Why is the cycle count found by a logarithm?

The yield is a power of two, so the base-two logarithm of the target fold change gives the number of cycles.

How does site density relate to recognition length?

Each extra base in the recognition site multiplies the average distance between sites by four.

S6 Biology: Biotechnology Paper 2 (cycle counts, site density and GM data)

2026-11-03

S · 6

Paper 2 reverses the formulas: find the number of cycles from a target fold change and the number of sites from fragment length.

Quick answer　Six cycles; T is 28%; every 256 bp; 4,000 bp; 1,050 bp; a 20% rise; four times; about 0.0002 expected hits; 500 mL; 2 to the power 5 is 32 times.

01　Paper details (check answers afterwards)

Item	Detail
Questions	10 questions
Suggested time	25 minutes
Difficulty mix	Foundation 4 · Intermediate 3 · Challenge 2 · Error redo 1
Chapter	Chapter: S6 Biology: Biotechnology
Level	S6

02　Questions (10 items)

FoundationPCR doubles the DNA every cycle. How many cycles turn one copy into 64 copies?
FoundationIn a double-stranded DNA molecule guanine is 22% of the bases. What percentage is thymine?
FoundationAn enzyme recognises four base pairs. With four bases equally likely, how many bp apart is a site on average?
FoundationA 3,200 bp plasmid takes an 800 bp insert. How long is the recombinant plasmid?
IntermediateA pre-mRNA of 1,500 bp carries three introns totalling 450 bp. How long is the mature mRNA?
IntermediateA GM rice rises from 15 to 18 tonnes per hectare. What is the percentage increase?
IntermediateIn a gel a 2,000 bp fragment moves 2.5 cm and a 500 bp fragment moves 10 cm. How many times further does the short one travel?
ChallengeA guide RNA is 22 nt and the genome is about 3.0 x 10^9 bp. How many random matches are expected?
ChallengeA vector holds 8 x 10^8 particles per millilitre and a treatment needs 4 x 10^11 particles. How many millilitres are needed?
Error redoError repair: a student says five PCR cycles give five times the DNA. What is correct?

03　Answers and one-line notes

#	Answer	One-line note
1	six cycles	Sixty-four is 2 to the power 6, so six doubling rounds are needed.
2	28%	G and C take 44% together, so A and T share the remaining 56% and T is 28%.
3	every 256 bp	Four to the power 4 is 256, so a site appears every 256 bp on average.
4	4,000 bp	Three thousand two hundred plus eight hundred gives 4,000 bp.
5	1,050 bp	One thousand five hundred minus four hundred and fifty leaves 1,050 bp of exons.
6	20%	A gain of three tonnes over the original fifteen, times one hundred, is 20%.
7	four times as far	Ten divided by 2.5 is 4, because shorter fragments migrate further in the gel.
8	about 0.0002 matches	Four to the power 22 is about 1.76 x 10^13, and 3.0 x 10^9 divided by it is about 0.0002, far below one.
9	500 mL	Four times 10 to the 11 divided by eight times 10 to the 8 gives 500.
10	32 times (2 to the power 5 is 32)	Each cycle doubles rather than adding one copy, so five cycles give 2 to the power 5, that is 32 times.

04　What to do after marking

After marking, redo only the wrong items and write down which step went wrong (formula, unit, or misread number).
Repeat the same item two days later; move to the next paper only when both attempts are correct.
Parents only need the answer and note columns; there is no need to explain every item.

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