Calculate endpoint-rate proxies and sampling limits
Use repeated completion times while distinguishing a proxy from a direct product rate.
Mapped to the named 0654 section using teaching from the corresponding single-science course. A 0654-specific review of every Core and Supplement objective is still in progress. Written practice is self-checked; it does not demonstrate supervised laboratory competence or award an official Cambridge grade.
Before you begin
- Recall protein building blocks and the distinction between a molecule and a living cell.
- Use the supplied observations, quantities and units rather than assuming an optimum for every enzyme.
Work on paper. Try each question before revealing help, and explain why your method works.
Quick readiness check
What units does 1/time have when time is in seconds?
What you will learn
- Use repeated completion times while distinguishing a proxy from a direct product rate.
- Apply the explanation to the stated evidence and recognise the limits of the model.
State the quantity being calculated
For equal starting starch amounts and the same iodine endpoint, 1 divided by completion time is a useful comparative endpoint-rate proxy. Its units are s⁻¹ when time is measured in seconds. It is not a direct product-formation rate in mg/s, because no product mass was measured.
For a question requesting a proxy from the mean completion time, first calculate the mean of repeated times, then take its reciprocal. The reciprocal of a mean time need not equal the mean of individual reciprocals, so follow the specified calculation.
Respect observation resolution
If samples are checked every 10 s and the 30 s sample is positive while the 40 s sample is negative, the detection endpoint occurred after 30 s and by 40 s. The reported first-negative time is 40 s, but the exact underlying transition time is not observed.
Repeat trials and report the stated endpoint consistently. An endpoint not reached before stopping is not a zero-second reaction, and does not justify division by zero. A proxy based on first-negative samples has sampling uncertainty and test-detection limits.
Sources for this lesson
Pause and explain
A 30 s sample is positive and a 40 s sample negative. What is supported?
Worked example
Repeated first-negative times are 50, 60 and 70 s. Calculate the mean and the proxy from that mean.
Show the worked solution
- Mean = (50 + 60 + 70) ÷ 3 = 60 s.
- Proxy = 1 ÷ 60.
- Keep s⁻¹ and suitable rounding.
Answer Mean 60 s; endpoint-rate proxy about 0.0167 s⁻¹.
Try a topic test
Choose Easy, Normal or Difficult. Save your answers and open worked review after finishing.
Test this topic →From guided practice to a new situation
Write your answer and reasoning first. Use a hint only if you are stuck. The model solution is for self-checking; your written work is not automatically marked.
Calculate the endpoint-rate proxy for a 40 s completion time.
Give me a hint
Take the reciprocal and label it.
Compare my reasoning
- 1 ÷ 40 = 0.025.
0.025 s⁻¹.
Look for these in your work
- Use the reciprocal.
- Identify it as a proxy.
Times are 80, 90 and 100 s. Calculate the mean time and the proxy from the mean.
Give me a hint
Find the mean first.
Compare my reasoning
- (80 + 90 + 100) ÷ 3 = 90 s.
- 1 ÷ 90 ≈ 0.0111 s⁻¹.
Mean 90 s; proxy about 0.0111 s⁻¹.
Look for these in your work
- Use the stated order.
- Keep seconds and reciprocal seconds separate.
A 50 s sample detects starch; the 60 s sample does not. A student reports an exact 55 s endpoint and a directly measured glucose rate. Identify both overclaims.
Give me a hint
Check what was sampled and what substance was measured.
Compare my reasoning
- The endpoint is after 50 s and by 60 s; 55 s is unmeasured.
- Iodine tested starch detection, not glucose production mass.
The exact midpoint is unsupported, and a starch-detection endpoint is not a direct glucose-production rate.
Look for these in your work
- State the interval.
- Distinguish tested starch from unmeasured glucose.
Common mistakes
- Do not label a reciprocal-time proxy mg/s.
- Do not assign an exact unsampled endpoint time.
What can you explain now?
A 30 s sample is positive and a 40 s sample negative. What is supported?
Compare with the explanation
The endpoint was after 30 s and by 40 s.
It lies within the sampled interval.
After trying it yourself, choose your next review. This is your self-assessment.
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Make it stick
Retrieve proxy units, mean-before-reciprocal order and the meaning of a first-negative interval.
If you needed the solution, close it and solve the problem again from a blank page. A correct answer is stronger when you can explain the reason for each step.