Maclaurin series — AS & A Level Further Mathematics (9231) questions by topic
Expanding functions as power series anchors this topic: building an early-terms expansion of a reciprocal exponential expression, combining two separate exponential expansions into one series, and combining two logarithmic expansions into a single quadratic approximation.
Find and deduce are the two command words across 7 questions from 2023 to 2025 papers, worth from 4 to 6 marks, so each short response depends on differentiating or expanding accurately up to a specified term. With no examiner-report extracts logged for this topic, submitting each series expansion for instant marking is the way to confirm every coefficient up to the required power of x is correct before combining separate series terms.
May–June 2025, Paper 23
Find the Maclaurin's series for e^(1/(x+2)) up to and including the term in x^2.
Answer this question and get it marked →May–June 2024, Paper 21
Find the Maclaurin's series for e^(1 + x^2) + e^(1 - x) up to and including the term in x^2.
Answer this question and get it marked →May–June 2024, Paper 22
Find the Maclaurin's series for e^(1 + x^2) + e^(1 - x) up to and including the term in x^2.
Answer this question and get it marked →May–June 2023, Paper 23
Find the Maclaurin series for sin^(-1) x up to and including the term in x^3.
Answer this question and get it marked →October–November 2023, Paper 21
Find the first three terms in the Maclaurin's series for tanh^(-1)((1/2) e^x) in the form (1/2) ln(a) + bx + cx^2, giving the exact values of the constants a, b and c.
Answer this question and get it marked →October–November 2023, Paper 22
Find the Maclaurin's series for ln(x + 2) + ln(x^2 + 5) up to and including the term in x^2.
Answer this question and get it marked →October–November 2023, Paper 23
Find the first three terms in the Maclaurin's series for tanh^(-1)((1/2) e^x) in the form (1/2) ln(a) + b x + c x^2, giving the exact values of the constants a, b and c.
Answer this question and get it marked →Other AS & A Level Further Mathematics topics
- Matrices (38)
- Inference and hypothesis testing (31)
- Summation of series (28)
- Differential equations (24)
- Hooke's law and elasticity (21)
- Hyperbolic functions (18)
- Projectiles (18)
- Non-parametric tests (18)
- Complex numbers (17)
- Vectors (16)
- Equilibrium of a rigid body (16)
- Continuous random variables (16)