6.1 Numerical-Response Format and Rounding

Why numerical response is a separate skill

The Mathematics 30-2 Diploma Examination has 32 machine-scored questions worth 75% of the exam mark. In the paper-format description, that machine-scored component is 24 multiple-choice questions and 8 numerical-response questions. The numerical-response questions are still machine scored, so the scorer reads the recorded value or code, not your scratch work. A correct method can be lost if the answer is rounded to the wrong place, recorded in the wrong order, entered as a percent when a decimal probability is required, or written without the leading 0 before a decimal between 0 and 1.

Alberta's bulletin also makes a practical point: when a numerical-response answer can be a decimal, the question tells you whether to record to the nearest tenth or nearest hundredth. If no rounding direction is given, expect an exact answer or a code exactly as requested. That means your first move on these items should not be calculating. Your first move should be underlining the recording instruction.

The four formats to recognize

A numerical-response item may look like a probability, rational-expression, exponential, regression, or logic question, but the answer box changes the job. In a multiple-choice item, you can compare options and estimate. In numerical response, you must manufacture the exact recordable answer. This is why final review should include stand-alone numerical-response practice, not only mixed multiple choice.

Recording workflow

Use a four-step routine. First, label the answer type: value, order, any order, or code pair. Second, keep full calculator precision while working. Third, apply the exact instruction: nearest tenth, nearest hundredth, first column, any order, or all digits. Fourth, reread the context and ask whether the recorded value is in the right form. Probability is especially vulnerable because students often switch between fraction, decimal, percent, and odds without noticing.

For paper-format recording, the official instructions say to enter the first digit in the left-hand box and leave unused boxes on the right blank. For decimal values between 0 and 1, record the 0 before the decimal. For digital format, the same mathematical care applies even though the response is entered on screen. In either format, the scratch work does not rescue a misrecorded machine-scored answer.

Worked example: probability as a decimal

A drawer has 5 red, 4 blue, and 3 green tiles. One tile is selected. The probability of selecting a tile that is not red, to the nearest hundredth, is required.

Favourable outcomes are blue or green, so there are 4 + 3 = 7 favourable tiles out of 12 total tiles. The probability is 7/12 = 0.583333.... The requested answer is nearest hundredth, so the recorded value is 0.58. The answer is not 58, 58%, or .58 without the leading 0 in a paper-style decimal record. The calculation is simple; the diploma risk is form.

Worked example: correct-order code

Four exponential models have bases 1.06, 0.92, 1.14, and 0.98. They are labelled 1 through 4 in that order. If the question asks for the models from greatest decay to greatest growth, compare the bases to 1. The strongest decay is 0.92, then 0.98, then 1.06, then 1.14. The recorded code is 2413. If the prompt instead asked from smallest base to largest base, the same code would still be 2413; if it asked from greatest growth to greatest decay, the code would reverse to 3142.

Diploma traps to remove in final practice

• Do not round regression coefficients before using them to make a prediction unless the question specifically says to use rounded coefficients.
• Do not enter a probability as a percent unless the response instruction asks for a percent.
• Do not sort odds ratios by comparing only the first number; convert odds in favour a:b to probability a/(a + b).
• Do not cancel factors in a rational expression before recording non-permissible values from the original denominator.
• Do not use the answer box as scratch space. Decide what belongs in each column before recording.

A good final-week drill is to take 12 old practice prompts from across the course and rewrite each as a numerical-response item. Make four calculation items, three correct-order items, three any-order items, and two code-pair items. The point is not to create official questions; it is to make your brain read recording directions before it starts calculating.

Self-check before recording

Before you darken boxes or submit a digital entry, do a 10-second self-check. Ask: Is the result a count, a decimal probability, an ordered code, or a rounded model value? Does the answer have to be exact, nearest tenth, nearest hundredth, or a whole number? Does the context make the size reasonable? A probability above 1, a negative count, or an answer outside a stated domain usually signals a form or setup error. This check is especially useful after calculator work because the screen can show many more digits than the response field needs.