Cambridge & Pearson Edexcel Past Paper Questions
Browse 35,704 questions from Cambridge O-Level & A-Level and Pearson Edexcel IGCSE & IAL exams. Click any question to practice.
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).
A function f is defined by f : x → 5 – 2 sin 2x for 0 ≤ x ≤ π.
Find the term independent of x in the expansion of (2x - 1/(4x²))⁹.
A function f is defined by f : x → 4 – 5x for x ∈ R.
Each year, the value of a certain rare stamp increases by 5% of its value at the beginning of the year. A collector bought the stamp for $10000 at ...
The diagram shows a semicircle with centre O and radius 6 cm. The radius OC is perpendicular to the diameter AB. The point D lies on AB, and DC is ...
Show that the equation cos 2x(tan² 2x + 3) + 3 = 0 can be expressed as 2 cos² 2x + 3 cos 2x + 1 = 0.
This question concerns properties of functions involving sine.
Points A and B lie on the curve y = x² – 4x + 7. Point A has coordinates (4, 7) and B is the stationary point of the curve. The equation of a line ...
A curve is such that dy/dx = -x² + 5x - 4.
The diagram shows a trapezium OABC in which OA is parallel to CB. The position vectors of A and B relative to the origin O are given by OA = (2, -2...
The diagram shows part of the curve y = √(5x – 1) and the normal to the curve at the point P (2, 3). This normal meets the x-axis at Q. [Figure X.X]
Solve the equation ln(3x + 1) – ln(x + 2) = 1, giving your answer in terms of e.
Solve the equation 5 cos θ(1 + cos 2θ) = 4 for 0° ≤ θ ≤ 360°.
It is given that the variable x is such that 1.3^(2x) < 80 and |3x-1| > |3x – 10| Find the set of possible values of x, giving your answer in the ...
Find ∫ (4 + sin²θ) / (1 - sin²θ) dθ.
The polynomial p(x) is defined by p(x) = ax³ + bx² + 37x + 10 where a and b are constants. It is given that (x + 2) is a factor of p(x). It is also...
The parametric equations of a curve are x = 2e^(2t) + 4e^t, y = 5te^(2t).
The diagram shows the curve [Figure X.X] y = x² + 3x + 1 + 5 cos (x/2). The curve crosses the y-axis at the point P and the gradient of the curve a...
Use logarithms to solve the equation 5³ˣ⁻¹ = 2⁴ˣ, giving your answer correct to 3 significant figures.
It is given that x satisfies the equation |x + 1| = 4. Find the possible values of |x + 4| - |x - 4|.
The equation of a curve is y = tan ½x + 3 sin ½x. The curve has a stationary point M in the interval π < x < 2π. Find the coordinates of M, giving ...
The polynomials p(x) and q(x) are defined by p(x) = x³ + x² + ax - 15 and q(x) = 2x³ + x² + bx + 21, where a and b are constants. It is given that ...
The diagram shows the curve y = 4e⁻²ˣ and a straight line. The curve crosses the y-axis at the point P. The straight line crosses the y-axis at the...
Find the exact value of ∫(from 0 to π/4) sinx(4 sinx + 6 cos x) dx.
The equation of a curve is x² + 4xy + 2y² = 7.
It is given that the variable x is such that 1.3²ˣ < 80 and |3x-1| > |3x – 10. Find the set of possible values of x, giving your answer in the form...
Find ∫ (4 + sin² θ) / (1 − sin² θ) dθ.
The parametric equations of a curve are x = 2e²ᵗ + 4eᵗ, y = 5te²ᵗ.