AS & A Level Mathematics (9709) — May–June 2023, Paper 12
11 questions · every question answerable online with instant point-by-point AI marking against the official mark scheme.
Start with Question 1 →The equation of a curve is such that dy/dx = 4/(x − 3)³ for x 3. The curve passes through the point (4, 5). Find the equation of the curve.
Answer this question and get it marked →The coefficient of x⁴ in the expansion of (x + a)⁶ is p and the coefficient of x² in the expansion of (ax + 3)⁴ is q. It is given that p + q = 276. Find the possible values of the…
Answer this question and get it marked →Express 4x² − 24x + p in the form a(x + b)² + c, where a and b are integers and c is to be given in terms of the constant p.
Answer this question and get it marked →Solve the equation 8x⁶ + 215x³ − 27 = 0.
Answer this question and get it marked →The diagram shows the curve with equation y = 10x^(1/2) − (5/2)x^(3/2) for x 0. The curve meets the x-axis at the points (0, 0) and (4, 0). Find the area of the shaded region.
Answer this question and get it marked →The diagram shows a sector OAB of a circle with centre O. Angle AOB = θ radians and OP = AP = x, where P lies on OB. Show that the arc length AB is 2xθ cos θ.
Answer this question and get it marked →By first expanding (cos θ + sin θ)², find the three solutions of the equation (cos θ + sin θ)² = 1 for 0 ≤ θ ≤ π.
Answer this question and get it marked →The diagram shows the graph of y = f(x), where the function f is defined by f(x) = 3 + 2 sin((1/4)x) for 0 ≤ x ≤ 2π. The grid has the x-axis marked at (1/2)π, π, (3/2)π, 2π,…
Answer this question and get it marked →The second term of a geometric progression is 16 and the sum to infinity is 100. Find the two possible values of the first term.
Answer this question and get it marked →The equation of a circle is (x − a)² + (y − 3)² = 20. The line y = (1/2)x + 6 is a tangent to the circle at the point P. Show that one possible value of a is 4 and find the other…
Answer this question and get it marked →The equation of a curve is y = k√(4x + 1) − x + 5, where k is a positive constant. Find dy/dx.
Answer this question and get it marked →