Cambridge & Pearson Edexcel Past Paper Questions

Solve the equation x³ + 1 = 6/x³.

A circle with centre C has the equation x²+y² - 10x-4y+24 = 0.

Find ∫₀^(π/2) sin θ dθ.

The polynomial p is such that p(x) = 3x³ − 7x² + ax + b, where a and b are integers. It is given that p'(-1) = 21 and that x-2 is a factor of p(x).

When ln y is plotted against x³, a straight line passing through the points (2,5) and (-8,25) is obtained.

A geometric progression has a 4th term of 8k⁶/27 and a 6th term of 32k¹⁰/243, where k is a constant. The common ratio of this geometric progression...

It is given that y = ln(3x² + 16) / (x+2).

It is given that f(x) = 2ln(3x-4), for x > a, and that f⁻¹ exists.

The diagram shows the shape OABCDEF. AOF is a straight line. OAB and OEF are sectors of a circle with centre O and radius r. Angle BOA = angle EOF....

The diagram shows the triangle OAB, where OA = a and OB = b. The point P lies on OA such that OP = (3/4)OA. The point Q lies on AB such that AQ = (...

A curve is such that its gradient at the point (x, y) is given by (5x-2)³ᐟ². The curve passes through the point (2, 32/5). Find the coordinates of ...

A curve has equation y = x²+2x-3.

In this question, k is a constant. It is given that 2x² + (3k-2)x+k = 0 has roots that are real and distinct. Find the set of possible values of k.

A sports club has the following members. 5 runners, 4 swimmers, 3 gymnasts

The coordinates of points A, B, C and D are as follows. A(-4,3) B(6, -9) C(15,10) D(14, -1) The line L has equation y = 11x-75. The perpendicular b...

Given that y = x² tan(x/2), use calculus to find the approximate change in y as x increases from π/3 to π/3 + h, where h is small.

Using an appropriate quadratic factorisation, find the first three terms in the binomial expansion of (9x²+12x+4)⁵, in ascending powers of x. You m...

The function f is defined by f(x) = 2e⁻ˣ +3 for x ∈ R. On the axes, sketch the graph of y = f(x) and hence, on the same axes, sketch the graph of y...

Solve the equation (2-3 cotx) cosx = 0 for 0 < x ≤ π/2.

In this question, all lengths are in centimetres and all angles are in radians. [Figure showing a sector AOB of a circle and a cone formed from it]...

A particle P moves in a straight line. t seconds after passing a fixed point, O, the acceleration of P, a m s⁻², is given by a = t²-2 for 0 ≤ t ≤ 4...

A geometric progression has first term a and common ratio r, where r > 0. The sum of the 2nd and 3rd terms of the progression is 168. The sum of th...

Solve the inequality |5x+2|≥3.

In this question, all lengths are in metres and time is in seconds. A particle P moves in a straight line such that its displacement s from a fixed...

Functions f and g are such that f(x) = 3x / (x+4) for x > 0 g(x)=√(x+2) for x >-2. Solve the equation fg(x) = 1.

Given that y = 4 sin 2x cos 2x, find the value of dy/dx when x = π/6.

A 4-digit number is to be formed using the digits 0, 2, 4, 5, 6 and 8. The 4-digit number must not start with 0. Any digit may be used at most once...

The volume, V, of a sphere is increasing at the constant rate of 2π cm³ s⁻¹. Find the rate of change of the surface area, S, of this sphere when th...

The first three terms of an arithmetic progression can be written as 2ln(x³), 51n(x²), 2ln(x⁷).

The diagram shows part of the curve y = 15/x - 5/x². The curve meets the x-axis at the point A. The curve has a maximum at the point B. Find the ar...

Solve the equation 3 sec 3x = √3 cosec 3x for -120° ≤ x ≤ 120°.

The first three terms, in descending powers of x, in the expansion of (3x²-a)ⁿ (1+2/x²)² can be written as 729x¹² - 972x¹⁰ + bx⁸, where a, b and n ...

The equation of a curve is given by y = 2x² + ax + 14, where a is a constant. Given that this equation can also be written as y = 2(x – 3)² + b, wh...

Sketch, on the same set of axes, the graphs of y = cos x and y = sin 2x for 0° ≤ x ≤ 180°.

Show that `cos x / (1 - sin x) + cos x / (1 + sin x) = 2 sec x.`

Factorise completely the expression 2x³ – 11x² – 20x – 7.

A curve has the equation y = 2x sin x + π/3. The curve passes through the point P(π/2, a).

Find, in ascending powers of x, the first 3 terms in the expansion of (2 – 5x)⁶, giving your answer in the form a + bx + cx², where a, b and c are ...

(a) Sets A and B are such that A = {x : sin x = 0.5 for 0° ≤ x ≤ 360°}, B = {x : cos (x − 30°) = − 0.5 for 0° ≤ x ≤ 360°}. Find the elements of

The figure shows a rectangular metal block of length 4x cm, with a cross-section which is a square of side xcm and area Acm². The block is heated a...

The diagram shows a circle, centre O, radius 4 cm, enclosed within a sector PBCDP of a circle, centre P. The circle centre O touches the sector at ...

Find `∫ (1/√(1 + x)) dx`.

Answer only one of the following two alternatives. EITHER

OR A curve has the equation `y = Ae^(2x) + Be⁻ˣ` where `x ≥ 0`. At the point where `x = 0`, `y = 50` and `dy/dx = -20`.

Show that COS X + COS X = 2 sec x. 1 - sin x 1 + sin x

A curve has the equation y = 2x sin x + π/3. The curve passes through the point P (π/2, a).

Sets A and B are such that A = {x : sin x = 0.5 for 0° ≤ x ≤ 360°}, B = {x : cos (x − 30°) = − 0.5 for 0° ≤ x ≤ 360°}. Find the elements of (i) A,

Find ∫ 1/(√1 + x) dx.

EITHER: A curve is such that dy/dx = 4x² – 9. The curve passes through the point (3, 1).

OR: A curve has the equation y = Ae²ˣ + Be⁻ˣ where x ≥ 0. At the point where x = 0, y = 50 and dy/dx = -20.