Thirty-Six

Unit 0 · Launch Prep

The 50-Minute Game Plan

Budget time, make strong guesses, and use review marks without giving away easy points.

  • 29 min
  • Desmos way

Ready when you are

7 steps · about 29 minutes

Start with the warm-up.

Start

Step 1 of 7Warm-upDone

Warm-up

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Key terms

First pass
Solve clear questions and mark time-consuming ones.
Review mark
A flag for a question worth revisiting.
Pace
Average time available per remaining question.

Step 2 of 7Try it firstDone

Try it first

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Take a shot before the lesson. Write one relationship from the stem, even if you do not finish.

Step 3 of 7LearnDone

The big idea

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See the structure

A 50-minute section allows about 67 seconds per item, but equal pacing is inefficient. Bank time on direct early questions and spend it where the late questions need it.

Key idea

Name quantities before calculating

Write what each number measures. A correct calculation with the wrong quantity or unit still misses the question.

Build a reliable method

Use a two-pass plan. On pass one, solve anything whose path is clear; after about 90 seconds without progress, guess, mark it, and move. On pass two, return with the time you protected.

Explore in Desmos

Turn remaining time into a pace

There are 13 minutes for 9 questions. The first line shows 86.6786.67 seconds per question; the second shows the greatest whole-number pace, 86. Explain why rounding up to 87 would exceed the available time.

The calculator is live: change anything and see what happens.

Turn remaining time into a pace

Degree mode

Press Escape to leave the calculator (twice if a menu is open).

Loading Desmos…

Stretch to a 36

There is no penalty for a wrong answer. Fill every answer, but make guesses from evidence: estimate, check units, and eliminate impossible signs before choosing.

Trap

A believable answer to the wrong question

The choices often include a correct intermediate number. Before selecting it, reread the highlighted ask and check the unit, sign, and domain.

Step 4 of 7Worked examplesDone

Worked examples

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Skip check · 2 questions

Already know this? Get both right on the first try and you can skip the worked examples.

Worked example

Example 1: Convert the clock to a per-question pace

Problem

With 12 minutes for 9 questions, how many seconds per question are available?
Convert first: 12(60)=72012(60)=720 seconds.

Which calculation uses the remaining time and questions correctly?

Distribute the time: 720/9=80720/9=80 seconds per question.

Which multiplication reconstructs the available time?

Worked example

Example 2: Recalculate from what remains

Problem

After 32 minutes, 29 of 45 questions are complete. What pace is available for the rest?
There are 5032=1850-32=18 minutes and 4529=1645-29=16 questions left.

Which calculation uses the remaining time and questions correctly?

18(60)/16=67.518(60)/16=67.5 seconds per remaining question.

Which multiplication reconstructs the available time?

Faded example · you finish it

Example 3: Complete the setup and result

Problem

How many seconds per question are available when 7 minutes remain for 6 questions?

Choose the setup that follows the stated relationship.

Choose the resulting value.

Desmos way

Build and check a seconds-per-question pace

Type 7*60/6 to convert 7 minutes to seconds and divide among 6 questions. The display gives 70 seconds per question; floor(7*60/6) confirms the whole-number pace.
Type 6*70 and read 420 seconds, exactly 7(60)7(60). This reverse multiplication checks that the pace uses all available time without exceeding it.

Build and check a seconds-per-question pace

Degree mode

Press Escape to leave the calculator (twice if a menu is open).

Loading Desmos…

Step 5 of 7PracticeDone

Practice

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Step 6 of 7Spot the mistakeDone

Spot the mistake

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Spot the mistake

Where did it go wrong?

One line has an error. Click the line where it first goes wrong.

Step 7 of 7Exit ticketDone

Exit ticket

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Optional · 4 questions · Hardest levelChallenge set: the kind of question that decides a 36

These are last-ten-questions hard. Take your time, use Desmos when it helps, and expect to miss some: that's where the learning is.