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.
Sales of cell phones at a certain shop occur singly, randomly and independently.
The diagram shows the graph of the probability density function, f, of a random variable X . The graph is a quarter circle entirely in the first qu...
Every July, as part of a research project, Rita collects data about sightings of a particular kind of bird. Each day in July she notes whether she ...
A random variable X has the distribution Po(145).
Henri wants to choose a random sample from the 804 students at his college. He numbers the students from 1 to 804 and then uses random numbers gene...
A student wishes to estimate the proportion, p, of students at her college who have exactly one brother. She surveys a random sample of 50 students...
A random variable X has the distribution N(10, 12). Two independent values of X, denoted by X₁ and X₂, are chosen at random.
The number of goals scored by a sports team in the first half of any match has the distribution X~ Po(3.1). The number of goals scored by the same ...
The masses of cereal boxes filled by a certain machine have mean 510 grams. An adjustment is made to the machine and an inspector wishes to test wh...
The probability density function, f, of a random variable X is given by [k(1+cosx) f(x) = 0 0 ≤ x ≤ π, otherwise, where k is a constant.
The random variable X has the distribution B (4000, 0.001).
The widths, wcm, of a random sample of 150 leaves of a certain kind were measured. The sample mean of w was found to be 3.12 cm. Using this sample,...
The masses in kilograms of large and small bags of cement have the independent distributions N(50, 2.4) and N(26, 1.8) respectively. Find the proba...
In this question you should not use an approximating distribution. At an election in Menham last year, 24% of voters supported the Today Party. A s...
A random variable X has probability density function f given by f(x) = {ax-x^3 for 0 ≤ x ≤ √2, 0 otherwise, where a is a constant.
The numbers of green sweets in 200 randomly chosen packets of Frutos are summarised in the table. Number of green sweets 0 1 2 3 > 3 Number of pack...
The independent random variables X and Y have the distributions Po(1.9) and Po(2.2) respectively.
The diagram shows the graphs with equations y = f(x) and y = g(x). Describe fully a sequence of two transformations which transforms the graph of y...
Find the coordinates of the points of intersection of the curve and the line with equations 2xy+5y2 = 24 and 2x+y+4 = 0.
The coefficient of x7 in the expansion of (px²+4/x)5 is 1280. Find the value of the constant p.
A point P is moving along the curve with equation y = ax^3/2 – 12x in such a way that the x-coordinate of P is increasing at a constant rate of 5 u...
The equation of a curve is y = 4 cos2x + 3 for 0 ≤ x ≤ 2π.
The diagram shows the curve with equation y = 9/(5x+4)^1/2 and the line y = 6-3x. The line and the curve intersect at the point P which has y-coord...
Prove the identity tanθ+7 / tan²θ−3 = sinθcosθ+7cos²θ / 1−4cos²θ
The diagram shows the circle with equation x²+y² – 14x+8y+36 = 0 and the line y=-2. The line intersects the circle at the points A and B. The centr...
The equation of a curve is such that d²y/dx² = 24/x³ . It is given that the curve has a stationary point at (-2, 19).
The first, second and third terms of an arithmetic progression are 4k, k² and 8k respectively, where k is a non-zero constant.
Express x² +4x+2 in the form (x+a)² + b, where a and b are integers.
Given that y = 6x cos(x²+1), find an expression for dy/dx.
Use logarithms to solve the inequality 4^x < 0.05. Give your answer in the form x < a, where the value of a is correct to 3 significant figures.
Sketch, on a single diagram, the graphs of y = 3e^-2x and y = secx for values of x such that 0 < x < π/2.
The diagram shows the curve with equation y = 6e^2x – e^3x. The shaded region is bounded by the axes and the curve.
The polynomial p(x) is defined by p(x) = ax³ + bx² - ax-24, where a and b are constants. It is given that (2x-3) is a factor of p(x) and that the r...
The parametric equations of a curve are x = (2t+1)/(3t+4), y = 2ln(3t+4), where t > -4/3.
Prove that sin² 2x+4 cos²x cos2x=4cos⁴x.
Show that ∫ from 2 to 11 (8 / (4x+1)) dx = ln a, where a is an integer to be found.
Sketch on the same diagram the graphs of y = |2x-9| and y=4x-5.
Find the coordinates of the stationary points of the curve with equation y = 8x / (2x+3) - 6x+5.
The diagram shows parts of the curves with equations y = 4e⁻²ˣ and y = 1+0.5 sin3x. Point P is a point of intersection of the curves, and the shade...
The polynomial p(x) is defined by p(x) = ax⁴ + bx³ +13x²-35x+15, where a and b are constants. It is given that (2x−1) and (x-3) are factors of p(x).
A curve has equation (x²-3)lny+6x = 14.
Express 4 cosθsin(θ+30°) in the form Rcos (2θ-α)+k, where R > 0, 0° < α < 90° and k is a constant.
Show that ∫₂¹¹ (8 / (4x+1)) dx = ln a, where a is an integer to be found.
Find the coordinates of the stationary points of the curve with equation y = 8x/(2x+3) - 6x + 5.
Express 4 cosθsin(θ+30°) in the form Rcos(2θ-α)+k, where R > 0, 0° < α < 90° and k is a constant.
Sketch the graph of y = |2x-3|.
It is given that 2 lnp+ln(p-1)-½ln(q+1) = 3. Find q in terms of p.
Find the complex numbers z for which z+5i / z-5 is real and |z|= √17. Give your answers in the form z = x+iy, where x and y are real.
The parametric equations of a curve are x = etant, y = 3 tan²t. Find the equation of the tangent to the curve at the point (e, 3). Give your answer...
The polynomial 3x³ +pax²+7a²x+qa³ is denoted by f(x), where p, q and a are constants and a ≠ 0. When f(x) is divided by (x+2a) the remainder is -22...