Timed AS91262 Mini-Set Practice and Reflection

Kia ora. In the previous lesson, you practised recognising the calculus method before doing any calculations: differentiate for a gradient or rate, anti-differentiate to recover a function, use derivative signs for increasing or decreasing intervals, and use stationary points for maxima and minima.

Now you will put that recognition routine under time pressure. The purpose is not to produce a perfect paper today. It is to practise making a decision, showing a usable first step, and leaving a clear record whenever you skip a part or become unsure. That record will be the starting point for the next lesson’s correction.

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Your mini-set: conditions and materials

Use ordinary exam conditions as closely as possible:

• paper and pen or pencil;
• your approved calculator;
• a timer;
• no notes, worked solutions, or marking schedule while the timer is running.

This mini-set uses selected parts from the 2023 AS91262 examination paper. You will attempt:

1. Question 1(a), (b), and (c)
2. Question 3(b)(i), (ii), and (iii)

These give you a compact range of AS91262 skills:

Part	Main task type
1(a)	Find a point where the gradient has a stated value
1(b)	Recover a function from its gradient and a point
1(c)	Determine intervals where a function is increasing
3(b)(i)	Find and interpret a rate at a specified time
3(b)(ii)	Find a maximum in a defined time interval
3(b)(iii)	Justify when a contextual quantity is decreasing

Before starting, prepare two headings on a spare page:

WORKING: 2023 AS91262 MINI-SET

UNCERTAINTY LOG

Your working must show your reasoning even if you are not sure it is correct. A line of imperfect algebra is more useful for later correction than an empty space.

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The rule for uncertainty: mark it, do not hide it

Timed practice only helps if it reveals what happens when you are under pressure. Do not spend ten minutes trying to make one line look perfect. Instead, record the moment where progress stopped.

Use these symbols beside your working:

Symbol	Meaning	What to write beside it
S	Skipped	The part or step you left and why
?	Method uncertainty	The method you considered but were not confident using
C	Calculation uncertainty	The exact line where algebra, differentiation, or calculator work became uncertain
I	Interpretation uncertainty	A word, unit, conclusion, or context decision you were unsure about

For example, your log could look like this:

Part	Symbol	Exact step or issue	What you did next
1(c)	?	“Increasing” means I need $f^{\prime }(x)>0$, but I was unsure how to test the intervals.	Found the roots, then moved on.
3(b)(ii)	C	I found two stationary times but was unsure which original-function values to compare.	Substituted one value only.
3(b)(iii)	I	I knew the followers were decreasing between two times, but did not know whether to state an interval or number of days.	Wrote both.

Be precise. “Did not get it” is not enough information to fix next lesson. “I differentiated correctly, but forgot to substitute the stationary time back into $F(t)$” is useful.

The 60-second move-on rule

If you cannot identify a productive first step within about 60 seconds:

1. Write the part label.
2. Write the information you do understand.
3. Add S or ?.
4. Move to the next part.

For instance, in a maximum question, you might still write:

$$F^{\prime }(t)=\dots$$

even if you are unsure how to establish which stationary point gives the maximum. This preserves a possible method mark and makes your uncertainty visible.

Do not use the 60-second rule to avoid challenging work. Use it when you are genuinely stuck and no longer making progress.

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Read the selected questions, then begin the timer

Open the official 2023 paper only at the selected parts. Read every instruction carefully, including contextual conditions such as the interval $0\le t\le 90$.

Three-minute planning scan

Before the main timer begins, spend three minutes writing only a method label beside each selected part. Do not solve yet.

Your labels can be very short:

Part	A useful planning label
1(a)	Differentiate; solve stated gradient; substitute into $f(x)$ for the coordinate
1(b)	Anti-differentiate; include $+c$; use the given point
1(c)	Differentiate; find critical values; identify where $f^{\prime }(x)>0$
3(b)(i)	Differentiate $F(t)$; evaluate at the stated day; use followers-per-day units
3(b)(ii)	Solve $F^{\prime }(t)=0$; determine the relevant maximum within the stated interval; evaluate $F(t)$
3(b)(iii)	Find where $F^{\prime }(t)<0$; justify the decreasing interval; convert interval length into days

If one of those labels does not make sense to you, put a ? in your uncertainty log before the timer starts. That is valuable information: it separates a method-selection gap from a calculation error.

