CAIE A-Level Mathematics 2.2.2 Exponential and Natural Logarithm Functions

CAIE A-Level Mathematics 2.2.2 Exponential and Natural Logarithm Functions
Cambridge International AS & A Level Mathematics 9709 syllabus for exams in 2028, 2029 and 20302028–2030

Practise using eˣ and ln x as inverse functions and sketching exponential curves with correct intercepts, monotonic direction and asymptotic behaviour against other graphs.

How this is tested

  • sketch y = Aeᵏˣ through its y-intercept with the correct growth or decay direction
  • use ln(eˣ) = x and e^(ln x) = x to convert exact exponential and logarithmic forms
  • compare curve placement and intersections with a line or modulus graph over the stated domain

Question 6(a)

[Maximum number: 2]

Sketch the graph of y=3sin⁡x+2y=3 \sin x+2 for 0⩽x⩽2π0 \leqslant x \leqslant 2 \pi.

Figure for Question 6(a) — CAIE A-Level Mathematics