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 lengths of a random sample of 50 roads in a certain region were measured. Using the results, a 95% confidence interval for the mean length, in ...
A factory owner models the number of employees who use the factory canteen on any day by the distribution B(25, p). In the past the value of p was ...
A population is normally distributed with mean 35 and standard deviation 8.1 . A random sample of size 140 is chosen from this population and the s...
A machine puts sweets into bags at random. The numbers of lemon and orange sweets in a bag have the independent distributions Po(3.7) and Po(2.6) r...
The time, X hours, taken by a large number of people to complete a challenge is modelled by the probability density function given by f(x) = { 2/...
The heights of one-year-old trees of a certain variety are known to have mean 2.3 m. A scientist believes that, on average, trees of this age and v...
A random variable X has probability density function f defined by f(x) = { a/x² - 18/x³ for 2 ≤ x ≤ 3, 0 otherwise, where a is a constant.
Express 9x²-36x+8 in the form p(x+q)²+r, where p, q and r are constants.
Find the term independent of x in the expansion of (2x² - 3/x)⁶
The graph of y = f(x) is transformed to the graph of y = f(3x) +2. Describe fully the two transformations which have been combined to give the resu...
The equation of a curve is such that dy/dx = kx³ + 2/x², where k is a constant. The curve passes through the point S (2, 20) and the gradient of th...
The equation of a curve is y = 4x^(1/2) - x. The curve has a maximum point when x = a and crosses the x-axis at the point with coordinates (b, 0), ...
Sketch the graph of y = 3 sinx+2 for 0 ≤ x ≤ 2π.
The coordinates of the points P and Q are (1, 1) and (7, 11) respectively. The line segment PQ forms a diameter of a circle.
The first three terms of a geometric progression are a, b and c respectively, where a, b and c are positive constants. The first three terms of an ...
The function f is defined by f(x) = 4/(3x-6)² + 1/(3x-6)³ for x > 2. The function g is defined by g(x) = 4x-3 for x > a.
The diagram shows a circle with centre A and radius r passing through points B, C and D. A larger circle of radius s has centre C and passes throug...
Find ∫ 6 sin²x dx.
Solve the equation e²ˣ (e²ˣ – 8) = 48.
Solve the equation |2x-3|=|5x+2|.
Solve the equation cotθ tan(θ+45°) = 7 for 0° < θ < 90°.
The diagram shows the curve with equation y = 8e⁻¹/²ˣ - 1. The curve meets the axes at the points A and B. The shaded region is bounded by the curv...
A curve has parametric equations x = tan θ, y = sin θ – 2 sin³θ, for 0 < θ < ½π.
The polynomial p(x) is defined by p(x) = 2x⁴ + kx³ + kx² + 17x + 18, where k is a constant. It is given that (x+2) is a factor of p(x).
The equation of a curve is y = 4e¹⁻²ˣ √(3x-1).
Solve the equation ln(3x+5) – ln(x - 2) = 4. Give your answer in an exact form.
Solve the equation 2tan²θ+3 secθ = 18 for −180° < θ < 180°.
Solve the inequality | 3x-4|<|2x+5|.
The polynomial p(x) is defined by 4 p(x) = x² - 10x³ +20x² - 30x+40.
The diagram shows the curve with equation y = 4 cos2x+8 sinx for 0 ≤ x ≤ π. The maximum points on the curve are denoted by A and B, and the shaded ...
Given that ∫[from -2a to a] (½ e²⁸+¼ e⁻⁸)dx = 5, where a is a positive constant, show that a = ½ ln(10+½ e⁻²⁸+¼ e⁻⁴⁸).
A curve has equation 5x²y +4e² - 7x+10 = 0.
Find ∫ 6 sin²x dx.
Solve the equation cotθ tan (θ+45°) = 7 for 0° < θ < 90°.
The diagram shows the curve with equation y = 8e⁻¹⁄₂ˣ - 1. The curve meets the axes at the points A and B. The shaded region is bounded by the curv...
A curve has parametric equations x = tan θ, y = sin θ-2 sin³θ, for 0 < θ < ½π.
The equation of a curve is y = 4e¹⁻²ˣ √3x-1.
Find the exact value of ∫ from 1 to 2 of ln 3x dx. Give your answer in the form a+lnb, where a and b are integers.
Show that the equation log₄(2x + 1) = 2log₄(3x-1)-2 can be written as a quadratic equation in x.
Express 3√2sin(x+45°) + cosx in the form Rcos(x−α), where R > 0 and 0° < α < 90°.
The diagram shows the graph of y = e^(sin 2x) cos 4x for 0 < x < 1/2π, and its maximum point M. [Figure 4.1]
Solve the quadratic equation (2+i)w²+4w+2-i = 0. Give your answers in the form x+iy, where x and y are real.
The parametric equations of a curve are x = t² - ln(t+1), y = t/(2t+1)
The variables x and y satisfy the differential equation (x²+1) dy/dx = kxe^(-2y), where k is a constant. It is given that y = 0 when x = 0 and that...
By sketching a suitable pair of graphs, show that the equation sec 2x = -e^(-x) has only one root in the interval 0 < x < 1/2π.
Let f(x) = (x²+2x-11) / ((3+x)(2+x²)).
With respect to the origin O, the points A, B, C and D have position vectors given by OA = (1 5 3), OB = (0 4 1), OC = (1 -3 1) and OD = (3 -5 4). ...
Sketch the graph of y = |x+3a|, where a is a positive constant.
Solve the equation 3 × 2x+1 = 4 × 32x-3. Give your answer correct to 3 significant figures.
The shaded region in the Argand diagram, bounded by a line and a circle, represents the complex numbers z satisfying Rez < 2 and |z-(3+i)|≤2. The p...