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 the curve y = sin³x √(cos x) for 0 ≤ x ≤ ½π, and its maximum point M. [Figure 10.1]
A small ring P of mass 0.03 kg is threaded on a rough vertical rod. A light inextensible string is attached to the ring and is pulled upwards at an...
A particle is projected vertically upwards with speed 30 m s¯¹ from a point on horizontal ground.
Four coplanar forces of magnitudes FN, 5 N, 25 N and 15 N are acting at a point P in the directions shown in the diagram. Given that the forces are...
A car of mass 1500 kg is pulling a trailer of mass 300 kg along a straight horizontal road at a constant speed of 20 m s⁻¹. The system of the car a...
The velocity of a particle moving in a straight line is v m s⁻¹ at time t seconds after leaving a fixed point O. The diagram shows a velocity-time ...
A particle moves in a straight line. It starts from rest at a fixed point O on the line. Its acceleration at time t s after leaving O is a m s⁻², w...
The diagram shows the vertical cross-section PQR of a slide. The part PQ is a straight line of length 8 m inclined at angle α to the horizontal, wh...
A particle is projected with speed 24 m s¯¹ at an angle of 30° above the horizontal. Find the speed and direction of motion of the particle at the ...
A uniform object is made by joining together three solid cubes with edges 3m, 2m and 1m. The object has an axis of symmetry, with the cubes stacked...
A small ball is projected from a point O on horizontal ground. At time ts after projection the horizontal and vertically upwards displacements of t...
A particle P of mass 0.3 kg is attached to a fixed point A by a light elastic string of natural length 0.8 m and modulus of elasticity 16 N. The pa...
A particle P of mass 0.3 kg is attached to one end of a light elastic string of natural length 0.6 m and modulus of elasticity 24 N. The other end ...
Fig. 1 shows the cross-section of a solid cylinder through which a cylindrical hole has been drilled to make a uniform prism. The radius of the cyl...
A particle P is projected horizontally from a point O on a rough horizontal surface. The coefficient of friction between the particle and the surfa...
On each day that Tamar goes to work, he wears either a blue suit with probability 0.6 or a grey suit with probability 0.4. If he wears a blue suit ...
For 40 values of the variable x, it is given that ∑(x − c)² = 3099.2, where c is a constant. The standard deviation of these values of x is 3.2.
The times taken, in minutes, for trains to travel between Alphaton and Beeton are normally distributed with mean 140 and standard deviation 12.
The random variable X takes the values −1, 1, 2, 3 only. The probability that X takes the value x is kx², where k is a constant.
The weights, in kg, of the 11 members of the Dolphins swimming team and the 11 members of the Sharks swimming team are shown below. Dolphins 62 75...
The results of a survey by a large supermarket show that 35% of its customers shop online.
Find the number of different arrangements that can be made of all 9 letters in the word CAMERAMAN in each of the following cases.
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)).