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 particle P is projected vertically upwards from horizontal ground with speed ums¯¹. P reaches a maximum height of 20m above the ground.
A car of mass mkg is towing a trailer of mass 300kg down a straight hill inclined at 3° to the horizontal at a constant speed. There are resistance...
The total mass of a cyclist and her bicycle is 70kg. The cyclist is riding with constant power of 180 W up a straight hill inclined at an angle a t...
Four coplanar forces act at a point. The magnitudes of the forces are 10N, FN, GN and 2FN. The directions of the forces are as shown in the diagram.
A cyclist starts from rest at a fixed point O and moves in a straight line, before coming to rest k seconds later. The acceleration of the cyclist ...
A bead, A, of mass 0.1kg is threaded on a long straight rigid wire which is inclined at sin¯¹(7/25) to the horizontal. A is released from rest and ...
A fair red spinner has edges numbered 1, 2, 2, 3. A fair blue spinner has edges numbered -3, -2, -1, -1. Each spinner is spun once and the number o...
In a certain country, the probability of more than 10cm of rain on any particular day is 0.18, independently of the weather on any other day.
At a summer camp an arithmetic test is taken by 250 children. The times taken, to the nearest minute, to complete the test were recorded. The resul...
The weights of male leopards in a particular region are normally distributed with mean 55kg and standard deviation 6kg.
A group of 12 people consists of 3 boys, 4 girls and 5 adults.
A factory produces chocolates in three flavours: lemon, orange and strawberry in the ratio 3 : 5 : 7 respectively. Nell checks the chocolates on th...
The lengths, in millimetres, of a random sample of 12 rods made by a certain machine are as follows. 200 201 198 202 200 199 199 201 197 202 200 199
Harry has a five-sided spinner with sectors coloured blue, green, red, yellow and black. Harry thinks the spinner may be biased. He plans to carry ...
A random sample of 500 households in a certain town was chosen. Using this sample, a confidence interval for the proportion, p, of all households i...
In the past the time, in minutes, taken by students to complete a certain challenge had mean 25.5 and standard deviation 5.2. A new challenge is de...
The heights of buildings in a large city are normally distributed with mean 18.3m and standard deviation 2.5 m.
In a game a ball is rolled down a slope and along a track until it stops. The distance, in metres, travelled by the ball is modelled by the random ...
(a) Two ponds, A and B, each contain a large number of fish. It is known that 2.4% of fish in pond A are carp and 1.8% of fish in pond B are carp. ...
A line has equation y = 3x – 2k and a curve has equation y = x² – kx + 2, where k is a constant. Show that the line and the curve meet for all valu...
A function f is defined by f(x) = x² – 2x + 5 for x ∈ R. A sequence of transformations is applied in the following order to the graph of y = f(x) t...
A curve has equation y = (1/60)(3x + 1)² and a point is moving along the curve. Find the x-coordinate of the point on the curve at which the x- and...
The circumference round the trunk of a large tree is measured and found to be 5.00m. After one year the circumference is measured again and found t...
Points A (7, 12) and B lie on a circle with centre (–2, 5). The line AB has equation y = −2x + 26. Find the coordinates of B.
In the expansion of (x/a + a/x²)⁷ , it is given that (the coefficient of x⁴) / (the coefficient of x) = 3. Find the possible values of the constant a.
By first obtaining a quadratic equation in cos θ, solve the equation tan θ sin θ = 1 for 0° < θ < 360°.
The diagram shows triangle ABC in which angle B is a right angle. The length of AB is 8 cm and the length of BC is 4 cm. The point D on AB is such ...
The function f is defined by f(x) = −3x² + 2 for x ≤ −1.
At the point (4, −1) on a curve, the gradient of the curve is -3/2. It is given that dy/dx = x^(-1/2) + k, where k is a constant.
The diagram shows the curve with equation x = y² + 1. The points A (5, 2) and B (2, -1) lie on the curve. [Figure 11.1]
Find the exact value of ∫₀^(π/2) 2 tan²(x) dx.
Solve the equation tan(θ – 60°) = 3 cot θ for −90° < θ < 90°.
The polynomial p(x) is defined by p(x) = ax³ – ax² + ax + b, where a and b are constants. It is given that (x + 2) is a factor of p(x), and that th...
Sketch, on the same diagram, the graphs of y = |2x – 11| and y = 3x – 3.
It is given that ∫₁ᵃ (4/(1 + 2x) + 3/x) dx = ln 10, where a is a constant greater than 1.
The diagram shows the curve with equation y = (4e^(2x) + 9)/(e^x + 2). The curve has a minimum point M and crosses the y-axis at the point P. [Figu...
The diagram shows the curve with parametric equations x = k tan t, y = 3 sin 2t - 4 sin t, for 0 < t < ½π. It is given that k is a positive constan...
It is given that x = ln(2y – 3) – ln(y + 4). Express y in terms of x.
On an Argand diagram, shade the region whose points represent complex numbers z satisfying the inequalities −⅓π ≤ arg(z − 1 − 2i) < π and Rez < 3.
The polynomial 2x⁴ + ax³ + bx − 1, where a and b are constants, is denoted by p(x). When p(x) is divided by x² – x + 1 the remainder is 3x + 2. Fin...
Solve the equation 5z / (1 + 2i) - zz* + 30 + 10i = 0, giving your answers in the form x + iy, where x and y are real.
The parametric equations of a curve are x = te²ᵗ, y = t² + t + 3.
Express 5 sin θ + 12 cos θ in the form R cos(θ – α), where R > 0 and 0 < α < ½π.
The diagram shows a circle with centre O and radius r. The angle of the minor sector AOB of the circle is x radians. The area of the major sector o...
The diagram shows the curve y = x³ ln x, for x > 0, and its minimum point M. [Figure 8.1]
The variables x and y satisfy the differential equation dy/dx = e³ʸ sin² 2x. It is given that y = 0 when x = 0. Solve the differential equation and...
With respect to the origin O, the points A, B, C and D have position vectors given by OA = (3, -1, 2), OB = (1, 2, -3), OC = (-2, 5, 1) and OD = (-...
Let f(x) = (5x² + x + 11) / ((4 + x²)(1 + x))
A crate of mass 200kg is being pulled at constant speed along horizontal ground by a horizontal rope attached to a winch. The winch is working at a...
A particle P is projected vertically upwards from horizontal ground with speed 15ms⁻¹.