Practice IB Mathematics Analysis and Approaches (AA) Topic SL 5.1—introduction of Differential Calculus with authentic exam-style questions for both SL and HL students. This question bank focuses on the exact syllabus content for SL 5.1—introduction of Differential Calculus and mirrors Paper 1, 2, 3 style where relevant.
Get instant solutions, detailed explanations, and build confidence with questions aligned to IB examiner expectations.
The function models the electric potential (in volts) at a point with coordinate metres on a straight sensor line.
(a) the vertical and horizontal asymptotes of .
(b) the behavior of the electric potential as and , and its significance.
(e) Find the critical -values of the function .
The function models the stress (in MPa) on a structural beam as a function of position (in metres) along the beam.
The function models the pressure variation (in kPa) in a pipeline as a function of position (in metres), measured relative to a monitoring station.
Consider the function .
(a) Given the function , find the derivative .
(c) Find the second derivative of the function .
This question focuses on the fundamentals of differential calculus and on using derivatives to analyse a function.
(a) For the function .
Find for this function.
(c) the nature of each critical point: local maximum, local minimum, or neither.
(a) the vertical and horizontal asymptotes of .
(b) the behavior of the stress as and , and its significance.
(c) the graph of , marking key points and asymptotes, to illustrate the beam's stress distribution.
(b) the behavior of the pressure variation as and , and its significance.
(c) the graph of , marking key points and asymptotes, to illustrate the pipeline pressure variation.
(b) the equation of the tangent line to the curve at .
(d) whether the curve is concave up or concave down at .
(b) the critical points for .
(d) the graph of , making clear the critical points and their nature.
(a) the vertical and horizontal asymptotes of .
