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 function f is defined by f(x) = 1 3x + 2 + x² for x < -1.
The graph of y = f(x) is transformed to the graph of y = 1 + f(x).
The diagram shows part of the curve with equation y = x² + 1. The shaded region enclosed by the curve, the y-axis and the line y = 5 is rotated thr...
A curve has equation y = x² – 2x – 3. A point is moving along the curve in such a way that at P the y-coordinate is increasing at 4 units per secon...
Solve the equation tan θ + 3 sin θ + 2 = 2 tan θ - 3 sin θ + 1 for 0° ≤ θ ≤ 90°.
The coefficient of 1/x in the expansion of (2x + a/x²)⁵ is 720.
The diagram shows a sector AOB which is part of a circle with centre O and radius 6cm and with angle AOB = 0.8 radians. The point C on OB is such t...
A woman's basic salary for her first year with a particular company is $30000 and at the end of the year she also gets a bonus of $600.
The function f is defined by f(x) = 2x² + 12x + 11 for x ≤ −4.
The gradient of a curve at the point (x, y) is given by dy/dx = 2(x + 3)¹/² - x. The curve has a stationary point at (a, 14), where a is a positive...
Solve the equation 3 tan²x – 5 tan x − 2 = 0 for 0° ≤ x ≤ 180°.
A diameter of a circle C₁ has end-points at (−3, −5) and (7, 3).
Solve the equation 2 sin(θ + 30°) + 5 cos θ = 2 sin θ for 0° < θ < 90°.
Find the quotient when 4x³ + 17x² + 9x is divided by x² + 5x + 6, and show that the remainder is 18.
It is given that ∫⁽³ᵃ⁾ₐ (2/(2x-5)) dx = ln(7/2). Find the value of the positive constant a.
A curve has equation 3x² - y² – 4 ln(2y + 3) = 26. Find the equation of the tangent to the curve at the point (3, −1).
Sketch, on the same diagram, the graphs of y = |x + 2k| and y = |2x – 3k|, where k is a positive constant. Give, in terms of k, the coordinates of ...
A curve has equation y = x³e⁻⁰.²ˣ where x ≥ 0. At the point P on the curve, the gradient of the curve is 15.
The diagram shows part of the curve with equation y = 4 sin²x + 8 sin x + 3, where x is measured in radians. The curve crosses the x-axis at the po...
Sketch the graph of y = |x − 2|.
Solve the equation In 3 + ln(2x + 5) = 2ln(x + 2). Give your answer in a simplified exact form.
By sketching a suitable pair of graphs, show that the equation secx = 2 – 5x has exactly one root in the interval 0 < x < ἐπ.
Find ∫(π/3 to π/6) x sec²x dx. Give your answer in a simplified exact form.
Show that cos 3x / sin x + sin 3x / cos x = 2 cot 2x.
The variables x and y satisfy the differential equation dy/dx = (1+4y²) / e^(x²). It is given that y = 0 when x = 1.
The equation of a curve is x³ + 3xy² – y³ = 5.
In the diagram, OABCDEFG is a cuboid in which OA = 2 units, OC = 3 units and OD = 2 units. Unit vectors i, j and k are parallel to OA, OC and OD re...
Let f(x) = (2 + 11x - 10x²) / ((1 + 2x)(1-2x)(2 + x)).
The complex numbers v and w satisfy the equations v + iw = 5 and (1 + 2i)v - w = 3i. Solve the equations for v and w, giving your answers in the fo...
A lorry of mass 16000 kg is travelling along a straight horizontal road. The engine of the lorry is working at constant power. The work done by the...
A particle P of mass 0.4 kg is on a rough horizontal floor. The coefficient of friction between P and the floor is μ. A force of magnitude 3 N is a...
The diagram shows the vertical cross-section of a surface. A, B and C are three points on the cross-section. The level of B is h m above the level ...
A cyclist travels along a straight road with constant acceleration. He passes through points A, B and C. The cyclist takes 2 seconds to travel alon...
Coplanar forces, of magnitudes FN, 3 N, 6 N and 4 N, act at a point P, as shown in the diagram. [Figure 5.1]
On a straight horizontal test track, driverless vehicles (with no passengers) are being tested. A car of mass 1600 kg is towing a trailer of mass 7...
A particle moves in a straight line through the point O. The displacement of the particle from O at time t s is s m, where s = t² - 3t + 2 for 0 ≤ ...
The 40 members of a club include Ranuf and Saed. All 40 members will travel to a concert. 35 members will travel in a coach and the other 5 will tr...
An ordinary fair die is thrown repeatedly until a 1 or a 6 is obtained.
The weights of apples of a certain variety are normally distributed with mean 82 grams. 22% of these apples have a weight greater than 87 grams.
Richard has 3 blue candles, 2 red candles and 6 green candles. The candles are identical apart from their colours. He arranges the 11 candles in a ...
In Greenton, 70% of the adults own a car. A random sample of 8 adults from Greenton is chosen.
Box A contains 7 red balls and 1 blue ball. Box B contains 9 red balls and 5 blue balls. A ball is chosen at random from box A and placed in box B....
Helen measures the lengths of 150 fish of a certain species in a large pond. These lengths, correct to the nearest centimetre, are summarised in th...
The booklets produced by a certain publisher contain, on average, 1 incorrect letter per 30 000 letters, and these errors occur randomly. A randoml...
Lengths of a certain species of lizard are known to be normally distributed with standard deviation 3.2 cm. A naturalist measures the lengths of a ...
In the past, the mean time taken by Freda for a particular daily journey was 39.2 minutes. Following the introduction of a one-way system, Freda wi...
The number of accidents on a certain road has a Poisson distribution with mean 0.4 per 50-day period.
Bottles of Lanta contain approximately 300 ml of juice. The volume of juice, in millilitres, in a bottle is 300 + X, where X is a random variable w...
The volumes, in millilitres, of large and small cups of tea are modelled by the distributions N(200, 30) and N(110, 20) respectively.
A national survey shows that 95% of year 12 students use social media. Arvin suspects that the percentage of year 12 students at his college who us...