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 curve has the equation y = 3/(2x²-5). Find the equation of the normal to the curve at the point $(2,1)$, giving your answer in the form ax+by+c =...
It is given that the coefficient of x³ in the expansion of (2+ax)⁴(5-ax) is 432. Find the value of the constant a.
The straight line y = x+5 meets the curve 2x² + 3y² = k at a single point P.
An arithmetic progression is such that its first term is 6 and its tenth term is 19.5. Find the sum of the first 100 terms of this arithmetic progr...
The functions f and g are defined for all real values of x by f(x) = (3x-2)²+k and g(x) = 5x-1, where k is a constant.
The diagram shows the circle with centre C(-4,5) and radius √20 units. The circle intersects the y-axis at the points A and B. The size of angle AC...
The diagram shows the curve with equation y = 2x^(3/2) - 3x^(1/2) + 1 for x > 0. The curve crosses the x-axis at points A and B and has a minimum p...
Use logarithms to solve the equation 3⁴ˣ⁺³ = 5²ˣ⁺⁷. Give your answer correct to 3 significant figures.
Sketch the graph of y = |3x-7|, stating the coordinates of the points where the graph meets the axes.
The polynomial p(x) is defined by p(x) = 6x³ + ax²+3x-10, where a is a constant. It is given that (2x – 1) is a factor of p(x).
The diagram shows the curve with equation y = √1+e⁰·⁵ˣ. The shaded region is bounded by the curve and the straight lines x = 0, x = 6 and y = 0. [D...
The diagram shows part of the curve with equation y = x³/(x+2). At the point P, the gradient of the curve is 6. [Diagram]
The diagram shows the curve with parametric equations x = 1 + √t, y = (lnt+2)(lnt-3), for 0 < t < 25. The curve crosses the x-axis at the points A ...
Prove that sin 2θ(a cotθ+b tan θ) ≡ a+b+ (a−b) cos 2θ, where a and b are constants.
Find the quotient and remainder when x⁴ - 3x³ + 9x² - 12x + 27 is divided by x² + 5.
Find the coefficient of x² in the expansion of (2x - 5)√4-x.
It is given that z = -√3 + i.
The positive numbers p and q are such that ln(p/q) = a and ln(q²p) = b. Express ln(p⁷q) in terms of a and b.
The equation of a curve is 2y² + 3xy + x = x².
The diagram shows the curve y = xe^(2x) - 5x and its minimum point M, where x = α. [Figure 7.1]
Express `3sinx + 2√2cos(x + (1/4)π)` in the form `Rsin(x + α)`, where `R > 0` and `0 < α < (1/2)π`. State the exact value of R and give α correct t...
Relative to the origin O, the position vectors of the points A, B and C are given by OA = 5i-2j+k, OB = 8i+2j-6k and OC = 3i+4j-7k.
Let `f(x) = 36a² / ((2a+x)(2a-x)(5a-2x))`, where a is a positive constant.
The variables y and θ satisfy the differential equation `(1+y)(1+cos2θ) dy/dθ = e^(3y)`. It is given that y = 0 when θ = (1/2)π. Solve the differen...
The displacement of a particle at time t s after leaving a fixed point O is s m. The diagram shows a displacement-time graph which models the motio...
A particle is projected vertically upwards from horizontal ground. The speed of the particle 2 seconds after it is projected is 5 m s⁻¹ and it is t...
A crate of mass 600 kg is being pulled up a line of greatest slope of a rough plane at a constant speed of 2 m s⁻¹ by a rope attached to a winch. T...
Four coplanar forces act at a point. The magnitudes of the forces are FN, 2FN, 3FN and 30N. The directions of the forces are as shown in the diagra...
A particle moves in a straight line starting from a point O. The velocity v m s⁻¹ of the particle t s after leaving O is given by v = t³ − 2t² + 1 ...
A car of mass 1800kg is towing a trailer of mass 300kg up a straight road inclined at an angle α to the horizontal, where sinα = 0.05. The car and ...
The diagram shows two particles P and Q which lie on a line of greatest slope of a plane ABC. Particles P and Q are each of mass m kg. The plane is...
A bag contains 9 blue marbles and 3 red marbles. One marble is chosen at random from the bag. If this marble is blue, it is replaced back into the ...
Sam is a member of a soccer club. She is practising scoring goals. The probability that Sam will score a goal on any attempt is 0.7, independently ...
The times taken, in minutes, by 150 students to complete a puzzle are summarised in the table. Time taken (t minutes) 0 < t < 20 20 ≤ t < 30 30 < t...
A company sells small and large bags of rice. The masses of the small bags of rice are normally distributed with mean 1.20 kg and standard deviatio...
Anil is taking part in a tournament. In each game in this tournament, players are awarded 2 points for a win, 1 point for a draw and 0 points for a...
A new village social club has 10 members of whom 6 are men and 4 are women. The club committee will consist of 5 members.
The lengths, Xcm, of a sample of 100 insects of a certain type were summarised as follows. n = 100 Σx = 36.8 Σχ² = 17.34
A random sample of 250 people living in Barapet was chosen. It was found that 78 of these people owned a BETEC phone.
In a certain lottery, on average 1 in every 10000 tickets is a prize-winning ticket. An agent sells 6000 tickets.
Each year a transport firm uses X litres of gasoline and Y litres of diesel fuel, where X and Y have the independent distributions X ~ N(10700, 950...
A teacher models the numbers of girls and boys who arrive late for her class on any day by the independent random variables G ~ Po(0.10) and B ~ Po...
The graph of the probability density function f of a random variable X is symmetrical about the line x = 2. It is given that P(2 < X < 5) = 117/256.
The heights, in centimetres, of adult females in Litania have mean μ and standard deviation σ. It is known that in 2004 the values of μ and σ were ...
A curve has equation y = 5+3x-2x² and a straight line has equation y = kx+13, where k is a constant. Find the set of values of k for which the curv...
The diagram shows the curve with equation y = 2x² - 5/x + 3. The curve crosses the x-axis at the point P(1,0) and M is a minimum point. [Figure X.X]
Find the complete expansion of (2x - 3/x)⁴.
The diagram shows a triangle OAB where OA = OB = 10cm and angle AOB = 0.8 radians. Points C and D on OA and OB respectively are such that the arc C...
An arithmetic progression has first term 5 and common difference 6. For this progression, find the sum of all the terms that lie between 150 and 400.
The diagram shows a circle C of radius r, where x > 0 and y > 0 for all points on C. The least distance between any point on C and the x-axis is 8 ...