IBDP Past Year Exam Questions – Introduction to Differential Calculus

1. [M15/P1/TZ1]

(a) Expand (x + h)3 .   [2 marks]
(b) Hence find the derivative of f (x) = x3 from first principles.   [3 marks]

2. [M16/P1/TZ2]

The function  f is defined as fx=ax2+bx+c where  a, b, c .
Hayley conjectures that  fx2fx1x2x1=fx2+fx12, x2x1

Show that Hayley’s conjecture is correct.   [6 marks]

3. [M12/P1/TZ2]

Using the definition of a derivative as  fx=limh0fx+hfxh , show that the derivative of 12x+1 is 22x+12 .             [4 marks]

4. [N18/P2/TZ0]

Differentiate from first principles the function  fx=3x3x .   [5 marks]