IGCSE Mathematics - Additional (0606) — May–June 2023, Paper 21
11 questions · every question answerable online with instant point-by-point AI marking against the official mark scheme.
Start with Question 1 →Variables x and y are such that when lg y is plotted against x a straight line passing through the points (1, 5) and (2.5, 8) is obtained. Show that y = A × b^x where A and b are…
Answer this question and get it marked →The function g is defined for 0° ≤ x ≤ 120° by g(x) = 2 + 4 cos 6x. On the axes, sketch the graph of y = g(x).
Answer this question and get it marked →The diagram shows the graph of y = h(x) where h(x) = (x + a)²(b + cx) and a, b and c are integers. The curve meets the x-axis at the points (−2, 0) and (1.5, 0) and the y-axis at…
Answer this question and get it marked →Solve the equation 5^(2y − 1) = 6 × 3^y, giving your answer correct to 3 decimal places.
Answer this question and get it marked →The volume, V, of a sphere of radius r is given by V = (4/3)πr³. The volume of a sphere is increasing at a constant rate of 24 cm³ s⁻¹. Find the rate of increase of the radius…
Answer this question and get it marked →The position vectors of the points P, Q and R relative to an origin O are (4, 7), (8, 5) and (x, y) respectively. The point R lies on PQ extended such that 3QR = 2PR. Use a vector…
Answer this question and get it marked →The diagram shows the curve y = 6x − x² for 0 ≤ x ≤ 5 and the line y = x. Find the area of the shaded region (between the curve and the line).
Answer this question and get it marked →The diagram shows the graph of y = f(x) where f is defined by f(x) = 3x/√(5x + 1) for 0 ≤ x ≤ 3. Given that f is a one-one function, find the domain and range of f⁻¹.
Answer this question and get it marked →In this question all lengths are in centimetres and all angles are in radians. The area of a sector of a circle of radius 24 is 432 cm². Find the length of the arc of the sector.
Answer this question and get it marked →In the expansion of (ax + b/x²)⁹, where a and b are constants with a 0, the term independent of x is −145152 and the coefficient of x⁶ is −6912. Show that a²b = −12 and find the…
Answer this question and get it marked →The line with equation x + 3y = k, where k is a positive constant, is a tangent to the curve with equation x² + y² + 2y − 9 = 0. Find the value of k and hence find the coordinates…
Answer this question and get it marked →