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.
Given that 9x + 3x = 240, find the value of 3x and hence, using logarithms, find the value of x correct to 4 significant figures.
The diagram shows the curve with equation y = 5 sin 2x – 3 tan 2x for values of x such that 0 < x < (1/2)π. Find the x-coordinate of the stationary...
Find the gradient of the curve 4x + 3ye2x + y² = 10 at the point (0, 2).
The curve with equation y = 5e2x – 8x2 – 20 crosses the x-axis at only one point. This point has coordinates (p, 0).
Show that ∫(from 1 to 6) (12 / (3x + 2)) dx = ln 256.
Use the factor theorem to show that (2x + 3) is a factor of 8x³ + 4x² - 10x + 3.
Show that ∫₇₁ (6 / (2x + 1)) dx = ln 125.
The diagram shows the curve with equation y = √(1 + 3cos²(x/2)) for 0 ≤ x ≤ π. The region R is bounded by the curve, the axes and the line x = π. [...
Find the set of values of x satisfying the inequality 2|2x – a| < |x + 3a|, where a is a positive constant.
Showing all necessary working, solve the equation (2eˣ + e⁻ˣ) / (eˣ - e⁻ˣ) = 4, giving your answer correct to 2 decimal places.
By sketching a suitable pair of graphs, show that the equation x³ = 3 − x has exactly one real root.
The parametric equations of a curve are x = 2 sin θ + sin 2θ, y = 2 cos θ + cos 2θ, where 0 < θ < π.
The coordinates (x, y) of a general point on a curve satisfy the differential equation x dy/dx = (2 − x²)y. The curve passes through the point (1, ...
Show that the equation (√2) cosec x + cot x = √3 can be expressed in the form R sin(x − α) = √2, where R > 0 and 0° < α < 90°.
The diagram shows the curve y = 5 sin²x cos³x for 0 ≤ x ≤ ½π, and its maximum point M. The shaded region R is bounded by the curve and the x-axis. ...
Showing all necessary working, express the complex number (2 + 3i) / (1 − 2i) in the form re^(iθ), where r > 0 and –π < θ < π. Give the values of r...
Let f(x) = (6x² + 8x + 9) / ((2 − x)(3 + 2x)²).
The planes m and n have equations 3x + y − 2z = 10 and x − 2y + 2z = 5 respectively. The line l has equation r = 4i + 2j + k + λ(i + j + 2k).
Solve the inequality 3|2x – 1| > |x + 4|.
Showing all necessary working, solve the equation sin(θ – 30°) + cos θ = 2 sin θ, for 0° < θ < 180°.
Find ∫ (ln x)/x³ dx.
Showing all necessary working, solve the equation (eˣ + e⁻ˣ)/(eˣ + 1) = 4, giving your answer correct to 3 decimal places.
The equation of a curve is y = x ln(8 – x). The gradient of the curve is equal to 1 at only one point, when x = a.
A certain curve is such that its gradient at a general point with coordinates (x, y) is proportional to y²/x The curve passes through the points wi...
A curve has equation y = (3 cos x)/(2 + sin x) for −½π < x < ½π.
Let f(x) = (7x² – 15x + 8) / ((1-2x)(2-x)²).
Without using a calculator, express the complex number (2 + 6i)/(1-2i) in the form x + iy, where x and y are real.
The line l has equation r = 5i – 3j – k + λ(i – 2j + k). The plane p has equation (r - i - 2j).(3i + j + k) = 0. The line l intersects the plane p ...
Showing all necessary working, solve the equation (2eˣ + e⁻ˣ) / (eˣ – e⁻ˣ) = 4, giving your answer correct to 2 decimal places.
Showing all necessary working, express the complex number (2 + 3i) / (1 - 2i) in the form re^(iθ), where r > 0 and –π < θ < π. Give the values of r...
Let f(x) = (6x² + 8x + 9) / ((2 - x)(3 + 2x)²).
A particle of mass 0.2 kg moving in a straight line experiences a constant resistance force of 1.5 N. When the particle is moving at speed 2.5 m s⁻...
A high-speed train of mass 490 000 kg is moving along a straight horizontal track at a constant speed of 85 m s⁻¹. The engines are supplying 4080 k...
A van of mass 2500kg descends a hill of length 0.4 km inclined at 4° to the horizontal. There is a constant resistance to motion of 600 N and the s...
Two particles A and B, of masses m kg and 0.3 kg respectively, are attached to the ends of a light inextensible string. The string passes over a fi...
Coplanar forces, of magnitudes 15 N, 25 N and 30 N, act at a point B on the line ABC in the directions shown in the diagram. [Figure 5.1]
A particle is projected from a point P with initial speed u m s⁻¹ up a line of greatest slope PQR of a rough inclined plane. The distances PQ and Q...
A smooth ring R of mass mkg is threaded on a light inextensible string ARB. The ends of the string are attached to fixed points A and B with A vert...
A block of mass 5 kg is being pulled by a rope up a rough plane inclined at 6° to the horizontal. The rope is parallel to a line of greatest slope ...
The velocity of a particle moving in a straight line is vms¯¹ at time t seconds. The diagram shows a velocity-time graph which models the motion of...
Two particles P and Q, of masses 0.4 kg and 0.7 kg respectively, are attached to the ends of a light inextensible string. The string passes over a ...
A particle moves in a straight line starting from a point O with initial velocity 1 ms¯¹. The acceleration of the particle at time t s after leavin...
A car of mass 1200 kg is driving along a straight horizontal road at a constant speed of 15 m s¯¹. There is a constant resistance to motion of 350 N.
A particle of mass 0.3 kg is released from rest above a tank containing water. The particle falls vertically, taking 0.8 s to reach the water surfa...
A small smooth ring R of mass 0.2 kg is threaded onto a light inextensible string ARB. The two ends of the string are attached to points A and B on...
A block is pushed along a horizontal floor by a force of magnitude 50N which acts at an angle of 20° to the horizontal (see diagram). The coefficie...
A particle of mass 1.2kg moves in a straight line AB. It is projected with speed 7.5 ms¯¹ from A towards B and experiences a resistance force. The ...
A runner sets off from a point P at time t = 0, where t is in seconds. The runner starts from rest and accelerates at 1.2ms¯² for 5s. For the next ...
Two particles P and Q, of masses 0.3 kg and 0.5 kg respectively, are attached to the ends of a light inextensible string. The string passes over a ...
A van of mass 3200 kg travels along a horizontal road. The power of the van's engine is constant and equal to 36 kW, and there is a constant resist...