Mathematics 0580 · IGCSE · Sketching curves

Sketching curves — practice question

A graph of $y=f(x)$ for $f(x)=x^2-\dfrac{2}{x}-2$, with $x\ne0$.
(a(i))[1]

Use the graph to determine $f(1)$.

(a(ii))[2]

Use the graph to determine $ff(-2)$.

(b)[4]

Draw a suitable straight line to solve $x^2-\dfrac{2}{x}-7=-3x$ over $-3\le x\le 3$.

(c)[3]

Estimate the gradient of the curve at $x=-2$ by drawing an appropriate tangent.

(d(i))[3]

Complete the table for $y=g(x)$ with $g(x)=2^{-x}$ when $-3\le x\le 3$.

(d(ii))[3]

Draw the graph for $y=g(x)$.

(d(iii))[1]

Use your graph to determine the positive solution of $f(x)=g(x)$.

Worked solution & mark scheme

This 17-mark question has a full step-by-step worked solution and mark scheme. One marking point: Correct result $-3$.

  • Full mark scheme, point by point
  • Step-by-step worked solution
  • Write your answer & get it marked instantly by AI