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 starting from rest from a point O. The acceleration of the particle at time t s after leaving O is a m s⁻², whe...
A toy railway locomotive of mass 0.8kg is towing a truck of mass 0.4kg on a straight horizontal track at a constant speed of 2ms⁻¹. There is a cons...
The diagram shows a block D of mass 100kg supported by two sloping struts AD and BD, each attached at an angle of 45° to fixed points A and B respe...
A block B, of mass 2kg, lies on a rough inclined plane sloping at 30° to the horizontal. A light rope, inclined at an angle of 20° above a line of ...
The diagram shows a smooth track which lies in a vertical plane. The section AB is a quarter circle of radius 1.8 m with centre O. The section BC i...
Each year the total number of hours, x, of sunshine in Kintoo is recorded during the month of June. The results for the last 60 years are summarise...
Alisha has four coins. One of these coins is biased so that the probability of obtaining a head is 0.6. The other three coins are fair. Alisha thro...
80% of the residents of Kinwawa are in favour of a leisure centre being built in the town. 20 residents of Kinwawa are chosen at random and asked, ...
The probability that it will rain on any given day is x. If it is raining, the probability that Aran wears a hat is 0.8 and if it is not raining, t...
Marco has four boxes labelled K, L, M and N. He places them in a straight line in the order K, L, M, N with K on the left. Marco also has four colo...
In a cycling event the times taken to complete a course are modelled by a normal distribution with mean 62.3 minutes and standard deviation 8.4 min...
Find the number of different arrangements of the 9 letters in the word DELIVERED in which the three Es are together and the two Ds are not next to ...
Anita carried out a survey of 140 randomly selected students at her college. She found that 49 of these students watched a TV programme called Bunch.
The number of orders arriving at a shop during an 8-hour working day is modelled by the random variable X with distribution Po(25.2).
The diagram shows the graph of the probability density function, f, of a random variable X that takes values between x = 0 and x = 3 only. The grap...
The number of accidents per 3-month period on a certain road has the distribution Po(λ). In the past the value of λ has been 5.7. Following some ch...
The masses, in grams, of large and small packets of Maxwheat cereal have the independent distributions N(410.0, 3.6²) and N(206.0, 3.7²) respectively.
Last year, the mean time taken by students at a school to complete a certain test was 25 minutes. Akash believes that the mean time taken by this y...
Find the exact value of ∫₃infty 2/(x²)dx.
The diagram shows part of the curve with equation y = k sin1/2x, where k is a positive constant and x is measured in radians. The curve has a minim...
A curve is such that dy/dx = 3(4x+5)^(1/2). It is given that the points $(1,9)$ and (5, a) lie on the curve. Find the value of a.
Prove that ((sinθ + cosθ)²-1)/(cos²θ) ≡ 2 tanθ.
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...