2022 H2 Maths ACJC P1.pdf

The exam is for H2 Mathematics, with a total of 100 marks, and consists of 12 questions. The questions cover various topics, including functions, calculus, complex numbers, and geometry.

Question 1 asks to sketch the graph of a function and find its asymptotes, axial intercepts, and turning points.
Question 2 requires finding the integral of a given function.
Question 3 involves vectors and finding the area of a triangle and the angle between a vector and a plane.
Question 4 deals with a continuous function that is strictly decreasing and asks to sketch its curve and compare areas under the curve.
Question 5 involves complex numbers and requires showing that a given expression is real and finding the possible values of another complex number.
Question 6 defines a function h and asks to find the maximum value of λ for which the inverse function exists, find the inverse function, sketch its graph, and find the solution set for a given equation.
Question 7 gives a function y = ln(2sin²x + 1) and asks to show a given derivative, find the Maclaurin series for y, verify the series using standard formulas, and deduce the series expansion for another function.
Question 8 uses a substitution to evaluate an integral and then asks to find the exact area of a shaded region and the volume generated when the region is rotated about the y-axis.
Question 9, 10, 11, and 12 are not provided in the given text.