2026 EVG P2 Q7

2026 EVG P2 Q7

Secondary 4
12 marks
  1. Complete the table of values for \(y=3x-2/x^2+2\), \(x\ne0\), correct to 1 decimal place.[1]
    \(x\)−3.5−3−2.5−2−1−0.5
    \(y\)
  2. On the grid, draw \(y=3x-2/x^2+2\) for \(-3.5\leq x\leq-0.5\).[2]
  3. The equation \(k=3x-2/x^2+2\) has only 1 solution for \(-3.5\leq x<0\). Use your graph to find k.[1]
  4. By drawing a suitable tangent, estimate the gradient where \(x=-2\).[2]
    1. On the same grid, draw the graph of \(2y-x=-8\) for \(-4\leq x\leq0\).[1]
    2. Show that the points of intersection of the line and curve give the solutions of \(5x^3+12x^2-4=0\).[1]
    3. Use your graph to solve \(5x^3+12x^2-4=0\).[2]
  6. By drawing a suitable straight line on the grid, solve \(3x^3+6x^2>2\).[2]

Solution:

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Answer:(a) −8.7,−7.2,−5.8,−4.5,−3.0,−7.5. (c) Intended k≈−2.95; additional values noted. (d) 2.5. (e) x≈−2.24,−0.682 on grid; also ≈0.523. (f) −1.790.515 over all reals.

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