6.2 Written-Response Modeling Practice

What written response is testing

The Math 30-2 written-response component is designed to assess whether you can use mathematical experience to solve problems, explain concepts, demonstrate algebraic skills, and connect ideas from more than one outcome. The 2025-2026 information bulletin states that the exam has 2 written-response questions worth 25% of the total exam mark. The two questions are equally weighted. Each is scored out of 7 marks, with a 1-mark opening part followed by three 2-mark parts.

This structure is important for final review. A written-response question is not supposed to be one huge mystery task. It is a sequence. The first part often checks entry-level understanding or setup; later parts ask you to determine, explain, compare, justify, sketch, or interpret. If you skip the setup because it looks easy, later work may lose labels, variables, or context. If you quit after one hard part, you may miss later marks that are independent or partially independent.

A response scaffold that works across topics

Use the same five moves for probability, functions, rational equations, and sinusoidal modeling.

Alberta's written-response instructions emphasize pertinent ideas, calculations, formulas, correct units, and organized presentation. That does not mean every response needs paragraphs. A clear point-form solution can work if the mathematical chain is visible. The danger is unlabeled calculator output: a table, regression equation, or graph screenshot copied into a response without explaining what it means.

Worked example: sinusoidal model in context

A town has about 16.2 hours of daylight at its yearly maximum and 7.8 hours at its yearly minimum. The maximum occurs on day 172 of the year. Model the daylight hours D on day t with a cosine function and estimate the daylight on day 90.

First find the midline and amplitude. The midline is (16.2 + 7.8)/2 = 12.0 hours. The amplitude is (16.2 - 7.8)/2 = 4.2 hours. A yearly daylight cycle has period 365 days, so a cosine model with maximum at day 172 is D(t) = 4.2 cos(2*pi/365(t - 172)) + 12.

Now substitute t = 90. The calculator gives D(90) about 12.66 when full precision is used. If the question asks for nearest tenth, report 12.7 hours. The interpretation sentence matters: on day 90, the model predicts about 12.7 hours of daylight, which is reasonable because it is between the yearly minimum and maximum and before the maximum day.

Written-response traps by directing word

• Determine: show the formula, substitution, procedure, or calculation. A final number alone is weak evidence.
• Justify: state a position and give mathematical reasons. For example, compare probabilities, intervals, or model features rather than saying one answer is obvious.
• Algebraically: use variables, equations, and symbolic steps. Calculator evidence may support the answer, but it cannot replace the algebraic process.
• Sketch: show key graph features such as intercepts, asymptotes, maximum, minimum, period, or domain restrictions. A decorative curve without scale usually does not communicate enough.
• Interpret: translate the result into the original context with units and meaning.

Building partial-mark resilience

Partial marks are earned by visible mathematical thinking. If a Venn diagram is needed, put only region counts in the diagram and put extra calculations outside it. If the problem uses odds or probability, label the notation carefully: odds in favour, odds against, or P(event). If a rational equation is involved, write the non-permissible values before solving and check proposed solutions against them. If a regression or financial model is involved, store the full model or use calculator variables so rounded coefficients do not damage a later prediction.

Your final practice should include at least two full written-response rehearsals under time pressure. After each rehearsal, score the work with a communication lens: Did every symbol have a meaning? Did every part have a final answer? Did the response answer the command word? Did units and rounding match the prompt? These checks are not extra polish. They are part of the mathematical performance being assessed.

How to practise without official prompts

You can build useful written-response practice from ordinary homework questions by adding communication demands. Take a probability question and add: explain whether the events are independent or dependent. Take a rational-equation question and add: state all restrictions and justify which proposed solutions are valid. Take a sinusoidal graph and add: interpret the amplitude, midline, and period in context. This turns short-answer review into diploma-style reasoning without copying secure exam material. It also trains you to write from a model to a conclusion, not just from a question to a number.