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.
(a) On the Venn diagrams below, draw sets A and B as indicated. (b) The universal set \mathcal{E} and sets P and Q are such that n(\mathcal{E}) = 2...
Sketch the graph of y = |(2x+1)(x-2)| for -2 ≤ x ≤ 3, showing the coordinates of the points where the curve meets the x- and y-axes.
The region enclosed by the curve y = 2 sin 3x, the x-axis and the line x = a, where 0 < a < 1 radian, lies entirely above the x-axis. Given that th...
Given that 2⁵ˣ × 4ʸ = 1/8, show that 5x + 2y = -3.
Matrices X, Y and Z are such that X = beginpmatrix 2 & 3 1 & 1/2 endpmatrix, Y = beginpmatrix 1 & 3 4 & 5 6 & 7 endpmatrix and Z = beginpma...
The diagram shows a circle, centre O, radius 8 cm. Points P and Q lie on the circle such that the chord PQ = 12 cm and angle POQ = θ radians.
How many different 5-digit numbers can be formed using the digits 1, 2, 4, 5, 7 and 9 if no digit is repeated?
A solid circular cylinder has a base radius of r cm and a volume of 4000 cm³.
In this question \mathbf{i} is a unit vector due East and \mathbf{j} is a unit vector due North. At 12 00 hours, a ship leaves a port P and travels...
Solve tan²x + 5 tan x = 0 for 0circ ≤ x ≤ 180circ.
Find the set of values of x for which x(x + 2) <x.
Without using a calculator, express 6(1 + √3)⁻² in the form a + b√3, where a and b are integers to be found.
On the axes below, sketch the graph of y = |(x - 4)(x + 2)| showing the coordinates of the points where the curve meets the x-axis.
The expression 2x³ + ax² + bx + 12 has a factor x - 4 and leaves a remainder of -12 when divided by x - 1. Find the value of each of the constants ...
Express 2x² - x + 6 in the form p(x - q)² + r, where p, q and r are constants to be found.
Find the coefficient of x⁵ in the expansion of (3 - 2x)⁸.
Given that a curve has equation y = 1/x + 2√x, where x > 0, find
A sector of a circle of radius r cm has an angle of θ radians, where θ < π. The perimeter of the sector is 30 cm.
Solutions to this question by accurate drawing will not be accepted. The points A(p,1), B(1, 6), C(4, q) and D(5, 4), where p and q are constants, ...
Find dy/dx when y = cos 2x sin(x/3),
Solve 2^(x²-5x) = 1/64.
The functions f and g are defined by f(x) = 2x/(x+1) for x > 0, g(x) = √(x+1) for x > -1.
Without using a calculator, express (2 + √5)² / (√5 – 1) in the form a + b√5, where a and b are constants to be found.
Find the values of k for which the line y+kx - 2 = 0 is a tangent to the curve y = 2x² – 9x + 4.
Given that x + 1 is a factor of 3x3 - 14x2 – 7x + d, show that d = 10.
Express 12x2 - 6x + 5 in the form p(x – q)² + r, where p, q and r are constants to be found.
Find and simplify the first three terms of the expansion, in ascending powers of x, of (1 – 4x)5.
State the value of u for which lgu = 0.
The line y=x-5 meets the curve x² + y² + 2x – 35 = 0 at the points A and B. Find the exact length of AB.
A curve is such that dy/dx = (2x + 1)². The curve passes through the point (4, 10).
Two variables x and y are connected by the relationship y = Abˣ, where A and b are constants. An experiment was carried out measuring values of y f...
The functions f and g are defined, for real values of x greater than 2, by f(x) = 2ˣ - 1, g(x) = x(x + 1).
A curve has equation y = x³ – 9x² + 24x.
State the period of sin 2x.
Do not use a calculator in this question. [Figure 2.1] The diagram shows the triangle ABC where angle B is a right angle, AB = (4 + 3√2) cm, BC = (...
Find the first 4 terms in the expansion of (2 + x²)⁶ in ascending powers of x.
Given that the matrix X = [2 -4; k 0], find X² in terms of the constant k.
The curve y = xy + x² – 4 intersects the line y = 3x – 1 at the points A and B. Find the equation of the perpendicular bisector of the line AB.
The polynomial f(x) = ax³ – 15x² + bx – 2 has a factor of 2x – 1 and a remainder of 5 when divided by x – 1.
The point A, where x = 0, lies on the curve y = ln(4x² + 3)/(x – 1). The normal to the curve at A meets the x-axis at the point B.
It is given that f(x) = 3e²ˣ for x ≥ 0, g(x) = (x + 2)² + 5 for x ≥ 0.
[Figure 9.1] The diagram shows parts of the line y = 3x + 10 and the curve y = x³ – 5x² + 3x + 10. The line and the curve both pass through the poi...
Solve 4 sin x = cosec x for 0° ≤ x ≤ 360°.
Given that the graph of y = (2k+ 5)x² + kx + 1 does not meet the x-axis, find the possible values of k.
Show that tan θ + cot θ / cosec θ = sec θ.
Find the inverse of the matrix (4 2 / 5 3) and hence solve the simultaneous equations 4x+2y-8 = 0, 5x + 3y - 9 = 0.
The diagram shows a circle, centre O, radius 12 cm. The points A, B and C lie on the circumference of this circle such that angle AOB is 1.7 radian...
(a) A security code is to be chosen using 6 of the following: • the letters A, B and C • the numbers 2, 3 and 5 • the symbols * and $. None of the ...
A particle moves in a straight line such that its displacement, x m, from a fixed point O after t s, is given by x = 10ln(t² + 4) – 4t.
In the diagram AB = 4a, BC = b and DC = 7a. The lines AC and DB intersect at the point X. Find, in terms of a and b,