Cambridge & Pearson Edexcel Past Paper Questions

The lines l and m have vector equations r = −i + 3j + 4k + λ(2i – j – k) and r = 5i + 4j + 3k + µ(ai + bj + k) respectively, where a and b are cons...

The complex number −1 + √7i is denoted by u. It is given that u is a root of the equation 2x³ + 3x² + 14x + k = 0, where k is a real constant.

Find, in terms of a, the set of values of x satisfying the inequality 2|3x + a| < |2x + 3a|, where a is a positive constant.

Solve the equation cos(θ – 60°) = 3 sin θ, for 0° ≤ θ ≤ 360°.

Show that the equation log₃(2x + 1) = 1 + 2log₃(x – 1) can be written as a quadratic equation in x.

The curve y = e⁻⁴ˣ tan x has two stationary points in the interval 0 < x < ½π.

The complex number 3 – i is denoted by u.

The parametric equations of a curve are x = 1/cos t, y = ln tan t, where 0 < t < ½π.

Let f(x) = (5x² + 8x - 3) / ((x-2)(2x² + 3)).

At time t days after the start of observations, the number of insects in a population is N. The variation in the number of insects is modelled by a...

With respect to the origin O, the point A has position vector given by OA = i + 5j + 6k. The line l has vector equation r = 4i + k + λ(−i + 2j + 3k).

The constant a is such that ∫(from 1 to a) x² ln x dx = 4.

A car starts from rest and moves in a straight line with constant acceleration for a distance of 200m, reaching a speed of 25 ms¯¹. The car then tr...

Two particles P and Q, of masses 0.5 kg and 0.3 kg respectively, are connected by a light inextensible string. The string is taut and P is vertical...

A crate of mass 300kg is at rest on rough horizontal ground. The coefficient of friction between the crate and the ground is 0.5. A force of magnit...

Three coplanar forces of magnitudes 20N, 100N and F N act at a point. The directions of these forces are shown in the diagram. Given that the three...

Two racing cars A and B are at rest alongside each other at a point O on a straight horizontal test track. The mass of A is 1200kg. The engine of A...

A particle starts from a point O and moves in a straight line. The velocity vms¯¹ of the particle at time ts after leaving O is given by v = k(3t² ...

Two particles A and B, of masses 0.4kg and 0.2kg respectively, are moving down the same line of greatest slope of a smooth plane. The plane is incl...

Small smooth spheres A and B, of equal radii and of masses 5 kg and 3 kg respectively, lie on a smooth horizontal plane. Initially B is at rest and...

Coplanar forces of magnitudes 60N, 20N, 16N and 14N act at a point in the directions shown in the diagram. [Figure 2.1]

Two particles A and B, of masses 2.4kg and 1.2kg respectively, are connected by a light inextensible string which passes over a fixed smooth pulley...

A particle A, moving along a straight horizontal track with constant speed 8ms⁻¹, passes a fixed point O. Four seconds later, another particle B pa...

A block of mass 12kg is placed on a plane which is inclined at an angle of 24° to the horizontal. A light string, making an angle of 36° above a li...

A car of mass 900kg is moving up a hill inclined at sin⁻¹ 0.12 to the horizontal. The initial speed of the car is 11 ms⁻¹. After 12s, the car has t...

A particle P moves in a straight line. The velocity vms⁻¹ at time t seconds is given by v = 0.5t for 0≤t≤ 10, v = 0.25t² – 8t + 60 for 10 ≤ t ≤ 20.

Two particles P and Q, of masses 0.3kg and 0.2kg respectively, are at rest on a smooth horizontal plane. P is projected at a speed of 4ms⁻¹ directl...

A particle P is projected vertically upwards from horizontal ground. P reaches a maximum height of 45 m. After reaching the ground, P comes to rest...

The displacement of a particle moving in a straight line is s metres at time t seconds after leaving a fixed point O. The particle starts from rest...

The diagram shows a block of mass 10kg suspended below a horizontal ceiling by two strings AC and BC, of lengths 0.8 m and 0.6 m respectively, atta...

A cyclist is riding along a straight horizontal road. The total mass of the cyclist and her bicycle is 70kg. At an instant when the cyclist's speed...

Two particles P and Q, of masses 0.3kg and 0.2kg respectively, are attached to the ends of a light inextensible string. The string passes over a fi...

A particle P moves in a straight line through a point O. The velocity vms⁻¹ of P, at time t s after passing O, is given by `v = 9/4 + b / (t+1)² - ...

Find the number of different arrangements of the 8 letters in the word DECEIVED in which all three Es are together and the two Ds are together.

There are 6 men and 8 women in a Book Club. The committee of the club consists of five of its members. Mr Lan and Mrs Lan are members of the club.

The times taken to travel to college by 2500 students are summarised in the table. Time taken (t minutes) | 0 ≤ t < 20 | 20 < t < 30 | 30 ≤ t < 40 ...

Jacob has four coins. One of the coins is biased such that when it is thrown the probability of obtaining a head is 7/10. The other three coins are...

The lengths, in cm, of the leaves of a particular type are modelled by the distribution N(5.2, 1.5²).

Janice is playing a computer game. She has to complete level 1 and level 2 to finish the game. She is allowed at most two attempts at any level. • ...

For n values of the variable x, it is given that Σ(x – 200) = 446 and Ex = 6846.

A fair 6-sided die has the numbers 1, 2, 2, 3, 3, 3 on its faces. The die is rolled twice. The random variable X denotes the sum of the two numbers...

The back-to-back stem-and-leaf diagram shows the diameters, in cm, of 19 cylindrical pipes produced by each of two companies, A and B. Company A | ...

The weights, in kg, of bags of rice produced by Anders have the distribution N(2.02, 0.03²).

In a large college, 28% of the students do not play any musical instrument, 52% play exactly one musical instrument and the remainder play two or m...

The 9 letters in the word CROCODILE are: C (2), R (1), O (2), D (1), I (1), L (1), E (1).

Hanna buys 12 hollow chocolate eggs that each contain a sweet. The eggs look identical but Hanna knows that 3 contain a red sweet, 4 contain an ora...

The time taken, t minutes, to complete a puzzle was recorded for each of 150 students. These times are summarised in the table. Time taken (t minut...

Twenty children were asked to estimate the height of a particular tree. Their estimates, in metres, were as follows. 4.1, 4.2, 4.4, 4.5, 4.6, 4.8, ...

The random variable X takes the values −2, 1, 2, 3. It is given that P(X = x) = kx², where k is a constant.

Ramesh throws an ordinary fair 6-sided die.