Cambridge & Pearson Edexcel Past Paper Questions

A circle C has equation x^2 + y^2 - 4x + 6y - 12 = 0. (a) Find the coordinates of the centre of C and the radius of C.

A circle C has equation x^2 + y^2 - 4x + 6y - 12 = 0. (b) The point P(5, -7) lies on C. Find the equation of the tangent to C at the point P.

Find ∫ ( 2x³ - 3 + 4/√x ) dx, giving each term in its simplest form.

A curve has equation y = x^2(x - 2) + 3. (a) Find dy/dx.

A curve has equation y = x^2(x - 2) + 3. (b) Find the exact coordinates of the stationary points of the curve.

A rectangular box has an open top. The box has length 3x cm, width x cm and height h cm. The volume of the box is 2250 ~cm³.

The equation e^(x) + 2x - 3 = 0 has a single root α. (a) Show that α lies between 0.5 and 0.6. (b) Using x₀ = 0.55 as a first approximation, apply...

Find the first four terms in ascending powers of x of the binomial expansion of (1 - x/2)¹⁰.

f(x) = x³ + px² + qx + 6 Given that (x + 1) is a factor of f(x) and that when f(x) is divided by (x - 2) the remainder is 30.

The circle C has equation x^2 + y^2 - 6x + 8y - 24 = 0. (a) Find the coordinates of the centre of C and the radius of C. (b) The line L has equati...

The curve C has equation y = 2e^x + 3. The line L has equation y = 7.

Prove that log_a(x) = (log_b(x)) / (log_b(a)), where a, b and x are positive and a ≠ 1, b ≠ 1.

The amount of a drug, D mg, in a patient's bloodstream t hours after it has been administered, is given by the formula D = 10e^(-0.2t).

Given that for all real values of x, 3x² + bx + 10 = A(x-2)² + C, where A, b and C are constants.

A rectangle has width x cm and length y cm. The perimeter of the rectangle is 20 cm.

Figure 1 shows a sketch of the curve C with equation y = 2^x. The curve C crosses the y-axis at the point A. The point B has x-coordinate 4 and li...

A curve has equation y = e^(-2x) sin x. (a) Show that dy/dx = e^(-2x) (cos x - 2sin x). (b) Find the x-coordinates of the stationary points of the ...

Solutions to this question by calculator technology are not acceptable. (a) Show that 2sin x tan x - 3 = 0 can be written as 2sin² x - 3cos x = 0.

Solve, for 0 ≤ x < 360°, the equation 2sin(x + 30°) = 1.

The curve C has equation y = (2x + 3)^3. (a) Find dy/dx. (b) Find the equation of the tangent to the curve C at the point where x = -1. Give your a...

Given that log₂ a = 3 and log₂ b = 5, find the value of log₂ (a²b).

A curve C has equation y = x³ - 6x² + 5x - 2.

A population of insects, P, is modelled by the differential equation dP/dt = kP(1000-P), where t is the time in days and k is a positive constant. ...

Use the substitution u = sec x to find the exact value of ∫(from 0 to π/3) (tan x)(sec^3 x) dx.

Find ∫ x² e³ˣ dx.

The curve C has parametric equations x = 3 cos t, y = 2 sin t, 0 ≤ t < 2π.

The value of a car, V, in pounds, can be modelled by the equation V = Ae^(-kt), where t is the age of the car in years, and A and k are positive co...

Given that θ is small and measured in radians, use the small angle approximations to show that (cos(3θ) - 1)/(θ sin(2θ)) ≈ -9/4.

Error: Source documents (Pearson Edexcel IAL Question Paper, Mark Scheme, and Examiner Report for Pure Mathematics 4 (WMA14)) were not provided in ...

Figure 1 shows a sketch of the curve with equation y = x² ln x, x>0. The curve has a minimum point M.

Relative to a fixed origin O, the points A and B have position vectors a = beginpmatrix 2 3 -4 endpmatrix and b = beginpmatrix 4 -2 3 endpm...

The amount of a drug in a patient's bloodstream, D mg, t hours after the drug has been administered, is modelled by the differential equation dD/dt...

The curve C has equation y = (2x + 1)e^(-2x). (b) Hence find the exact coordinates of the stationary point of C.

Show that ∫(from 1 to 4) (x + 4)/(x(x + 2)) dx = ln(k), where k is a rational number to be found.

A curve C has parametric equations x = 3cos(t) + 2, y = 4sin(t) - 1, for 0 ≤ t < 2π. (a) Show that the Cartesian equation of C is (x - 2)²/9 + (y ...

A curve C has parametric equations x = 3cos(t) + 2, y = 4sin(t) - 1, for 0 ≤ t < 2π. (b) Hence, sketch the curve C, clearly indicating the coordin...

With respect to a fixed origin O, the lines L₁ and L₂ are given by the equations: L₁: r = ⟨1, 2, -1⟩ + λ⟨-2, 1, 3⟩ L₂: r = ⟨-1, 1, 4⟩ + μ⟨0, 1, -1...

With respect to a fixed origin O, the lines L₁ and L₂ are given by the equations: L₁: r = ⟨1, 2, -1⟩ + λ⟨-2, 1, 3⟩ L₂: r = ⟨-1, 1, 4⟩ + μ⟨0, 1, -1...

The value, V, of a product, t years after it was launched, is modelled by the differential equation dV/dt = kV/(t + 1), where k is a constant. Giv...

The value, V, of a product, t years after it was launched, is modelled by the differential equation dV/dt = kV/(t + 1), where k is a constant. Giv...

The value, V, of a product, t years after it was launched, is modelled by the differential equation dV/dt = kV/(t + 1), where k is a constant. (c)...

Use the substitution u = sec(x) to show that ∫tan(x)secⁿ(x) dx = (secⁿ(x))/n + C for n ≠ 0.