1.2 Machine-Scored Versus Written Response
Key Takeaways
- Machine-scored questions reward accurate final selection or entry; written response can reward valid reasoning even when a final detail is imperfect.
- Multiple-choice questions require the correct or best answer from four alternatives, so elimination and checking against context both matter.
- Numerical-response questions may ask for rounded decimals, whole numbers, ordered digits, any-order digits, or coded answers.
- For decimal numerical-response answers between 0 and 1, the bulletin tells students to record the leading zero before the decimal place.
- Written response expects connections across outcomes, so a response should show method, context, units, and a conclusion.
Two formats, two scoring habits
The Math 30-2 diploma uses both machine-scored questions and written response because mathematics is not only answer-getting. Machine-scored items check whether you can identify or record a correct result under exam conditions. Written-response items check whether you can build, explain, and communicate a solution across several linked parts. The content overlaps, but the habits are different enough that you should practise them separately.
A multiple-choice question asks for the correct or best possible answer from four alternatives. A numerical-response question asks you to calculate or determine an answer and enter it in the requested format on the answer sheet or screen. A written-response question asks for visible work and mathematical communication. On machine-scored items, the scoring system sees the choice or entry. On written response, human markers can evaluate the reasoning, the setup, the method, and the communication even if one detail goes wrong.
| Feature | Machine-scored questions | Written-response questions |
|---|---|---|
| Scored evidence | Final selected or entered answer | Work, explanation, notation, units, conclusion |
| Typical risk | Knowing the math but recording the wrong format | Knowing the answer but not showing enough reasoning |
| Best habit | Read the requested form before calculating | Write a complete mathematical trail as you solve |
| Common Math 30-2 topics | odds, counting, graph features, restrictions, function values | modeling, parameter interpretation, algebraic solving, graph explanation |
Multiple choice is not only recognition
A strong multiple-choice process still looks like mathematics. Read the information box, identify the topic, solve or reason independently, and then compare your result to the choices. If you go to the choices too early, distractors can pull you toward a common mistake: using nPr when order does not matter, choosing probability when the problem asks for odds, forgetting a non-permissible value, or reading the maximum of a sinusoidal graph as the amplitude.
Use elimination when it is mathematical, not emotional. For example, if a probability answer is greater than 1, it cannot be a probability. If a logarithmic input would be negative, that value cannot be in the domain. If a rational equation solution makes a denominator zero, it is not allowed even if it appears after algebraic cancellation. These are not guessing tricks; they are content checks.
Numerical response is a format test as well as a math test
The bulletin highlights several numerical-response patterns. Some questions require a decimal rounded to the nearest tenth or hundredth. When the answer is between 0 and 1, record the zero before the decimal, such as 0.25 rather than .25. Keep full decimals throughout the work and round only at the final answer. Other questions ask for a whole number, such as a degree, a number of people, or a count of arrangements.
Some numerical-response items are not ordinary decimals at all. A correct-order question may ask you to record digits in a particular sequence. An any-order question may accept a set of digits in any arrangement. A multiple-answer coded question may ask for code numbers rather than the actual mathematical values. Before pressing keys, underline the recording instruction: nearest hundredth, whole number, first column, order from most likely to least likely, any order, or both digits.
Worked example: a problem gives odds in favour of a club winning as 3:5 and asks for the probability of winning as a decimal to the nearest hundredth. Odds in favour compare favourable to unfavourable outcomes, so probability is 3/(3 + 5) = 3/8 = 0.375. The recorded value should be 0.38, not 0.37 if rounding correctly, not 3:5 because odds were converted, and not .38 if the platform or answer sheet expects the leading zero.
Written response needs a visible chain
Written response is designed to cover more than one specific outcome and to require connections between concepts. A question might begin with a graph, move to a function model, ask for a value or time, and then ask for an interpretation. A final answer alone may not show enough evidence, because the scoring guide is looking for understanding, correct application, problem-solving strategy, explanation, and communication.
A useful written-response structure is setup, solve, state, and check. Setup identifies the function, diagram, equation, restrictions, or variables. Solve shows algebraic or calculator-supported work. State gives the answer with units and rounding. Check connects the answer back to the original context. If the problem asks to compare two exponential models, the comparison must mention both initial values and growth rates in context. If it asks to sketch, the graph must show key features, not just a vague curve.
Diploma traps
- Multiple choice: selecting the only answer that looks familiar instead of checking the word asked, such as odds, probability, or percent.
- Numerical response: rounding midway through a logarithm or probability calculation, then recording a final value that is off by a hundredth.
- Numerical response: entering actual values when the question asks for code digits or order digits.
- Written response: giving a correct number without units, context, or explanation when the command word asks to justify, interpret, compare, or explain.
The best exam habit is to switch modes deliberately. For machine-scored questions, protect the answer format. For written response, protect the reasoning record. Both are Math 30-2 skills, but they leave different evidence on the page.
A numerical-response item asks for a probability between 0 and 1 rounded to the nearest hundredth. The unrounded value is 0.375. Which recorded answer best follows the bulletin guidance?
Which situation is most likely to earn some written-response credit even if the final numerical answer is not perfect?
A multiple-choice probability question asks for odds in favour, but a student selects favourable outcomes divided by total outcomes. What is the likely error?