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) Find the number of different 3-digit numbers greater than 300 that can be made from the digits 1, 2, 3, 4, 6, 8 if (b) A team of 5 is chosen fr...
In Jimpuri the weights, in kilograms, of boys aged 16 years have a normal distribution with mean 61.4 and standard deviation 12.3. In Brigville the...
A statistics student asks people to complete a survey. The probability that a randomly chosen person agrees to complete the survey is 0.2. Find the...
Tien measured the arm lengths, x cm, of 20 people in his class. He found that Σx = 1218 and the standard deviation of x was 4.2. Calculate Σ(x – 45...
At the end of a revision course in mathematics, students have to pass a test to gain a certificate. The probability of any student passing the test...
A fair die with faces numbered 1, 2, 2, 2, 3, 6 is thrown. The score, X, is found by squaring the number on the face the die shows and then subtrac...
The number of Olympic medals won in the 2012 Olympic Games by the top 27 countries is shown below. 104 88 82 65 44 38 35 34 28 28 18 18 17 17 14 13...
A car park has spaces for 18 cars, arranged in a line. On one day there are 5 cars, of different makes, parked in randomly chosen positions and 13 ...
Josie aims to catch a bus which departs at a fixed time every day. Josie arrives at the bus stop T minutes before the bus departs, where T ~ N(5.3,...
Find the coefficient of 1/x² in the expansion of (3x + 2/(3x²))⁷.
Showing all necessary working, find ∫₁⁴ (√x + 2/√x) dx.
The diagram shows part of the curve y = x(9 – x²) and the line y = 5x, intersecting at the origin O and the point R. Point P lies on the line y = 5...
Functions f and g are defined by f: x → 2 – 3 cos x for 0 ≤ x ≤ 2π, g: x → ½x for 0 ≤ x ≤ 2π.
The first three terms of an arithmetic progression are 4, x and y respectively. The first three terms of a geometric progression are x, y and 18 re...
The diagram shows a triangle ABC in which BC = 20 cm and angle ABC = 90°. The perpendicular from B to AC meets AC at D and AD = 9 cm. Angle BCA = θ°.
The diagram shows a solid cylinder standing on a horizontal circular base with centre O and radius 4 units. Points A, B and C lie on the circumfere...
The diagram shows an isosceles triangle ACB in which AB = BC = 8 cm and AC = 12 cm. The arc XC is part of a circle with centre A and radius 12 cm, ...
The function f is defined by f : x → 2x² – 12x + 7 for x ∈ R.
The equation of a curve is y = 2x + 12/x and the equation of a line is y + x = k, where k is a constant.
The diagram shows part of the curve y = 3√(4x + 1) – 2x. The curve crosses the y-axis at A and the stationary point on the curve is M.
Solve the equation |9x – 2| = |3x + 2|.
Show that ∫₁⁷ (6 / (2x + 1)) dx = ln 125.
Solve the equation sec² θ = 3 cosec θ for 0° < θ < 180°.
The diagram shows the curve with equation y = x⁴ + 2x³ + 2x² – 12x – 32. The curve crosses the x-axis at points with coordinates (α, 0) and (β, 0)....
A curve has parametric equations x = t + ln(t + 1), y = 3te²ᵗ.
The diagram shows the curve with equation y = √(1 + 3cos²(x)) for 0 ≤ x ≤ π. The region R is bounded by the curve, the axes and the line x = π. [Fi...
The diagram shows the curve with equation y = sin 2x + 3 cos 2x for 0 ≤ x ≤ π. At the points P and Q on the curve, the gradient of the curve is 3. ...
Solve the inequality |3x – 5| < 2|x|.
Given that 9x + 3x = 240, find the value of 3x and hence, using logarithms, find the value of x correct to 4 significant figures.
The diagram shows the curve with equation y = 5 sin 2x – 3 tan 2x for values of x such that 0 < x < (1/2)π. Find the x-coordinate of the stationary...
Find the gradient of the curve 4x + 3ye2x + y² = 10 at the point (0, 2).
The curve with equation y = 5e2x – 8x2 – 20 crosses the x-axis at only one point. This point has coordinates (p, 0).
Show that ∫(from 1 to 6) (12 / (3x + 2)) dx = ln 256.
Use the factor theorem to show that (2x + 3) is a factor of 8x³ + 4x² - 10x + 3.
Show that ∫₇₁ (6 / (2x + 1)) dx = ln 125.
The diagram shows the curve with equation y = √(1 + 3cos²(x/2)) for 0 ≤ x ≤ π. The region R is bounded by the curve, the axes and the line x = π. [...
Find the set of values of x satisfying the inequality 2|2x – a| < |x + 3a|, where a is a positive constant.
Showing all necessary working, solve the equation (2eˣ + e⁻ˣ) / (eˣ - e⁻ˣ) = 4, giving your answer correct to 2 decimal places.
By sketching a suitable pair of graphs, show that the equation x³ = 3 − x has exactly one real root.
The parametric equations of a curve are x = 2 sin θ + sin 2θ, y = 2 cos θ + cos 2θ, where 0 < θ < π.
The coordinates (x, y) of a general point on a curve satisfy the differential equation x dy/dx = (2 − x²)y. The curve passes through the point (1, ...
Show that the equation (√2) cosec x + cot x = √3 can be expressed in the form R sin(x − α) = √2, where R > 0 and 0° < α < 90°.
The diagram shows the curve y = 5 sin²x cos³x for 0 ≤ x ≤ ½π, and its maximum point M. The shaded region R is bounded by the curve and the x-axis. ...
Showing all necessary working, express the complex number (2 + 3i) / (1 − 2i) in the form re^(iθ), where r > 0 and –π < θ < π. Give the values of r...
Let f(x) = (6x² + 8x + 9) / ((2 − x)(3 + 2x)²).
The planes m and n have equations 3x + y − 2z = 10 and x − 2y + 2z = 5 respectively. The line l has equation r = 4i + 2j + k + λ(i + j + 2k).
Solve the inequality 3|2x – 1| > |x + 4|.
Showing all necessary working, solve the equation sin(θ – 30°) + cos θ = 2 sin θ, for 0° < θ < 180°.
Find ∫ (ln x)/x³ dx.
Showing all necessary working, solve the equation (eˣ + e⁻ˣ)/(eˣ + 1) = 4, giving your answer correct to 3 decimal places.