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 = (x + 1)e^(-x/3) and its maximum point M. [Figure X.X]
Let f(x) = (x - 4x²) / ((3-x)(2 + x²))
Two lines l and m have equations r = 2i – j + k + s(2i + 3j – k) and r = i + 3j + 4k + t(i + 2j + k) respectively.
Expand 4 / √(4-3x) in ascending powers of x, up to and including the term in x², simplifying the coefficients.
Showing all necessary working, solve the equation 5^(2x) = 5^x + 5. Give your answer correct to 3 decimal places.
Showing all necessary working, find the value of ∫(from 0 to π/3) x cos 3x dx, giving your answer in terms of π.
The curve with equation y = (ln x)/(3+x) has a stationary point at x = p.
5 By first expanding (cos²x + sin²x)³, or otherwise, show that cos⁶x + sin⁶x = 1 - (3/4)sin²2x.
6 Express 1/(4-y²) in partial fractions.
The equation of a curve is 2x³ – y³ – 3xy² = 2a³, where a is a non-zero constant.
9 Find the complex number z satisfying the equation 3z - iz* = 1 + 5i, where z* denotes the complex conjugate of z.
The points A and B have position vectors 2i + j + 3k and 4i + j + k respectively. The line l has equation r = 4i + 6j + μ(i + 2j – 2k).
A particle P is projected vertically upwards with speed 24 m s¯¹ from a point 5 m above ground level. Find the time from projection until P reaches...
The diagram shows three coplanar forces acting at the point O. The magnitudes of the forces are 6N, 8 N and 10 N. The angle between the 6 N force a...
A particle P of mass 8 kg is on a smooth plane inclined at an angle of 30° to the horizontal. A force of magnitude 100 N, making an angle of θ° wit...
A particle P moves in a straight line starting from a point O. At time t s after leaving O, the displacement s m from O is given by s = t³ – 4t² + ...
A sprinter runs a race of 200 m. His total time for running the race is 20 s. He starts from rest and accelerates uniformly for 6 s, reaching a spe...
A car has mass 1250 kg. The car is moving along a straight level road at a constant speed of 36 m s¯¹ and is subject to a constant resistance of ma...
The diagram shows a triangular block with sloping faces inclined to the horizontal at 45° and 30°. Particle A of mass 0.8 kg lies on the face incli...
The diagram shows the velocity-time graph for a train which travels from rest at one station to rest at the next station. The graph consists of thr...
A small ball is projected vertically downwards with speed 5 m s⁻¹ from a point A at a height of 7.2 m above horizontal ground. The ball hits the gr...
Coplanar forces of magnitudes 8 N, 12 N and 18 N act at a point in the directions shown in the diagram. Find the magnitude and direction of the sin...
Two particles A and B, of masses 0.8 kg and 1.6 kg respectively, are connected by a light inextensible string. Particle A is placed on a smooth pla...
A particle of mass 3 kg is on a rough plane inclined at an angle of 20° to the horizontal. A force of magnitude P N acting parallel to a line of gr...
A car of mass 1400 kg travelling at a speed of v m s⁻¹ experiences a resistive force of magnitude 40v N. The greatest possible constant speed of th...
A particle P moves in a straight line starting from a point O. The velocity v m s⁻¹ of P at time t s is given by v = 12t - 4t² for 0 ≤ t ≤ 2, v = 1...
A small ball B is projected from a point O on horizontal ground. The initial velocity of B has horizontal and vertically upwards components of 18ms...
A non-uniform rod AB of length 0.5 m and weight 8 N is freely hinged to a fixed point at A. The rod makes an angle of 30° with the horizontal with ...
A particle P of mass 0.4 kg is projected horizontally along a smooth horizontal plane from a point O. At time t s after projection the velocity of ...
A small object is projected from a point O with speed V m s¯¹ at an angle of 45° above the horizontal. At time t s after projection, the horizontal...
A particle P of mass 0.7 kg is attached by a light elastic string to a fixed point O on a smooth plane inclined at an angle of 30° to the horizonta...
A particle P of mass 0.2 kg is attached to one end of a light inextensible string of length 0.6 m. The other end of the string is attached to a par...
A uniform solid cone has height 1.2 m and base radius 0.5 m. A uniform object is made by drilling a cylindrical hole of radius 0.2 m through the co...
A small ball B is projected from a point O on horizontal ground towards a point A 12m above the ground. 0.9 s after projection B has travelled a ho...
One end of a light elastic string is attached to a fixed point O. The other end of the string is attached to a particle P of mass 0.4 kg. The strin...
ABC is an object made from a uniform wire consisting of two straight portions AB and BC, in which AB = a, BC = x and angle ABC = 90°. When the obje...
A particle P is projected from a point O on horizontal ground with initial speed 20 m s⁻¹ and angle of projection 30°. At the instant t s after pro...
A uniform object is made by joining a solid cone of height 0.8 m and base radius 0.6 m and a cylinder. The cylinder has length 0.4 m and radius 0.5...
A particle P of mass 0.2 kg is released from rest at a point O above horizontal ground. At time t s after its release the velocity of P is v m s⁻¹ ...
A small object is projected from a point O with speed V m s⁻¹ at an angle of 45° above the horizontal. At time t s after projection, the horizontal...
In a statistics lesson 12 people were asked to think of a number, x, between 1 and 20 inclusive. From the results Tom found that Σx = 186 and that ...
In a survey 55 students were asked to record, to the nearest kilometre, the total number of kilometres they travelled to school in a particular wee...
Andy has 4 red socks and 8 black socks in his drawer. He takes 2 socks at random from his drawer.
The distance that car tyres of a certain make can travel before they need to be replaced has a normal distribution. A survey of a large number of t...
In Pelmerdon 22% of families own a dishwasher.
Vehicles approaching a certain road junction from town A can either turn left, turn right or go straight on. Over time it has been noted that of th...
Find the number of different ways in which all 9 letters of the word MINCEMEAT can be arranged in each of the following cases. (A, E, I are vowels)
Each of a group of 10 boys estimates the length of a piece of string. The estimates, in centimetres, are as follows. 37 40 45 38 36 38 42 38 40 39
In a group of students, ¾ are male. The proportion of male students who like their curry hot is ⅗ and the proportion of female students who like th...
(i) The volume of soup in Super Soup cartons has a normal distribution with mean μ millilitres and standard deviation 9 millilitres. Tests have sho...