2025 CGSS PRELIMS P2 Q4

2025 CGSS PRELIMS P2 Q4

Secondary 4
12 marks

The variables \(x\) and \(y\) are connected by the equation \(y=\dfrac7x+2x-11\). Some corresponding values are given in the table below. Values are given to 1 decimal place where appropriate.

\(x\)\(0.5\)\(1\)\(1.5\)\(2\)\(3\)\(4\)\(5\)\(6\)\(6.5\)
\(y\)\(4\)\(-2\)\(-3.3\)\(-3.5\)\(-2.7\)\(-1.25\)\(0.4\)\(2.2\)\(3.1\)
  1. Fill in the missing value in the table.[1]
  2. On the grid below, draw the graph of \(y=\dfrac7x+2x-11\) for \(0.5\leq x\leq6.5\).[2]
  3. By drawing a tangent, find the gradient of the curve at \(x=2\).[2]
  4. Using your graph,
    1. explain why the equation \(2x+\dfrac7x-7=0\) has no solution,[2]
    2. find the \(x\)-coordinate of the points where the line \(2y=4-x\) intersects the curve,[2]
    3. These values of \(x\) are the solutions of the equation \(Ax^2+Bx+14=0\). Find the value of \(A\) and of \(B\).[3]

Solution:

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Answer:(a) \(-1.25\) (b) graph (c) \(0.25\) (d)(i) No solution (d)(ii) \(x\approx0.6,4.6\) (d)(iii) \(A=5,B=-26\)

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