Why check the order of magnitude?

Biology sums often involve powers of ten, so an answer that is off by several orders usually means a missed power of two or bp mixed with kb.

How does recovery enter the sum?

The theoretical yield times the recovery fraction gives the mass actually obtained, and the two steps should be written separately.

S6 Biology: Biotechnology Paper 4 (combined calculations and error spotting)

2026-11-03

S · 6

Paper 4 chains length, base ratios, fold increase and recovery yield: list what is known, decide whether to multiply or divide, then check that the units and order of magnitude make sense.

Quick answer　4,800 bp; T is 22%; 40 copies; ten sites; about 5.24 x 10^7 copies; eight times; 20%; about 0.0027 matches; 30 g; 24 g recovered; about 1.07 x 10^9 fold.

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)

FoundationA 3,500 bp plasmid takes a 1,300 bp insert. What is the recombinant length?
FoundationIn a double-stranded DNA guanine is 28% of the bases. What percentage is thymine?
FoundationStarting from five copies, three PCR cycles run. How many copies result?
FoundationAn enzyme recognises four base pairs. How many sites does a 2,560 bp plasmid have on average?
IntermediateFifty copies run through twenty cycles. How many copies are expected?
IntermediateIn a gel a 4,000 bp fragment moves 1.2 cm and a 500 bp fragment moves 9.6 cm. How many times further does the short one travel?
IntermediateA 4.8 kb vector takes a 1.2 kb insert. What percentage of the recombinant plasmid is the insert?
ChallengeA guide RNA is 20 nt and the genome is about 3.0 x 10^9 bp. How many random matches are expected?
ChallengeA plant runs three 400 L batches at 25 mg per litre with eighty per cent recovery. What are the theoretical and actual masses in grams?
Error redoError repair: a student says thirty PCR cycles make thirty times the DNA. What is correct?

03　Answers and one-line notes

#	Answer	One-line note
1	4,800 bp	Three thousand five hundred plus one thousand three hundred is 4,800 bp, the sum of both segments.
2	22%	G and C take 56% together, so A and T share the remaining 44% and T is 22%.
3	40 copies	Three cycles multiply by eight, and five times eight is 40 copies.
4	ten sites	A four-base cutter averages one site every 256 bp, and 2,560 divided by 256 is ten.
5	about 5.24 x 10^7 copies	Two to the power 20 is 1,048,576, and times fifty gives about 5.24 x 10^7 copies.
6	eight times as far	Nine point six divided by 1.2 is 8, and shorter fragments travel further within the same gel.
7	20%	The total is 6.0 kb, and 1.2 divided by 6.0 times one hundred is 20%.
8	about 0.0027 matches	Four to the power 20 is about 1.10 x 10^12, and 3.0 x 10^9 divided by it is about 0.0027, fewer than one.
9	30 g theoretically, 24 g recovered	Three times 400 is 1,200 L, times 25 mg gives 30,000 mg that is 30 g, and times 0.8 gives 24 g.
10	about 1.07 x 10^9 fold, doubling every cycle	Each cycle multiplies by two rather than adding one, so thirty cycles give two to the power 30, about 1.07 x 10^9 fold.

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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