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.
Show that 3 sin 2θ cot θ = 6 cos² θ.
Find the set of values of x for which 2(3^(1−2x)) < 5^x. Give your answer in a simplified exact form.
Expand (2 – 3x)¯² in ascending powers of x, up to and including the term in x², simplifying the coefficients.
Express the equation tan(θ+ 60°) = 2 + tan(60° – θ) as a quadratic equation in tan θ, and hence solve the equation for 0° ≤ θ ≤ 180°.
The curve with equation y = e^(2x)(sin x + 3 cos x) has a stationary point in the interval 0 ≤ x ≤ π.
Find the quotient and remainder when 2x³ – x² + 6x + 3 is divided by x² + 3.
The diagram shows a circle with centre O and radius r. The tangents to the circle at the points A and B meet at T, and angle AOB is 2x radians. The...
Let f(x) = cos x / (1 + sin x)
A certain curve is such that its gradient at a point (x, y) is proportional to y / (x√x). The curve passes through the points with coordinates (1, ...
With respect to the origin O, the vertices of a triangle ABC have position vectors OA = 2i + 5k, OB = 3i + 2j + 3k and OC = i + j + k.
The complex number u is defined by u = 3i / (a + 2i), where a is real.
Find the quotient and remainder when 6x⁴ + x³ − x² + 5x – 6 is divided by 2x² − x + 1.
The variables x and y satisfy the equation y² = Aekx, where A and k are constants. The graph of In y against x is a straight line passing through t...
Find the exact value of ∫₄¹ x^(3/2) ln x dx.
A curve has equation y = cos x sin 2x. Find the x-coordinate of the stationary point in the interval 0 < x < ½π, giving your answer correct to 3 si...
Express √2 cos x – √5 sin x in the form Rcos(x + α), where R > 0 and 0° < α < 90°. Give the exact value of R and the value of α correct to 3 decima...
The diagram shows the curve y = x / (1 + 3x⁴) for x ≥ 0, and its maximum point M. [Figure 6.1]
The variables x and y satisfy the differential equation dy/dx = (y - 1) / ((x + 1)(x + 3)). It is given that y = 2 when x = 0. Solve the differenti...
Solve the equation (1 + 2i)w + iw* = 3 + 5i. Give your answer in the form x + iy, where x and y are real.
The diagram shows the curves y = cos x and y = k/(1 + x), where k is a constant, for 0 ≤ x ≤ ½π. The curves touch at the point where x = p. [Figure...
With respect to the origin O, the points A and B have position vectors given by OA = 6i + 2j and OB = 2i + 2j + 3k. The midpoint of OA is M. The po...
Solve the inequality |2x - 1 | > 3|x + 2|.
Find the exact value of ∫₀¹ (2-x)e⁻²ˣ dx.
Show that the equation ln(1 + e⁻ˣ) + 2x = 0 can be expressed as a quadratic equation in eˣ.
The equation of a curve is y = x tan⁻¹(½x).
By first expressing the equation tan θ tan(θ + 45°) = 2 cot 2θ as a quadratic equation in tan θ, solve the equation for 0° < θ < 90°.
By sketching a suitable pair of graphs, show that the equation x⁵ = 2 + x has exactly one real root.
Let f(x) = 2 / ((2x−1)²(2x + 1)).
Relative to the origin O, the points A, B and D have position vectors given by OA = i + 2j + k, OB = 2i + 5j + 3k and OD = 3i + 2k. A fourth point ...
The complex numbers u and w are such that u - w = 2i and uw = 6. Find u and w, giving your answers in the form x + iy, where x and y are real and e...
A tank containing water is in the form of a hemisphere. The axis is vertical, the lowest point is A and the radius is r, as shown in the diagram. T...
Three coplanar forces of magnitudes 100 N, 50 N and 50 N act at a point A, as shown in the diagram. The value of cos α is 3/5. [The diagram]
A car of mass 1800 kg is towing a trailer of mass 400 kg along a straight horizontal road. The car and trailer are connected by a light rigid tow-b...
A particle P is projected vertically upwards with speed 5 m s⁻¹ from a point A which is 2.8 m above horizontal ground.
The diagram shows a ring of mass 0.1 kg threaded on a fixed horizontal rod. The rod is rough and the coefficient of friction between the ring and t...
A child of mass 35 kg is swinging on a rope. The child is modelled as a particle P and the rope is modelled as a light inextensible string of lengt...
A particle moves in a straight line AB. The velocity v m s⁻¹ of the particle t s after leaving A is given by v = k(t² – 10t + 21), where k is a con...
A particle P of mass 0.3 kg, lying on a smooth plane inclined at 30° to the horizontal, is released from rest. P slides down the plane for a distan...
Particles P of mass mkg and Q of mass 0.2 kg are free to move on a smooth horizontal plane. P is projected at a speed of 2ms⁻¹ towards Q which is s...
A minibus of mass 4000 kg is travelling along a straight horizontal road. The resistance to motion is 900 N.
Four coplanar forces of magnitudes 40 N, 20 N, 50 N and F N act at a point in the directions shown in the diagram. The four forces are in equilibrium.
A car starts from rest and moves in a straight line with constant acceleration am s⁻² for a distance of 50 m. The car then travels with constant ve...
A block B of mass 4 kg is pushed up a line of greatest slope of a smooth plane inclined at 30° to the horizontal by a force applied to B, acting in...
A particle travels in a straight line PQ. The velocity of the particle t s after leaving P is v m s⁻¹, where v = 4.5 + 4t – 0.5t².
Two particles A and B, of masses 3m kg and 2m kg respectively, are attached to the ends of a light inextensible string. The string passes over a fi...
The score when two fair six-sided dice are thrown is the sum of the two numbers on the upper faces.
Find the number of different arrangements that can be made from the 9 letters of the word JEWELLERY in which the three Es are together and the two ...
A company produces small boxes of sweets that contain 5 jellies and 3 chocolates. Jemeel chooses 3 sweets at random from a box.
In a music competition, there are 8 pianists, 4 guitarists and 6 violinists. 7 of these musicians will be selected to go through to the final. How ...
On Mondays, Rani cooks her evening meal. She has a pizza, a burger or a curry with probabilities 0.35, 0.44, 0.21 respectively. When she cooks a pi...