IGCSE Mathematics - Additional (0606) — October–November 2023, Paper 23
10 questions · every question answerable online with instant point-by-point AI marking against the official mark scheme.
Start with Question 1 →The functions f and g are defined as follows, for all real values of x: f(x) = 2 sin x + 3 cos x, g(x) = e^(3x) − 1. Find fg(0).
Answer this question and get it marked →Find the values of k for which the curve y = x² + kx + (4k − 15) is completely above the x-axis.
Answer this question and get it marked →Solve the following simultaneous equations: 3 log₂ x + 2 log₂ y = 24 and 5 log₂ x − 3 log₂ y = 2.
Answer this question and get it marked →Find the exact value of ∫₃⁵ (x − 1)²/x³ dx.
Answer this question and get it marked →The curved surface area of a cylinder with radius r and height h is 2πrh. A closed cylinder has radius r cm and volume 1000 cm³. Show that the total surface area of the cylinder…
Answer this question and get it marked →A particle travels in a straight line. Its displacement, s metres, from the origin, at time t seconds, where t 2, is given by s = ln(4t² − 5) − t. Find expressions for the…
Answer this question and get it marked →DO NOT USE A CALCULATOR IN THIS QUESTION. In triangle ABC, angle A = 60°, angle B = 75°, angle C = 45°. You may use the trigonometrical ratios: sin 60° = √3/2, sin 45° = √2/2, cos…
Answer this question and get it marked →Show that sin x/(tan x − 1) − cos x/(tan x + 1) = cos x/(sin²x − cos²x).
Answer this question and get it marked →A curve has equation y = xe^(2x). Find dy/dx.
Answer this question and get it marked →In an arithmetic progression the 5th term is 11. The 7th term is three times the 2nd term. Find the 1st term and the common difference.
Answer this question and get it marked →