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.
Solutions to this question by accurate drawing will not be accepted. The points A(-6, 2), B(2, 6) and C are the vertices of a triangle.
The graph of y = k(3ˣ) + c passes through the points (0, 14) and (–2, 6). Find the value of k and of c.
The function f is defined, for 0° < x < 360°, by f(x) = 1 + 3 cos 2x.
A curve has equation y = 3x + 1/(x-4)³.
Show that tan θ + cos θ / (1 + sin θ) = sec θ.
Vectors a, b and c are such that a = (4, 3), b = (2, 2) and c = (-5, 2)
On the Venn diagrams below, shade the regions indicated.
Find the set of values of k for which the line y = k(4x – 3) does not intersect the curve y = 4x² + 8x - 8.
Given that y = e^(x²), find dy/dx.
Matrices A and B are such that A = (-1 4; 7 6) and B = (2 1; 3 5)
A curve is such that dy/dx = 4x + 1/(x+1)² for x > 0. The curve passes through the point (1/2, 5/6).
The table shows values of variables V and p. V 10 50 100 200 p 95.0 8.5 3.0 1.1
The diagram shows the velocity-time graph of a particle P moving in a straight line with velocity v ms⁻¹ at time t s after leaving a fixed point. [...
How many even numbers less than 500 can be formed using the digits 1, 2, 3, 4 and 5? Each digit may be used only once in any number.
Solve 5 sin 2x + 3 cos 2x = 0 for 0° ≤ x ≤ 180°.
Show that (cos A)/(1 + sin A) + (1 + sin A)/(cos A) can be written in the form p sec A, where p is an integer to be found.
(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.