Cambridge & Pearson Edexcel Past Paper Questions

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 ...

Show that 3 tan²θ + 5 sin²θ = (8 sin²θ - 5 sin⁴θ) / (1 - sin²θ)

A geometric progression is such that its second term is – 120 and its sum to infinity is 160.

A curve is such that d²y/dx² = 6/x⁴ - 5/x³. It is given that the curve has a stationary point at (1/2, 9).

The diagram shows the curve with equation y = 4(3x+4)¹ᐟ² - 2x - 6 for values of x such that 0 ≤ x ≤ 7. The tangent to the curve at the point P (7,0...

Functions f and g are defined for all real values of x by f(x) = 4x² - c and g(x) = 2x+k, where c and k are positive constants. It is given that g⁻...

Solve the equation ln(3x+1) – ln(x - 5) = ln 7.

A curve passes through the point with coordinates (½π, 5) and is such that dy/dx = 4 sec²(½x). Find the equation of the curve.

The diagram shows the curves y = e^2x and y = 8e^-x. The shaded region is bounded by the two curves and the y-axis. [Figure]

A curve has equation y = 4 sinx / (3 + cos 2x) for values of x such that 0 ≤ x ≤ 2π.

Sketch on the same diagram the graphs of y = |2x-3| and y = ln(x+1).

Find the quotient and remainder when 18x³ – 6x² – 30x+4 is divided by (3x-1).

Express 6 sin θ-4 cosθ in the form Rsin(θ-α), where R > 0 and 0° < α < 90°. Give the exact value of R and the value of α correct to 2 decimal places.

A curve has equation 3e^2xy + 4e^3x + y³ = 18.

Solve the equation In(1-e-2x) + 3 = 0. Give your final answer correct to 4 decimal places.

The equation of a curve is xy² +ln(x+2y) = 1. Find the gradient of the curve at the point where x = 0.

The shaded region on the Argand diagram shows points representing complex numbers z defined by two inequalities. The shaded region is bounded by a ...

By first expressing the equation tan(x-60°) = 2cotx as a quadratic equation in tanx, solve the equation for 0° ≤ x ≤ 180°.

The square roots of -4+6√5i can be expressed in the Cartesian form x+iy, where x and y are real and exact. By first forming a quartic equation in x...

The variables x and θ satisfy the differential equation dx/dθ = (½x+1)sin²2θ, and x = 5 when θ = 0. Solve the differential equation and obtain an e...

The diagram shows the curve y = x³cos2x for 0 ≤ x ≤ ¼π. The curve has a maximum point at M, where x = p. [Figure 7.1]

Two lines have equations r = (-1 3 -4) + λ(2 3 -1) and r = (2 -3 -1) + μ(-1 -2 1).

The polynomial 6x³ + ax² + bx + 9 is denoted by p(x), where a and b are constants. It is given that (x-3) is a factor of p(x), and when the first d...

Let f(x) = (-7x²+2x-6)/((1+x)(4+x²))

Find the exact value of ∫[from 0 to π/2] x² cos(x/3)dx.

Three coplanar forces of magnitudes 40N, 30N and X N act at a point in the directions shown in the diagram. [Figure X.X]

A cyclist is travelling along a straight horizontal road at a speed of 4 ms⁻¹ when she passes a point O. She accelerates at a constant rate for a d...

An aeroplane is flying at a constant speed.

Two particles A and B have masses 0.3kg and 0.1kg respectively. The particles are attached to the ends of a light inextensible string. The string p...