Mathematics 0580 · IGCSE · Differentiation

Differentiation — practice question

The grid displays the graph of $y = a + bx^2$. The curve passes through the points $(0,4)$ and $(1,1)$.
(a(i))[2]

Find the value of $a$ together with the value of $b$.

(a(ii))[1]

Write down the equation of the tangent line at $(0,4)$.

(a(iii))[2]

Find the equation of the tangent line at $x=1$.

(b(i))[3]

Complete the table.

(b(ii))[4]

On the grid, sketch the graph of $y = 1 + \frac{5}{3-x}$ for $-2 \leq x \leq 1.5$.

(c(i))[2]

Write down the $x$-values where the two graphs meet.

(c(ii))[4]

Find this equation in the form $ax^3 + bx^2 + cx + d = 0$, where $a$, $b$, $c$ and $d$ are integers.

Worked solution & mark scheme

This 18-mark question has a full step-by-step worked solution and mark scheme. One marking point: The value of $a$ is $a=4$.

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