IGCSE Mathematics - Additional (0606) — May–June 2025, Paper 23
13 questions · every question answerable online with instant point-by-point AI marking against the official mark scheme.
Start with Question 1 →Solve the inequality (x + 2)(4x − 5) ≤ 0.
Answer this question and get it marked →Given that y = (4x^3 − 5) / x^2, show that dy/dx can be written as 2(2x^3 + 5) / x^3.
Answer this question and get it marked →Variables x and y are such that when sqrt(y) is plotted against x^3 a straight line graph passing through the points (2, 5) and (10, 21) is obtained. Find y in terms of x.
Answer this question and get it marked →The function f is defined by f(x) = 2x − 1 for x ∈ ℝ. Explain why the function f^2 can be formed.
Answer this question and get it marked →In this question, all angles are in radians. Write down the period of 5 tan(x/4) + 1.
Answer this question and get it marked →Five of the digits 1 2 3 4 5 6 7 8 9 are used to make a 5-digit number. Find how many ways this can be done when the 5-digit number is greater than 50 000.
Answer this question and get it marked →Find the term independent of x in the expansion of (x^2 − 3/x^4)^15.
Answer this question and get it marked →It is given that y = e^(3x+2) tan x. Use calculus to find the approximate change in y as x increases from 0.1 to 0.1 + h, where h is small.
Answer this question and get it marked →The 1st term of an arithmetic progression is 9. The last term of this progression is 159. The sum of all the terms is 2604. The 12th term of this arithmetic progression is the 1st…
Answer this question and get it marked →In this question, time is in seconds. At time t = 0, particle P starts from the point with position vector −30j. P travels with speed 58 m s^(-1) in the direction 20i + 21j. Find…
Answer this question and get it marked →Given that ((n+1)P5) / 437 = (nP3), use an algebraic method to find the value of n.
Answer this question and get it marked →The function f is defined by f(x) = 15 cos^2(3x + 1.5) + 7 sin(3x + 1.5) − 13 for −0.3 ≤ x ≤ 0.5, where x is in radians. Solve the equation f(x) = 0.
Answer this question and get it marked →Solve the equation 64^(x + 1/3) + 2^(3x) − 3 = 0.
Answer this question and get it marked →