IGCSE Mathematics - Additional (0606) — May–June 2024, 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 point A has coordinates (1, 4) and the point B has coordinates (5, 6). The perpendicular bisector of AB intersects the x-axis at the point C and the y-axis at the point D.…
Answer this question and get it marked →Given that the equation kx² + (2k − 1)x + k + 1 = 0 has no real roots, find the set of possible values of k.
Answer this question and get it marked →Draw the graphs of y = 2x − 5 and y = 4 − x for −2 ≤ x ≤ 6.
Answer this question and get it marked →Find and simplify the term independent of x in the expansion of (x² − 1/(2x³))¹⁰.
Answer this question and get it marked →The function f is defined by f(x) = (1 + 2 sin²x)/cos²x for −π/2 < x < π/2. Show that f(x) can be written as a tan²x + b, where a and b are integers.
Answer this question and get it marked →DO NOT USE A CALCULATOR IN THIS QUESTION. Given that x − 3 and x + 1 are both factors of 2x³ − 3x² − 8x − 3, solve the equation 2x³ − 3x² − 8x − 3 = 0.
Answer this question and get it marked →In the diagram, AD and BC are arcs of circles with common centre O. ODC and OAB are straight lines with OA = 5 cm and AB = 4 cm. Angle BOC = θ radians. The area of the shaded…
Answer this question and get it marked →A curve is such that d²y/dx² = cos(4x − π/4). Given that dy/dx = 3/4 at the point (3π/16, 3/4) on the curve, find the equation of the curve.
Answer this question and get it marked →The diagram shows a sketch of part of the curve y = 4 + (3x − 1)⁻¹ and the line x = 9. The point A has x-coordinate 1. The tangent to the curve at A meets the x-axis at the point…
Answer this question and get it marked →The diagram shows a parallelogram OABC. The point D divides the line OC in the ratio 2 : 3. OA = a and OC = c. The point P lies on AD such that OP = m·OB and AP = n·AD, where m…
Answer this question and get it marked →