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 diagram shows a water container in the form of an inverted pyramid, which is such that when the height of the water level is h cm the surface o...
In the diagram, AB = AC = 8 cm and angle CAB = 2/7 π radians. The circular arc BC has centre A, the circular arc CD has centre B and ABD is a strai...
The diagram shows the graphs of y = tan x and y = cos x for 0 ≤ x ≤ π. The graphs intersect at points A and B. [Figure 5.1]
Relative to an origin O, the position vectors of the points A and B are given by OA = 2i + 3j + 5k and OB = 7i + 4j + 3k.
The function f is defined for x ≥ 0 by f(x) = (4x + 1)³ᐟ².
The functions f and g are defined for x ≥ 0 by f : x → 2x² + 3, g: x → 3x + 2.
The point A (2, 2) lies on the curve y = x² – 2x + 2.
The diagram shows the curve y = f(x) defined for x > 0. The curve has a minimum point at A and crosses the x-axis at B and C. It is given that dy/d...
Solve the equation 2 ln(2x) – ln(x + 3) = ln(3x + 5).
Given that tan 2θ cot θ = 8,
Solve the inequality |2x – 5| < |x + 3|.
Find the gradient of the curve x² sin y + cos 3y = 4 at the point (2, ½π).
It is given that a is a positive constant such that ∫[0 to a] (1 + 2x + 3e³ˣ) dx = 250.
The polynomial p(x) is defined by p(x) = ax³ + bx² – 17x – a, where a and b are constants. It is given that (x + 2) is a factor of p(x) and that th...
The diagram shows part of the curve y = 2 cos 2x cos(2x + ⅙π). The shaded region is bounded by the curve and the two axes.
A particle of mass 0.4 kg is projected with a speed of 12 m s⁻¹ up a line of greatest slope of a smooth plane inclined at 30° to the horizontal.
A particle P of mass 1.6 kg is suspended in equilibrium by two light inextensible strings attached to points A and B. The strings make angles of 20...
A particle of mass 0.6 kg is placed on a rough plane which is inclined at an angle of 21° to the horizontal. The particle is kept in equilibrium by...
A car of mass 900 kg is moving on a straight horizontal road ABCD. There is a constant resistance of magnitude 800 N in the sections AB and BC, and...
A particle P moves in a straight line starting from a point O and comes to rest 35 s later. At time t s after leaving O, the velocity v m s⁻¹ of P ...
Two particles of masses 1.2 kg and 0.8 kg are connected by a light inextensible string that passes over a fixed smooth pulley. The particles hang v...
A small ball is projected with speed 15 m s¯¹ at an angle of 60° above the horizontal. Find the distance from the point of projection of the ball a...
A cylindrical container is open at the top. The curved surface and the circular base of the container are both made from the same thin uniform mate...
A particle P is projected with speed 20 m s¯¹ at an angle of 60° below the horizontal, from a point O which is 30 m above horizontal ground.
The diagram shows a uniform lamina ABCD with AB = 0.75 m, AD = 0.6m and BC = 0.9 m. Angle BAD = angle ABC = 90°. [Figure X.X]
Two particles P and Q have masses 0.4 kg and m kg respectively. P is attached to a fixed point A by a light inextensible string of length 0.5 m whi...
O and A are fixed points on a rough horizontal surface, with OA = 1 m. A particle P of mass 0.4 kg is projected horizontally with speed U m s⁻¹ fro...
One end of a light elastic string of natural length 0.6 m and modulus of elasticity 24 N is attached to a fixed point O. The other end of the strin...
Twelve values of x are shown below. 1761.6 1758.5 1762.3 1761.4 1759.4 1759.1 1762.5 1761.9 1762.4 1761.9 1762.8 1761.0 Find the mean and standard ...
A bag contains 10 pink balloons, 9 yellow balloons, 12 green balloons and 9 white balloons. 7 balloons are selected at random without replacement. ...
It is found that 10% of the population enjoy watching Historical Drama on television. Use an appropriate approximation to find the probability that...
The weights in kilograms of packets of cereal were noted correct to 4 significant figures. The following stem-and-leaf diagram shows the data. 747 ...
A plate of cakes holds 12 different cakes. Find the number of ways these cakes can be shared between Alex and James if each receives an odd number ...
Pack A consists of ten cards numbered 0, 0, 1, 1, 1, 1, 1, 3, 3, 3. Pack B consists of six cards numbered 0, 0, 2, 2, 2, 2. One card is chosen at r...
The lengths, in centimetres, of middle fingers of women in Raneland have a normal distribution with mean u and standard deviation σ. It is found th...
Solve the inequality |5x + 2| > |4x + 3|.
A curve has equation y = 4x sin ½ x. Find the equation of the tangent to the curve at the point for which x = π.
Use the trapezium rule with four intervals to find an approximation to ∫₀⁸ ln(x + 2) dx, giving your answer correct to 3 significant figures.
The polynomial p(x) is defined by p(x) = 4x³ + 4x² – 29x – 15.
It is given that ∫₋ₐ²ᵃ 4e⁻²ˣ dx = 25, where a is a positive constant.
Show that cosec 2x + cot 2x = cotx.
The diagram shows part of the curve defined by the parametric equations x = t² + 4t, y = t³ – 3t². The curve has a minimum point at M and crosses t...
Use the trapezium rule with three intervals to estimate the value of ∫₀^(π/4) √(1 – tan x) dx, giving your answer correct to 3 decimal places.
Expand ∛(1 – 4x) in ascending powers of x, up to and including the term in x³, simplifying the coefficients.
Using the expansions of cos(3x + x) and cos(3x – x), show that ½(cos 4x + cos 2x) = cos 3x cos x.
The variables x and y satisfy the equation yⁿ = Ax³, where n and A are constants. It is given that y = 2.58 when x = 1.20, and y = 9.49 when x = 2.51.
The parametric equations of a curve are x = 2t + sin 2t, y = 1 – 2 cos 2t, for −½π < t < ½π.
The variables x and θ satisfy the differential equation x cos² θ (dx/dθ) = 2 tan θ + 1, for 0 ≤ θ < ½π and x > 0. It is given that x = 1 when θ = ¼π.
By sketching suitable graphs, show that the equation e²ˣ = 6 + e⁻ˣ has exactly one real root.
Let f(x) = (5x² + x + 27) / ((2x + 1)(x² + 9)).