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Timed attempt: 28 minutes

Set a timer for 28 minutes. Work in the following order unless you have a clear reason to change it.

Time window	Parts	Aim
First 10 minutes	1(a), 1(b), 1(c)	Build confidence with direct derivative, anti-derivative, and derivative-sign work
Next 14 minutes	3(b)(i), 3(b)(ii)	Show a connected rate-and-maximum argument
Final 4 minutes	3(b)(iii) and any return attempts	State and justify the decreasing period

During the timer

Keep these exam habits in view:

• Write the derivative or anti-derivative clearly. It is often essential evidence even when later arithmetic goes wrong.
• When finding a coordinate, calculate the $x$-value from a derivative condition, then return to the original function for the matching $y$-value.
• When recovering a function, include the arbitrary constant:

$$f(x)=\int f^{\prime }(x)dx+c$$

Then use the supplied point to determine $c$.

• For “increasing” or “losing followers,” roots of the derivative are boundaries, not the final conclusion. You need to determine where the derivative is positive or negative.
• For a maximum, do not stop merely because you solved $F^{\prime }(t)=0$. A stationary value is a candidate; the question asks for the maximum value in the stated context.
• Put units into contextual conclusions. A rate of followers is measured in followers per day, not simply “followers.”

Your calculator may help with evaluating expressions, solving a quadratic, or checking roots. However, still write the equation you solved and the reasoning that connects it to the question.

If you finish early

Do not check online solutions or the assessment schedule. Instead, use remaining time to:

1. underline every final answer;
2. check that each requested coordinate has both components;
3. check that you included $+c$ when anti-differentiating;
4. check that contextual answers include units or a time interval;
5. add C beside any line you are no longer confident about.

At the 28-minute mark, stop writing calculations. Preserve the paper exactly as it stands.

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Complete your uncertainty log: 5 minutes

Now take five minutes to complete the log. Do not correct the mathematics yet.

Copy and complete this table:

Part	Completed, partial, or skipped?	First uncertain or skipped step	Code	Likely topic
1(a)				Gradient and coordinates
1(b)				Anti-differentiation and $c$
1(c)				Derivative signs and intervals
3(b)(i)				Rate of change and units
3(b)(ii)				Stationary points and maxima
3(b)(iii)				Negative derivative and interpretation

Use one of these sentence stems to make your record specific:

• “I did not know whether to differentiate or anti-differentiate because…”
• “I knew the required method, but became unsure when…”
• “I skipped this after ___ minutes because…”
• “I got a value of ___, but was uncertain whether it was valid because…”
• “I had two possible values and did not know how to choose between them.”
• “My answer may have the wrong units or conclusion because…”

A strong record might say:

3(b)(ii), C: I set $F^{\prime }(t)=0$ and found two values of $t$, but I did not confidently compare the corresponding values of $F(t)$. I selected one based only on the sketch in my head.

That identifies a very different issue from:

3(b)(ii), ?: I saw “maximum” but could not remember why the derivative should be set equal to zero.

The first is a completion/classification gap; the second is a method-selection gap.

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Preserve the evidence for correction

Put your completed mini-set and uncertainty log aside without looking at the marking schedule. In the next lesson, you will compare your work with the official 2023 schedule and identify the first incorrect or missing piece of evidence in each part.

For now, success means that you have:

• attempted a genuine AS91262 mini-set under a fixed time limit;
• moved on rather than becoming trapped by one question;
• shown enough working to reveal your method;
• recorded skipped and uncertain steps precisely.

The next lesson will turn this attempt into a targeted revision plan: not simply “get more practice,” but identify whether each issue came from differentiation, anti-differentiation, stationary-point reasoning, interval signs, contextual interpretation, or incomplete exam evidence.