The answer
(a) $0.37
(b) 6 cartridges
(c) about $9 to $10 per year (total cost \(\approx \$1314\), \(\approx \$8.76\) per subscriber)
O-Level E-Math 2016 Paper 2 Question 10 · Verified worked solution by the Genius Plus Academy teaching team
What this question tests
This is Question 10 of the O-Level E-Math 2016 Paper 2. It tests reading rate tables, in the Rate & everyday-money problem solving area. It is worth 10 marks: 1 + 2 + 7. It is a worded / diagram-based question, so open your Ten-Year Series (TYS) or the official paper at this question, then follow our full worked solution below.
(a) A C5 envelope of 25 g is standard regular mail (the table lists C5/C6/DL as standard regular). 25 g falls in the "up to 40 g" regular step, costing $0.37.
(b) Each newsletter is 4 sheets printed on both sides \(= 8\) printed pages. For 150 subscribers, 6 times a year: total printed pages \(= 150 \times 6 \times 8 = 7200\) pages. One black cartridge yields 1300 pages, so cartridges needed \(= \dfrac{7200}{1300} = 5.54\), which rounds up to 6 cartridges (you cannot buy part of a cartridge).
(c) Work out the total annual cost, then set the price to cover it. - Paper. Total sheets \(= 150 \times 6 \times 4 = 3600\) sheets. A4 comes in packs of 500, so \(\lceil 3600 / 500 \rceil = 8\) packs. Eight packs is below the 10-pack bulk threshold, so they cost $3.90 each: \(8 \times \$3.90 = \$31.20\). - Toner. 6 black cartridges (from part b) at $147.00 each \(= \$882.00\). - Envelopes. \(150 \times 6 = 900\) C5 envelopes needed. Cheapest is packs of 500 ($34.00, i.e. $0.068 each) rather than packs of 10 ($0.15 each); buy 2 packs of 500 to cover 900: \(2 \times \$34.00 = \$68.00\). - Postage. 900 copies at $0.37 each \(= \$333.00\).
Total annual cost \(= 31.20 + 882.00 + 68.00 + 333.00 = \$1314.20\). Per subscriber \(= \dfrac{1314.20}{150} = \$8.76\). To be sure of covering all costs (with a little to spare), a sensible charge is about $9 to $10 per one-year subscription. For example, $10 per subscriber gives income \(150 \times \$10 = \$1500\), comfortably above the $1314.20 cost. (This is an open justification question; any clear model giving a price at or above about $8.76 with the costs shown is acceptable.)
Answer: (a) $0.37
(b) 6 cartridges
(c) about $9 to $10 per year (total cost \(\approx \$1314\), \(\approx \$8.76\) per subscriber)
Same structure, different numbers
Swap the constants, dress a quadratic as a length, hide a derivative inside an integral, and a student sees a brand new problem. The structure underneath is the same, and so is the method. Once a student can name the structure, a whole row of questions that look different start to open the same way.
That is where marks really leak: in choosing the method, not in the algebra that follows. We call it Lock and Key, name the lock, then the key follows.
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Genius Plus Academy · O-Level & IP Mathematics
Our O-Level E-Math tuition trains the same recognise-the-structure method these worked solutions show, taught by a team that has marked these papers for years. It runs within our weekly Secondary Math programme, Sec 1 to 4 and IP.
It is a reading rate tables question from Rate & everyday-money problem solving, worth 10 marks: 1 + 2 + 7.
Yes. IP (Integrated Programme) schools teach the same O-Level Mathematics content; they just sequence it differently and set their own internal exams, so these worked solutions apply to IP students too.
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