2025 MGS(S) PRELIMS P2 Q4

2025 MGS(S) PRELIMS P2 Q4

Secondary 4
12 marks

The table contains values of \(y=\dfrac{x^2}{3}+\dfrac3x-4\), given to two decimal places where appropriate.

\(x\)\(0.5\)\(1\)\(1.5\)\(2\)\(3\)\(4\)\(5\)\(6\)
\(y\)\(2.08\)\(-0.67\)\(-1.25\)\(0\)\(2.08\)\(4.93\)\(8.5\)
  1. Complete the table.[1]
  2. Draw the graph for \(0.5\leq x\leq6\).[3]
  3. By drawing a tangent, find the gradient at \((3,0)\).[2]
    1. On the same axes, draw the line with gradient \(\dfrac43\) that passes through \((3,2)\).[2]
    2. Write down the (x)-coordinate(s) where the line intersects the curve.[1]
    3. The \(x\)-coordinates satisfy \(x^3+Ax^2+Bx+C=0\). Find \(A\), \(B\) and \(C\).[3]

Solution:

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Answer:(a) \(-1.17\) (b) graph (c) approximately \(1.65\) (d)(i) line drawn (ii) \(1.00,4.85\) (iii) \(A=-4,\ B=-6,\ C=9\)

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