Mathematics 4024 · O Level · Sketching curves

Sketching curves — practice question

(a)[2]

The equations are $y = 2x + 1$, $y = 2x - 1$, $y = -2x + 1$ and $y = -2x - 1$. The diagrams below contain sketches of two of these lines. Write the correct equation under each diagram.

(b)[2]

The diagram shows a sketch of the graph of $y = x^2 + ax + b$. Determine the value of $a$ and the value of $b$.

(c(i))[2]

The grid displays the graph of $y = x^3 - 2x^2 - 5x + 6$. $x^3 - 2x^2 - 5x + 6 = k$ has exactly $2$ solutions. Use the graph to identify the possible values of $k$.

(c(ii))[4]

By drawing a suitable line on the grid, determine the solutions of $x^3 - 2x^2 - 7x + 5 = 0$.

Worked solution & mark scheme

This 10-mark question has a full step-by-step worked solution and mark scheme. One marking point: $y=2x-1$

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