Free Maclaurin series & limits questions for IB Mathematics: Analysis & Approaches (SL & HL), HL only, part of Calculus. Each question has the answer and the marking points an examiner would look for.
Generate a full Maclaurin Series & Limits worksheet →All Calculus questionsFind limx→0sin 3x − 3xx3.
| Part | Answer and marking points | Marks |
|---|---|---|
| −92 recognising the 00 indeterminate form R1 use of L’Hôpital’s rule or a Maclaurin series M1 correct derivatives or series A1 repeat (or simplify) to remove the indeterminate form M1 −92 A1 | 5 |
Using the Maclaurin series for standard functions, find the Maclaurin series for cos x ln(1 + 2x), up to and including the term in x3.
| Part | Answer and marking points | Marks |
|---|---|---|
| 2x − 2x2 + 53x3 writing down the standard series (to x3) A1 attempt to multiply the series M1 2x − 2x2 + 53x3 A3 award A1 for each correct non-zero term | 5 |
Find limx→0e3x − 1 − 3xx2.
| Part | Answer and marking points | Marks |
|---|---|---|
| 92 recognising the 00 indeterminate form R1 use of L’Hôpital’s rule or a Maclaurin series M1 correct derivatives or series A1 repeat (or simplify) to remove the indeterminate form M1 92 A1 | 5 |
Using the Maclaurin series for standard functions, find the Maclaurin series for excos x, up to and including the term in x3.
| Part | Answer and marking points | Marks |
|---|---|---|
| 1 + x − 13x3 writing down the standard series (to x3) A1 attempt to multiply the series M1 1 + x − 13x3 A3 award A1 for each correct non-zero term | 5 |
Find limx→01 − cos 2xx2.
| Part | Answer and marking points | Marks |
|---|---|---|
| 2 recognising the 00 indeterminate form R1 use of L’Hôpital’s rule or a Maclaurin series M1 correct derivatives or series A1 repeat (or simplify) to remove the indeterminate form M1 2 A1 | 5 |
Using the Maclaurin series for standard functions, find the Maclaurin series for exln(1 + x), up to and including the term in x3.
| Part | Answer and marking points | Marks |
|---|---|---|
| x + 12x2 + 13x3 writing down the standard series (to x3) A1 attempt to multiply the series M1 x + 12x2 + 13x3 A3 award A1 for each correct non-zero term | 5 |
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Meet Riyaz →Original IB-style practice questions written for mentorriyaz.in. These are not IB past paper questions, and this site is not affiliated with or endorsed by the International Baccalaureate Organization. Updated 2026-11-04. Paper generator · mentorriyaz.in