Cambridge & Pearson Edexcel Past Paper Questions

A function f is such that f(x) = (√(x + 3) / 2) + 1, for x ≥ −3.

The diagram shows a plan for a rectangular park ABCD, in which AB = 40 m and AD = 60 m. Points X and Y lie on BC and CD respectively and AX, XY and...

The line y = x/k + k, where k is a constant, is a tangent to the curve 4y = x² at the point P.

The diagram shows a triangle ABC in which A has coordinates (1, 3), B has coordinates (5, 11) and angle ABC is 90°. The point X (4, 4) lies on AC. ...

Show that the equation 2 cos x = 3 tan x can be written as a quadratic equation in sin x.

The position vectors of the points A and B, relative to an origin O, are given by OA = (1, 0, 2) and OB = (k, -k, 2k), where k is a constant.

In a geometric progression, all the terms are positive, the second term is 24 and the fourth term is 13½. Find the first term,

The diagram shows part of the curve y = 9/(2x + 3), crossing the y-axis at the point B (0, 3). The point A on the curve has coordinates (3, 1) and ...

A curve is defined for x > 0 and is such that dy/dx = x + 4/x². The point P (4, 8) lies on the curve.

The diagram shows a sector of a circle with centre O and radius 20 cm. A circle with centre C and radius x cm lies within the sector and touches it...

Given that cosx = p, where x is an acute angle in degrees, find, in terms of p,

Fig. 1 shows a hollow cone with no base, made of paper. The radius of the cone is 6 cm and the height is 8 cm. The paper is cut from A to O and ope...

The equation of a curve is y = 2 / √(5x-6)

Relative to an origin O, the position vectors of points A and B are given by OA = i + 2j and OB = 4i + pk.

The diagram shows a rectangle ABCD in which point A is (0, 8) and point B is (4, 0). The diagonal AC has equation 8y + x = 64. Find, by calculation...

In the diagram, S is the point (0, 12) and T is the point (16, 0). The point Q lies on ST, between S and T, and has coordinates (x, y). The points ...

An athlete runs the first mile of a marathon in 5 minutes. His speed reduces in such a way that each mile takes 12 seconds longer than the precedin...

A function f is defined by f : x → 3 cos x − 2 for 0 ≤ x ≤ 2π.

The diagram shows part of the curve y = 8/x + 2x and three points A, B and C on the curve with x-coordinates 1, 2 and 5 respectively.

A curve has equation y = 2x² – 3x.

The diagram shows part of the curve y = x² + 1. Find the volume obtained when the shaded region is rotated through 360° about the y-axis. [Figure w...

The diagram shows a triangle AOB in which OA is 12 cm, OB is 5 cm and angle AOB is a right angle. Point P lies on AB and OP is an arc of a circle w...

Find the first 3 terms, in ascending powers of x, in the expansion of (1 + x)⁵.

A curve has equation y = 12 / (3-2x)

Show that the equation 1 + sin x tan x = 5 cos x can be expressed as 6 cos²x - cos x − 1 = 0.

The equation of a curve is y = x³ + ax² + bx, where a and b are constants.

The diagram shows a pyramid OABCX. The horizontal square base OABC has side 8 units and the centre of the base is D. The top of the pyramid, X, is ...

The sum, Sₙ, of the first n terms of an arithmetic progression is given by Sₙ = 32n – n². Find the first term and the common difference.

The diagram shows a trapezium ABCD in which AB is parallel to DC and angle BAD is 90°. The coordinates of A, B and C are (2, 6), (5, −3) and (8, 3)...

A curve is such that d²y/dx² = 24/x³ - 4. The curve has a stationary point at P where x = 2.

The function f : x → 6 − 4 cos(½x) is defined for 0 ≤ x ≤ 2π.

Functions f and g are defined by f: x → 3x + 2, x ∈ R, g: x → 4x – 12, x ∈ R. Solve the equation f⁻¹(x) = gf(x).

In the expansion of (x + 2k)⁷, where k is a non-zero constant, the coefficients of x⁴ and x are equal. Find the value of k.

[Figure 1] shows an open tank in the shape of a triangular prism. The vertical ends ABE and DCF are identical isosceles triangles. Angle ABE = angl...

Prove the identity `(1/(sin x) - 1/(tan x))² = (1 - cos x) / (1 + cos x)`

The diagram shows a metal plate OABC, consisting of a right-angled triangle OAB and a sector OBC of a circle with centre O. Angle AOB = 0.6 radians...

Points A, B and C have coordinates A (−3, 7), B (5, 1) and C (−1, k), where k is a constant.

Relative to an origin O, the position vectors of points A, B and C are given by `OA = (0, 2, -3)` `OB = (2, 5, -2)` `OC = (3, p, q)`

The function f is defined, for x ∈ R, by f : x → x² + ax + b, where a and b are constants.

The curve `y = f(x)` has a stationary point at `(2, 10)` and it is given that `f'(x) = 12/x³`.

The diagram shows part of the curve `y = √(9 – 2x²)`. The point P (2, 1) lies on the curve and the normal to the curve at P intersects the x-axis a...

A curve is such that dy/dx = 8/√(4x + 1). The point (2, 5) lies on the curve. Find the equation of the curve.

Express the equation sin 2x + 3 cos 2x = 3(sin 2x – cos 2x) in the form tan 2x = k, where k is a constant.

A curve has equation y = 2x² – 6x + 5.

In the expansion of (3 – 2x) (1 + x/2)^n, the coefficient of x is 7. Find the value of the constant n and hence find the coefficient of x².

The line x/a + y/b = 1, where a and b are positive constants, intersects the x- and y-axes at the points A and B respectively. The mid-point of AB ...

[Figure 6.1] The diagram shows a metal plate ABCD made from two parts. The part BCD is a semicircle. The part DAB is a segment of a circle with cen...

The equation of a curve is y = 2 + 3/(2x – 1).

How far will he travel on May 15th?

Relative to an origin O, the position vectors of the points A, B and C are given by OA = (-2, 3, -1), OB = (-2, 6, 5) and OC = (2, -2, 6).