The answer
(a) \(k = 4\), \(a = 5\)
(b) \(y = -48x + 4\)
O-Level E-Math 2016 Paper 1 Question 17 · Verified worked solution by the Genius Plus Academy teaching team
What this question tests
This is Question 17 of the O-Level E-Math 2016 Paper 1. It tests find constants of an exponential from two points, in the Functions & graphs area. It is worth 4 marks: 2 + 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 \(B(0, 4)\): \(4 = k a^{-0} = k\), so \(k = 4\). At \(A(-2, 100)\): \(100 = 4 a^{-(-2)} = 4a^2\), so \(a^2 = 25\) and \(a = 5\) (taking the positive base). Thus \(k = 4\), \(a = 5\).
(b) Gradient of \(AB = \dfrac{4 - 100}{0 - (-2)} = \dfrac{-96}{2} = -48\). The line meets the \(y\)-axis at \(B(0, 4)\), so its intercept is \(4\). Equation: \(y = -48x + 4\).
Answer: (a) \(k = 4\), \(a = 5\)
(b) \(y = -48x + 4\)
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 find constants of an exponential from two points question from Functions & graphs, worth 4 marks: 2 + 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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