IGCSE Mathematics - Additional (0606) — May–June 2023, Paper 22
10 questions · every question answerable online with instant point-by-point AI marking against the official mark scheme.
Start with Question 1 →Solve the inequality 3x² − 12x + 16 3x + 4.
Answer this question and get it marked →A curve has equation y = 32x² + 1/(8x²) where x ≠ 0. Find the coordinates of the stationary points of the curve.
Answer this question and get it marked →DO NOT USE A CALCULATOR IN THIS QUESTION. Show that x + 3 is a factor of −12 + 23x + 3x² − 2x³.
Answer this question and get it marked →Variables x and y are related by the equation y = 2 + tan(1 − x) where 0 ≤ x ≤ π/2. Given that x is increasing at a constant rate of 0.04 radians per second, find the…
Answer this question and get it marked →Variables P and T are known to be connected by the relationship P = Ab^T, where A and b are constants. Values of P are found for certain values of time, T. Show that a graph of lg…
Answer this question and get it marked →Find the first three terms in the expansion of (1 + x/7)⁵, in ascending powers of x. Simplify the coefficient of each term.
Answer this question and get it marked →f(x) = 3 + √((4x − 2)⁵) where x 1. (Given f(x) = 3 + (4x − 2)^(5/2).) Find an expression for f′(x), giving your answer as a simplified algebraic fraction.
Answer this question and get it marked →A curve has equation y = cos(x/4) where x is in radians. The normal to the curve at the point where x = 4π/3 cuts the x-axis at the point P. Find the exact coordinates of P.
Answer this question and get it marked →A particle travels in a straight line so that, t seconds after passing a fixed point, its velocity, v m s⁻¹, is given by v = e^(t/4) for 0 ≤ t ≤ 4, and v = 16e/t² for 4 ≤ t ≤ k.…
Answer this question and get it marked →The diagram shows a triangle OAB. The point C is the mid-point of OA. The point D lies on CB such that CD : DB = 2 : 3. OC = c and CB = b. The point E lies on AB such that OE =…
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