IGCSE Mathematics - Additional (0606) — May–June 2025, Paper 12
12 questions · every question answerable online with instant point-by-point AI marking against the official mark scheme.
Start with Question 1 →The diagram shows the graph of y = f(x) , where f is a cubic polynomial. The graph touches the x-axis at x = -2, touches the x-axis at x = -0.5, has a y-intercept at y = 2, and…
Answer this question and get it marked →Solve the equation x^(1/3) + 1 = 6 / x^(1/3).
Answer this question and get it marked →A circle with centre C has the equation x^2 + y^2 - 10x - 4y + 24 = 0. Show that the line y = 2x - 3 is a tangent to this circle.
Answer this question and get it marked →Find the integral from 0 to pi of sin(theta) d(theta).
Answer this question and get it marked →The polynomial p is such that p(x) = 3x^3 - 7x^2 + ax + b, where a and b are integers. It is given that p'(-1) = 21 and that x - 2 is a factor of p(x). Find the values of a and b.
Answer this question and get it marked →When ln(y) is plotted against x^3, a straight line passing through the points (2, 5) and (-8, 25) is obtained. Find y in terms of x.
Answer this question and get it marked →A geometric progression has a 4th term of (8k^6)/27 and a 6th term of (32k^10)/243, where k is a constant. The common ratio of this geometric progression is positive. Find the…
Answer this question and get it marked →It is given that y = ln(3x^2 + 16) / (x + 2). Find dy/dx when x = 0. Give your answer in the form ln(p), where p is a constant.
Answer this question and get it marked →It is given that f(x) = 2 ln(3x - 4), for x a, and that f^(-1) exists. Find the least possible value of a.
Answer this question and get it marked →The diagram shows the shape OABCDEF. AOF is a straight line. OAB and OEF are sectors of a circle with centre O and radius r. Angle BOA = angle EOF. OCD is a sector of a circle…
Answer this question and get it marked →The diagram shows the triangle OAB, where vector OA = a and vector OB = b. The point P lies on OA such that vector OP = (3/4) vector OA. The point Q lies on AB such that vector AQ…
Answer this question and get it marked →A curve is such that its gradient at the point (x, y) is given by (5x - 2)^(1/3). The curve passes through the point (2, 32/5). Find the coordinates of the stationary point on the…
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