Mathematics 4024 · O Level · Sketching curves

Sketching curves — practice question

(a)[1]

Use $y = \frac{x^3}{2} - 3x - 1$ to complete the table.

(b)[3]

On the grid, draw the curve for $y = \frac{x^3}{2} - 3x - 1$ for $-3 \leq x \leq 3$.

(c)[2]

Use your graph to show why $x^3 - 6x - 2 = 6$ has only one solution.

(d(i))[1]

Draw line $L$ on the grid.

(d(ii))[2]

Find the gradient of line $L$.

(d(iii))[2]

Use your graph to find the $x$-coordinates of the points where line $L$ meets the curve $y = \frac{x^3}{2} - 3x - 1$.

Worked solution & mark scheme

This 11-mark question has a full step-by-step worked solution and mark scheme. One marking point: $-\tfrac{11}{2}$

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