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 number of absences per week by workers at a factory has the distribution Po(2.1).
The time, in minutes, for Anjan's journey to work on Mondays has mean 38.4 and standard deviation 6.9.
On average, 1 in 50000 people have a certain gene.
A six-sided die has faces marked 1, 2, 3, 4, 5, 6. When the die is thrown 300 times it shows a six on 56 throws.
A random variable X takes values between 0 and 3 only and has probability density function as shown in the diagram, where c is a constant. [Figure ...
The areas, X cm², of petals of a certain kind of flower have mean µ cm². In the past it has been found that μ = 8.9. Following a change in the clim...
Customers arrive at a shop at a constant average rate of 2.3 per minute. It is now given that the number of customers arriving per minute has the d...
A biscuit manufacturer claims that, on average, 1 in 3 packets of biscuits contain a prize offer. Gerry suspects that the proportion of packets con...
Before a certain type of book is published it is checked for errors, which are then corrected. For costing purposes each error is classified as eit...
Solve the equation 2 cos θ = 7 - 3/cos θ for -90° < θ < 90°.
The graph of y = f(x) is transformed to the graph of y = f(2x) – 3.
The function f is defined as follows: f(x) = (x + 3)/(x - 1) for x > 1.
A curve is such that dy/dx = 8 / (3x + 2)². The curve passes through the point (2, 5²/₃). Find the equation of the curve.
The first, third and fifth terms of an arithmetic progression are 2 cos x, -6√3 sin x and 10 cos x respectively, where π/6 < x < π.
The second term of a geometric progression is 54 and the sum to infinity of the progression is 243. The common ratio is greater than ¹/₂. Find the ...
In the diagram the lengths of AB and AC are both 15 cm. The point P is the foot of the perpendicular from C to AB. The length CP = 9cm. An arc of a...
It is given that in the expansion of (4 + 2x)(2 – ax)⁵, the coefficient of x² is −15. Find the possible values of a.
The volume V m³ of a large circular mound of iron ore of radius r m is modelled by the equation V = (9/2)(r - 1/2)³ – 1 for r ≥ 2. Iron ore is adde...
The function f is defined by f(x) = x² + k/x + 2 for x > 0.
The diagram shows the line x = 5/2, part of the curve y = (1/2)x + 7/10 - 1/(x-2)³ and the normal to the curve at the point A (3, 5/2). [Figure X.X]
The diagram shows the circle with equation x² + y² – 6x + 4y – 27 = 0 and the tangent to the circle at the point P (5, 4). [Figure X.X]
Find the exact value of ∫₋₁² (4e²ˣ - 2e⁻ˣ) dx.
Sketch, on the same diagram, the graphs of y = 3x and y = |x − 3|.
The variables x and y satisfy the equation aʸ = kx, where a and k are constants. The graph of y against In x is a straight line passing through the...
The curve with equation y = xe²ˣ + 5e⁻ˣ has a minimum point M.
The diagram shows the curve with parametric equations x = ln(2t + 3), y = (2t-3)/(2t+3). [Figure 5.1] The curve crosses the y-axis at the point A a...
The polynomials f(x) and g(x) are defined by f(x) = 4x³ + ax² + 8x + 15 and g(x) = x² + bx + 18, where a and b are constants.
By first expanding cos(2θ + θ), show that cos 3θ = 4 cos³ θ – 3 cos θ.
The polynomial p(x) is defined by p(x) = ax³ + bx – 10, where a and b are constants. It is given that (x + 2) is a factor of p(x) and that the rema...
Sketch, on the same diagram, the graphs of y = x + 3 and y = |2x – 1|.
The curve with equation y = 5x – 2 tan 2x has exactly one stationary point in the interval 0 ≤ x < ¼π. Find the coordinates of this stationary poin...
Given that ∫ (from a to a+14) (1/3x) dx = ln 2, find the value of the positive constant a.
A curve has equation x² + 4x cos 3y = 6. Find the exact value of the gradient of the normal to the curve at the point (√2, π/12).
By sketching a suitable pair of graphs on the same diagram, show that the equation ln x = 2e^(–x) has exactly one root.
Prove that 4 sin x sin(x + π/6) = √3 – √3 cos 2x + sin 2x.
Find the exact value of ∫₂₋₁(4e²ˣ - 2e⁻ˣ) dx.
The variables x and y satisfy the equation aʸ = kx, where a and k are constants. The graph of y against ln x is a straight line passing through the...
The curve with equation y = xe²ˣ + 5e⁻ˣ has a minimum point M.
The diagram shows the curve with parametric equations x = ln(2t + 3), y = (2t-3)/(2t+3). The curve crosses the y-axis at the point A and the x-axis...
The polynomials f(x) and g(x) are defined by f(x) = 4x³ + ax² + 8x + 15 and g(x) = x² + bx + 18, where a and b are constants.
By first expanding cos(2θ + θ), show that cos 3θ = 4 cos³ θ – 3 cos θ.
Solve the equation 4|5ˣ – 1| = 5ˣ, giving your answers correct to 3 decimal places.
Express 5 sin x – 3 cos x in the form Rsin(x – α), where R > 0 and 0 < α < ½π. Give the exact value of R and give α correct to 2 decimal places.
The curve with equation y = xe¹⁻²ˣ has one stationary point.
Using the substitution u = √x, find the exact value of ∫₈₃ (1 / (x+1)√x) dx.
Show that the equation cot 2θ + cot θ = 2 can be expressed as a quadratic equation in tan θ.
When (a + bx)√1 + 4x, where a and b are constants, is expanded in ascending powers of x, the coefficients of x and x² are 3 and –6 respectively. Fi...
Given that y = ln(lnx), show that `dy/dx = 1/(x lnx)`.
The constant a is such that ∫ᵃ₁ (lnx / √x) dx = 6. [exp(x) is an alternative notation for eˣ.]
Two lines l and m have equations r = 3i + 2j + 5k + s(4i – j + 3k) and r = i − j − 2k + t(−i + 2j + 2k) respectively.