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 masses, in grams, of plums of a certain type have the distribution N(40.4, 5.2²). The plums are packed in bags, with each bag containing 6 rand...
A shop obtains apples from a certain farm. It has been found that 5% of apples from this farm are Grade A. Following a change in growing conditions...
In the data-entry department of a certain firm, it is known that 0.12% of data items are entered incorrectly, and that these errors occur randomly ...
The score on one spin of a 5-sided spinner is denoted by the random variable X with probability distribution as shown in the table. x | 0 | 1 | 2 |...
The random variable X has the distribution Po(λ).
A random variable X has probability density function given by f(x) = { k/x² 1 ≤ x ≤ a, 0 otherwise, where k and a are positive constants.
A random sample of 100 values of a variable X is taken. These values are summarised below. n = 100 Σχ = 1556 Σχ² = 29004 Calculate unbiased estimat...
Each day at the gym, Sarah completes three runs. The distances, in metres, that she completes in the three runs have the independent distributions ...
The number of customers who visit a particular shop between 9.00 am and 10.00 am has the distribution Po(λ). In the past the value of λ was 5.2. Fo...
The random variable A has the distribution Po(1.5). A₁ and A₂ are independent values of A.
Sunita has a six-sided die with faces marked 1, 2, 3, 4, 5, 6. The probability that the die shows a six on any throw is p. Sunita throws the die 50...
The length, X centimetres, of worms of a certain type is modelled by the probability density function f(x) = { (1/125)(10-x)(x - 5) 5 ≤ x ≤ 10,...
A market researcher is investigating the length of time that customers spend at an information desk. He plans to choose a sample of 50 customers on...
Express 16x² – 24x + 10 in the form (4x + a)² + b.
The graph of y = f(x) is transformed to the graph of y = 2f(x – 1). Describe fully the two single transformations which have been combined to give ...
The equation of a curve is y = (x − 3)√x + 1 + 3. The following points lie on the curve. Non-exact values are rounded to 4 decimal places. A (2, k)...
The coefficient of x in the expansion of (4x + 10/x)³ is p. The coefficient of 1/x in the expansion of (2x + k/x)⁵ is q. Given that p = 6q, find th...
The function f is defined by f(x) = 2x² + 3 for x ≥ 0.
Points A and B have coordinates (8, 3) and (p, q) respectively. The equation of the perpendicular bisector of AB is y = −2x + 4. Find the values of...
The point A has coordinates (1, 5) and the line l has gradient −2/3 and passes through A. A circle has centre (5, 11) and radius √52.
The first, second and third terms of an arithmetic progression are a, 3/2a and b respectively, where a and b are positive constants. The first, sec...
The diagram shows part of the curve with equation y² = x – 2 and the lines x = 5 and y = 1. The shaded region enclosed by the curve and the lines i...
Prove the identity (1 + sin x) / (1 - sin x) - (1 - sin x) / (1 + sin x) = 4 tan x / cos x
The gradient of a curve is given by dy/dx = 6(3x – 5)³ – kx², where k is a constant. The curve has a stationary point at (2, -3.5).
The diagram shows a cross-section of seven cylindrical pipes, each of radius 20 cm, held together by a thin rope which is wrapped tightly around th...
Solve the equation ln(2 + x) – ln x = 2 ln 3.
The solutions of the equation 5|x| = 5 – 2x are x = a and x = b, where a < b. Find the value of |3a – 1| + |7b – 1|.
Solve the equation sin(2θ + 30°) = 5 cos(2θ + 60°) for 0° < θ < 180°.
Find the exact value of ∫₀² 6e²ˣ⁺¹ dx.
Find the quotient when x⁴ – 32x + 55 is divided by (x – 2)² and show that the remainder is 7.
The diagram shows the curve with equation y = (ln x)² – 2 ln x. The curve crosses the x-axis at the points A and B, and has a minimum point M.
The diagram shows the curve with parametric equations x = 4t + e²ᵗ, y = 6t sin 2t, for 0 ≤ t ≤ 1. The point P on the curve has parameter p and y-co...
Solve the equation In(2 + x) – lnx = 2 ln 3.
Find the exact value of ∫₀² 6e^(2x+1) dx.
The diagram shows the curve with equation y = (lnx)² – 2 lnx. The curve crosses the x-axis at the points A and B, and has a minimum point M. [Figur...
The diagram shows the curve with parametric equations x = 4t + e^(2t), y = 6t sin 2t, for 0 ≤ t ≤ 1. The point P on the curve has parameter p and y...
Solve the inequality 2|3x – 1| < |x + 1|.
Find the real root of the equation (2eˣ + e⁻ˣ) / (2 + eˣ) = 3, giving your answer correct to 3 decimal places. Your working should show clearly tha...
Given that cos(x – 30°) = 2 sin(x + 30°), show that tan x = (2-√3) / (1-2√3)
Prove that (1 - cos 2θ) / (1 + cos 2θ) = tan² θ.
Solve the equation z² – 2piz – q = 0, where p and q are real constants.
The parametric equations of a curve are x = ln(2 + 3t), y = t / (2 + 3t)
The diagram shows the curve y = (tan⁻¹ x) / √x and its maximum point M where x = a. [Figure 7.1]
With respect to the origin O, the points A and B have position vectors given by OA = (1, 2, 1) and OB = (3, 1, -2). The line l has equation r = (2,...
The equation of a curve is y = x⁻² ln x for x > 0. The curve has one stationary point.
The variables x and t satisfy the differential equation dx/dt = x²(1 + 2x), and x = 1 when t = 0. Using partial fractions, solve the differential e...
Solve the inequality |2x – 1| < 3|x + 1|.
The variables x and y satisfy the equation x = A(3⁻ʸ), where A is a constant.
Using integration by parts, find the exact value of ∫₀² tan⁻¹(½x)dx.
The complex number u is given by u = 10 – 4√6i. Find the two square roots of u, giving your answers in the form a + ib, where a and b are real and ...