. A omits setup, C treats setup as a per-batch cost, and D charges the complete one-batch session cost five times.
The passage provides the entire model. Outside assumptions about laboratory equipment would change the task rather than solve it.
Apply a budget constraint
The same passage can ask a different question: with 30 energy units available, how many batches are possible? A budget is an upper bound, so write 12 + 3n ≤ 30 rather than assuming that all budgets must be spent exactly.
Subtract setup first: 3n ≤ 18. Then divide by 3: n ≤ 6. Six fits the whole-number range. If the division had produced 6.5, only 6 complete batches would fit; rounding upward would violate the budget.
Common mistakes
- Reading every term as variable: setup is charged once, not once per batch.
- Replacing the supplied model: do not add real-world costs that the passage explicitly excludes.
- Ignoring a domain: negative or fractional batches do not meet the stated definition.
- Overclaiming: a conclusion under one model is not evidence that every laboratory behaves that way.
Two short exercises
1. With a 30-unit budget, choose the largest allowed number of batches: A. 4; B. 5; C. 6; D. 10.
Reveal exercise 1
C: 6. E(6) = 30, while E(7) = 33 exceeds the budget. Ten also falls outside the model’s 0–8 domain.
2. With a 25-unit budget, can the group meet its requirement of at least 5 batches?
Reveal exercise 2
No. Five batches require 27 units. The largest feasible whole number is 4 because (25 − 12) ÷ 3 = 4⅓. Producing 4 meets the energy constraint but fails the group’s separate minimum requirement.
This introductory passage trains interpretation rather than covering a syllabus. Use other original practice passages to learn how the same discipline applies to tables, processes and relationships.
By the Aptitrail editorial team. AI-assisted original teaching examples checked with automated tests. These checks do not constitute an independent expert review. Report a correction.