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.
A particle moves in a straight line. The particle is initially at rest at a point O on the line. At time t s after leaving O, the acceleration a m ...
A small ball B is projected with speed 30ms¯¹ at an angle of 60° to the horizontal from a point on horizontal ground. Find the time after projectio...
A uniform object is made by attaching the base of a solid hemisphere to the base of a solid cone so that the object has an axis of symmetry. The ba...
A particle P of mass 0.4 kg is attached to a fixed point O by a light elastic string of natural length 0.5 m and modulus of elasticity 20 N. The pa...
A particle P of mass 0.5 kg is projected along a smooth horizontal surface towards a fixed point A. Initially P is at a point O on the surface, and...
A particle P of mass 0.1 kg is attached to one end of a light inextensible string of length 0.5 m. The other end of the string is attached to a fix...
Fig. 1 shows the cross-section ABCDE through the centre of mass G of a uniform prism. The cross-section consists of a rectangle ABCF from which a t...
A small object is projected with speed 24 m s¯¹ from a point O at the foot of a plane inclined at 45° to the horizontal. The angle of projection of...
A small ball B is projected with speed 38 m s⁻¹ at an angle of 30° to the horizontal from a point on horizontal ground. Find the speed of B when th...
A uniform solid object is made by attaching a cone to a cylinder so that the circumferences of the base of the cone and a plane face of the cylinde...
A small object is projected horizontally with speed V m s⁻¹ from a point O above horizontal ground. At time t s after projection, the horizontal an...
A particle P of mass 0.7 kg is attached to a fixed point O by a light elastic string of natural length 0.6 m and modulus of elasticity 15 N. The pa...
The diagram shows a uniform lamina ABCDEFGH. The lamina consists of a quarter-circle OAB of radius r m, a rectangle DEFG and two isosceles right-an...
A rough horizontal rod AB of length 0.45 m rotates with constant angular velocity 6 rad s⁻¹ about a vertical axis through A. A small ring R of mass...
A small ball B is projected with speed 30 m s⁻¹ at an angle of 60° to the horizontal from a point on horizontal ground. Find the time after project...
A small object is projected with speed 24 m s⁻¹ from a point O at the foot of a plane inclined at 45° to the horizontal. The angle of projection of...
9 people are to be divided into a group of 4, a group of 3 and a group of 2. In how many different ways can this be done?
A random variable X has the probability distribution shown in the following table, where p is a constant. X -1 0 1 2 4 P(X = x) p p 2p 2p 0.1
In an orchestra, there are 11 violinists, 5 cellists and 4 double bass players. A small group of 6 musicians is to be selected from these 20.
It is given that X ~ N(31.4, 3.6). Find the probability that a randomly chosen value of X is less than 29.4.
At the Nonland Business College, all students sit an accountancy examination at the end of their first year of study. On average, 80% of the studen...
The daily rainfall, x mm, in a certain village is recorded on 250 consecutive days. The results are summarised in the following cumulative frequenc...
In a group of students, the numbers of boys and girls studying Art, Music and Drama are given in the following table. Each of these 160 students is...
How many different arrangements are there of the 11 letters in the word MISSISSIPPI?
The following back-to-back stem-and-leaf diagram shows the reaction times in seconds in an experiment involving two groups of people, A and B. ...
Jake attempts the crossword puzzle in his daily newspaper every day. The probability that he will complete the puzzle on any given day is 0.75, ind...
Find the number of different ways that 5 boys and 6 girls can stand in a row if all the boys stand together and all the girls stand together.
The Quivers Archery club has 12 Junior members and 20 Senior members. For the Junior members, the mean age is 15.5 years and the standard deviation...
A fair red spinner has 4 sides, numbered 1, 2, 3, 4. A fair blue spinner has 3 sides, numbered 1, 2, 3. When a spinner is spun, the score is the nu...
The time, X hours, for which students use a games machine in any given day has a normal distribution with mean 3.24 hours and standard deviation 0....
A group consists of 5 men and 2 women. Find the number of different ways that the group can stand in a line if the women are not next to each other.
A fair 6-sided die has the numbers -1, -1, 0, 0, 1, 2 on its faces. A fair 3-sided spinner has edges numbered -1, 0, 1. The die is thrown and the s...
A box contains 3 red balls and 5 blue balls. One ball is taken at random from the box and not replaced. A yellow ball is then put into the box. A s...
Out of a class of 8 boys and 4 girls, a group of 7 people is chosen at random.
The weights of apples sold by a store can be modelled by a normal distribution with mean 120 grams and standard deviation 24 grams. Apples weighing...
The lifetimes, in hours, of a particular type of light bulb are normally distributed with mean 2000 hours and standard deviation σ hours. The proba...
The heights, in cm, of the 11 members of the Anvils athletics team and the 11 members of the Brecons swimming team are shown below. Anvils 173 158 ...
The coefficient of x² in the expansion of (4 + ax)(1 + x/2)^6 is 3. Find the value of the constant a.
The point M is the mid-point of the line joining the points (3, 7) and (−1, 1). Find the equation of the line through M which is parallel to the li...
A curve is such that dy/dx = k/√x, where k is a constant. The points P (1, -1) and Q (4, 4) lie on the curve. Find the equation of the curve.
The diagram shows a circle with centre O and radius r cm. Points A and B lie on the circle and angle AOB = 2θ radians. The tangents to the circle a...
The diagram shows a solid cone which has a slant height of 15 cm and a vertical height of h cm. [Figure 5]
Given that x > 0, find the two smallest values of x, in radians, for which 3 tan(2x + 1) = 1. Show all necessary working.
The diagram shows a three-dimensional shape OABCDEFG. The base OABC and the upper surface DEFG are identical horizontal rectangles. The parallelogr...
Find the distance she runs on the last day of the 21-day period.
Functions f and g are defined by f(x) = 2x² + 8x + 1 for x ∈ R, g(x) = 2x - k for x ∈ R, where k is a constant.
The diagram shows part of the curve y = 1 - 4/(2x + 1)². The curve intersects the x-axis at A. The normal to the curve at A intersects the y-axis a...
Solve the inequality |2x – 7| < |2x – 9|.
Find the exact value of ∫₀¹ (2e^(2x) – 1)² dx. Show all necessary working.
A curve has equation y = (3 + 2 ln x) / (1 + ln x). Find the exact gradient of the curve at the point for which y = 4.