Cambridge & Pearson Edexcel Past Paper Questions

The circumference round the trunk of a large tree is measured and found to be 5.00m. After one year the circumference is measured again and found t...

Points A (7, 12) and B lie on a circle with centre (–2, 5). The line AB has equation y = −2x + 26. Find the coordinates of B.

In the expansion of (x/a + a/x²)⁷ , it is given that (the coefficient of x⁴) / (the coefficient of x) = 3. Find the possible values of the constant a.

By first obtaining a quadratic equation in cos θ, solve the equation tan θ sin θ = 1 for 0° < θ < 360°.

The diagram shows triangle ABC in which angle B is a right angle. The length of AB is 8 cm and the length of BC is 4 cm. The point D on AB is such ...

The function f is defined by f(x) = −3x² + 2 for x ≤ −1.

At the point (4, −1) on a curve, the gradient of the curve is -3/2. It is given that dy/dx = x^(-1/2) + k, where k is a constant.

The diagram shows the curve with equation x = y² + 1. The points A (5, 2) and B (2, -1) lie on the curve. [Figure 11.1]

Find the exact value of ∫₀^(π/2) 2 tan²(x) dx.

Solve the equation tan(θ – 60°) = 3 cot θ for −90° < θ < 90°.

The polynomial p(x) is defined by p(x) = ax³ – ax² + ax + b, where a and b are constants. It is given that (x + 2) is a factor of p(x), and that th...

Sketch, on the same diagram, the graphs of y = |2x – 11| and y = 3x – 3.

It is given that ∫₁ᵃ (4/(1 + 2x) + 3/x) dx = ln 10, where a is a constant greater than 1.

The diagram shows the curve with equation y = (4e^(2x) + 9)/(e^x + 2). The curve has a minimum point M and crosses the y-axis at the point P. [Figu...

The diagram shows the curve with parametric equations x = k tan t, y = 3 sin 2t - 4 sin t, for 0 < t < ½π. It is given that k is a positive constan...

It is given that x = ln(2y – 3) – ln(y + 4). Express y in terms of x.

On an Argand diagram, shade the region whose points represent complex numbers z satisfying the inequalities −⅓π ≤ arg(z − 1 − 2i) < π and Rez < 3.

The polynomial 2x⁴ + ax³ + bx − 1, where a and b are constants, is denoted by p(x). When p(x) is divided by x² – x + 1 the remainder is 3x + 2. Fin...

Solve the equation 5z / (1 + 2i) - zz* + 30 + 10i = 0, giving your answers in the form x + iy, where x and y are real.

The parametric equations of a curve are x = te²ᵗ, y = t² + t + 3.

Express 5 sin θ + 12 cos θ in the form R cos(θ – α), where R > 0 and 0 < α < ½π.

The diagram shows a circle with centre O and radius r. The angle of the minor sector AOB of the circle is x radians. The area of the major sector o...

The diagram shows the curve y = x³ ln x, for x > 0, and its minimum point M. [Figure 8.1]

The variables x and y satisfy the differential equation dy/dx = e³ʸ sin² 2x. It is given that y = 0 when x = 0. Solve the differential equation and...

With respect to the origin O, the points A, B, C and D have position vectors given by OA = (3, -1, 2), OB = (1, 2, -3), OC = (-2, 5, 1) and OD = (-...

Let f(x) = (5x² + x + 11) / ((4 + x²)(1 + x))

A crate of mass 200kg is being pulled at constant speed along horizontal ground by a horizontal rope attached to a winch. The winch is working at a...

A particle P is projected vertically upwards from horizontal ground with speed 15ms⁻¹.

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.