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 polynomial p(x) is defined by 4 p(x) = x² - 10x³ +20x² - 30x+40.
The diagram shows the curve with equation y = 4 cos2x+8 sinx for 0 ≤ x ≤ π. The maximum points on the curve are denoted by A and B, and the shaded ...
Given that ∫[from -2a to a] (½ e²⁸+¼ e⁻⁸)dx = 5, where a is a positive constant, show that a = ½ ln(10+½ e⁻²⁸+¼ e⁻⁴⁸).
A curve has equation 5x²y +4e² - 7x+10 = 0.
Find ∫ 6 sin²x dx.
Solve the equation cotθ tan (θ+45°) = 7 for 0° < θ < 90°.
The diagram shows the curve with equation y = 8e⁻¹⁄₂ˣ - 1. The curve meets the axes at the points A and B. The shaded region is bounded by the curv...
A curve has parametric equations x = tan θ, y = sin θ-2 sin³θ, for 0 < θ < ½π.
The equation of a curve is y = 4e¹⁻²ˣ √3x-1.
Find the exact value of ∫ from 1 to 2 of ln 3x dx. Give your answer in the form a+lnb, where a and b are integers.
Show that the equation log₄(2x + 1) = 2log₄(3x-1)-2 can be written as a quadratic equation in x.
Express 3√2sin(x+45°) + cosx in the form Rcos(x−α), where R > 0 and 0° < α < 90°.
The diagram shows the graph of y = e^(sin 2x) cos 4x for 0 < x < 1/2π, and its maximum point M. [Figure 4.1]
Solve the quadratic equation (2+i)w²+4w+2-i = 0. Give your answers in the form x+iy, where x and y are real.
The parametric equations of a curve are x = t² - ln(t+1), y = t/(2t+1)
The variables x and y satisfy the differential equation (x²+1) dy/dx = kxe^(-2y), where k is a constant. It is given that y = 0 when x = 0 and that...
By sketching a suitable pair of graphs, show that the equation sec 2x = -e^(-x) has only one root in the interval 0 < x < 1/2π.
Let f(x) = (x²+2x-11) / ((3+x)(2+x²)).
With respect to the origin O, the points A, B, C and D have position vectors given by OA = (1 5 3), OB = (0 4 1), OC = (1 -3 1) and OD = (3 -5 4). ...
Sketch the graph of y = |x+3a|, where a is a positive constant.
Solve the equation 3 × 2x+1 = 4 × 32x-3. Give your answer correct to 3 significant figures.
The shaded region in the Argand diagram, bounded by a line and a circle, represents the complex numbers z satisfying Rez < 2 and |z-(3+i)|≤2. The p...
Find the exact value of ∫(from 0 to 1) x tan⁻¹x dx.
It is given that f(x) = (x−a)²g(x), where f(x) and g(x) are polynomials. Show that (x-a) is a factor of f'(x) .
By sketching a suitable pair of graphs, show that the equation cot2x = 2 sin 2x-1 has exactly one root in the interval 0 < x < π.
The equation of a curve is 2y³ – 3x²y-x³ = 16.
Prove the identity sin 4x = 4 sinx(2 cos³x-cosx).
Let f(x) = (x²+4ax+6a²) / ((x+2a)(x+3a)), where a is a positive constant.
The diagram shows a tank for holding water. The tank is in the shape of a cube of side 50 cm. At time t seconds, the depth of water in the tank is ...
Relative to the origin O, the position vectors of the points A, B and C are OA = 4i−2j, OB = 2i+8j+4k, and OC = -2i+6k. The midpoint of AB is M, as...
Solve the inequality | 3x+2|<3|2x-1|.
Find the quotient and the remainder when 3x⁴ – 2x² is divided by x + 1.
Solve the equation 2^(3x-4) = 3/5^x. Give your answer in the form (ln m)/(ln n), where m and n are integers.
Show that cos4x+2sin²x-1 = 8sin⁴x-6 sin²x.
Find the exact value of ∫(from 0 to π/2) x² sin 2x dx.
Solve the equation (5z)/(2-i) - zz* + 20+8i = 0. Give your answers in the form x+iy, where x and y are real.
The curve with equation y = e⁻⁵ˣln 5x has a stationary point at x = p.
The line l₁ passes through the point (3, 1, −6) and is parallel to the vector 2i+j+4k. The line l₂ passes through the point (−1, 3, −6) and is perp...
Express 2/(1-9y²) in partial fractions.
The diagram shows the graph of y = sec²x√(3+2 tanx) for -¼π ≤ x ≤ ¼π, and its minimum point M. [Figure 11.1]
A car of mass 900kg is moving along a straight horizontal road against a constant resistance to motion of 350N. At an instant when the car is movin...
Two particles, P and Q, of masses 3 kg and 5kg respectively, are at rest on a smooth horizontal plane. P is projected at a speed of 4 ms⁻¹ directly...
Coplanar forces of magnitudes 45N, 28N, 72N and 35N act at a point in the directions shown in the diagram. [Figure 3.1] Find, in either order, the ...
Two particles, A and B, of masses mkg and 3kg respectively, are connected by a light inextensible string. Particle B is on a fixed plane which is a...
A particle P of mass mkg is in equilibrium on a rough plane inclined at an angle θ° to the horizontal. The equilibrium of P is maintained by a forc...
A particle A of mass 2.5kg is released from rest from the top of a smooth plane, which makes an angle of sin⁻¹ 0.2 with the horizontal. The particl...
A particle P starts from a point O and moves in a straight line. The velocity v ms⁻¹ of P, at time t s after leaving O, is given by v = ¹/₃(2t-3)(t...
A block A of mass 2kg and a particle B of mass 0.5kg are connected by a light inextensible string inclined at 15° to the horizontal. They are pulle...
The diagram shows the displacement-time graph for the motion of a particle. The particle starts from rest at a point O and travels with constant ac...
A railway locomotive of mass 240000 kg is towing a coach of mass 36000 kg down a hill inclined at an angle of sin⁻¹ 0.04 to the horizontal. The dri...