The answer
(a) \(p = 5.05\)
(c) \(x \approx 1.6\) and \(x \approx 2.8\)
(d) gradient \(\approx 1.35\)
(e)(ii) \(y = -1.5x + 4\)
(iii) \(\approx (0.7, 3.0)\) and \(\approx (2.7, -0.06)\)
O-Level E-Math 2015 Paper 2 Question 4 · Verified worked solution by the Genius Plus Academy teaching team
What this question tests
This is Question 4 of the O-Level E-Math 2015 Paper 2. It tests evaluate to complete a table, in the Functions & graphs area. It is worth 12 marks: (a) 1, (b) 3, (c) 2, (d) 2, (e) 1 + 1 + 2. 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) At \(x = 0.5\): \(p = \dfrac{0.25}{5} + \dfrac{4}{0.5} - 3 = 0.05 + 8 - 3 = 5.05\) (2 d.p.).
(c) \(\dfrac{x^2}{5} + \dfrac{4}{x} = 3\) is the same as \(y = 0\). The curve crosses the \(x\)-axis between \(x = 1.5\) and \(x = 2\) and again between \(x = 2.5\) and \(x = 3\), giving \(x \approx 1.6\) and \(x \approx 2.8\). (Read from graph.)
(d) Draw a tangent to the curve at \((4, 1.20)\), read two points that lie on the tangent line, and work out rise \(\div\) run. A carefully drawn tangent gives a gradient of about \(1.35\). *(Read from the drawn tangent; accept roughly \(1.2\) to \(1.5\).)*
(e)(i) Through \((2, 1)\) with gradient \(-1.5\): \(y - 1 = -1.5(x - 2)\).
(ii) \(y = -1.5x + 4\).
(iii) Reading where this line crosses the curve gives approximately \((0.7, 3.0)\) and \((2.7, -0.06)\). (Read from graph.)
Answer: (a) \(p = 5.05\)
(c) \(x \approx 1.6\) and \(x \approx 2.8\)
(d) gradient \(\approx 1.35\)
(e)(ii) \(y = -1.5x + 4\)
(iii) \(\approx (0.7, 3.0)\) and \(\approx (2.7, -0.06)\)
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 evaluate to complete a table question from Functions & graphs, worth 12 marks: (a) 1, (b) 3, (c) 2, (d) 2, (e) 1 + 1 + 2.
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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