AS & A Level Mathematics (9709) — October–November 2023, Paper 11

11 questions · every question answerable online with instant point-by-point AI marking against the official mark scheme.

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Question 1 · 4 marks · 1.6 Series (binomial expansion)

Expand (1 + 3x)⁶ in ascending powers of x up to, and including, the term in x².

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Question 2 · 4 marks · 1.1 Quadratics (discriminant)

A line has equation y = 2cx + 3 and a curve has equation y = cx² + 3x − c, where c is a constant. Showing all necessary working, determine which of the following statements is…

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Question 3 · 3 marks · 1.7 Differentiation (connected rates of change)

The diagram shows a cubical closed container made of a thin elastic material which is filled with water and frozen. During the freezing process the length, x cm, of each edge of…

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Question 4 · 6 marks · 1.2 Functions (transformations)

The transformation R denotes a reflection in the x-axis and the transformation T denotes a translation of the vector (3, −1). Find the equation, y = g(x), of the curve with…

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Question 5 · 6 marks · 1.5 Trigonometry

Show that the equation 4 sin x + 5/(tan x) + 2/(sin x) = 0 may be expressed in the form a cos²x + b cos x + c = 0, where a, b and c are integers to be found.

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Question 6 · 7 marks · 1.4 Circular measure

Given that angle ACB = kπ radians, state the value of the fraction k.

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Question 7 · 7 marks · 1.6 Series (geometric progression)

The sum of the first two terms of a geometric progression is 15 and the sum to infinity is 125/7. The common ratio of the progression is negative. Find the third term of the…

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Question 8 · 9 marks · 1.1 Quadratics (substitution)

The curves with equations y = 2(2x − 3)⁴ and y = (2x − 3)² + 1 meet at points A and B. By using the substitution u = 2x − 3 find, by calculation, the coordinates of A and B.

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Question 9 · 9 marks · 1.1 Quadratics (completing the square)

Express 4x² − 12x + 13 in the form (2x + a)² + b, where a and b are constants.

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Question 10 · 11 marks · 1.8 Integration

A curve has a stationary point at (2, −10) and is such that d²y/dx² = 6x. Find dy/dx.

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Question 11 · 9 marks · 1.3 Coordinate geometry (circles)

The circle has equation (x − 4)² + (y + 1)² = 40. Parallel tangents, each with gradient 1, touch the circle at points A and B. Find the equation of the line AB, giving the answer…

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