The answer
(a) \(a = -7\), \(b = 24\)
(b) \(x = 7\)
O-Level E-Math 2023 Paper 1 Question 6 · Verified worked solution by the Genius Plus Academy teaching team
The question
The expression \(x^2 - 14x + b\) is equivalent to \((x + a)^2 - 25\).
(a) Find the value of \(a\) and the value of \(b\). [2]
(b) The curve \(y = x^2 - 14x + b\) is drawn. Write down the equation of the line of symmetry of the curve. [1]
(a) \((x + a)^2 - 25 = x^2 + 2ax + a^2 - 25\). Comparing with \(x^2 - 14x + b\): \(2a = -14 \Rightarrow a = -7\); then \(b = a^2 - 25 = 49 - 25 = 24\).
(b) The vertex is at \(x = -a = 7\), so the line of symmetry is \(x = 7\).
Answer: (a) \(a = -7\), \(b = 24\)
(b) \(x = 7\)
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 completing the square question from Equations & inequalities / Functions & graphs, worth 3 marks: 2 + 1.
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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