Cambridge & Pearson Edexcel Past Paper Questions

Mrs Rupal chooses 3 animals at random from 5 dogs and 2 cats. The random variable X is the number of cats chosen.

The lengths, t minutes, of 242 phone calls made by a family over a period of 1 week are summarised in the frequency table below. Length of phone ca...

(a) Find the number of ways in which all 9 letters of the word AUSTRALIA can be arranged in each of the following cases. (i) All the vowels (A, I, ...

In a certain country, 60% of mobile phones sold are made by Company A, 35% are made by Company B and 5% are made by other companies.

The masses in kilograms of 50 children having a medical check-up were recorded correct to the nearest kilogram. The results are shown in the table....

The random variable X has the distribution N(−3, σ²). The probability that a randomly chosen value of X is positive is 0.25.

The members of a swimming club are classified either as 'Advanced swimmers' or 'Beginners'. The proportion of members who are male is x, and the pr...

Farfield Travel and Lacket Travel are two travel companies which arrange tours abroad. The numbers of holidays arranged in a certain week are recor...

A game is played with 3 coins, A, B and C. Coins A and B are biased so that the probability of obtaining a head is 0.4 for coin A and 0.75 for coin...

The diameters of apples in an orchard have a normal distribution with mean 5.7cm and standard deviation 0.8 cm. Apples with diameters between 4.1 c...

Find the number of ways the 9 letters of the word SEVENTEEN can be arranged in each of the following cases. 5 letters are chosen from the 9 letters...

Find the coefficient of x in the expansion of (2/x - 3x)^5

Two points A and B have coordinates (1, 3) and (9, –1) respectively. The perpendicular bisector of AB intersects the y-axis at the point C. Find th...

A curve is such that dy/dx = x^3 - 4/x^2. The point P (2, 9) lies on the curve.

Angle x is such that sinx = a + b and cos x = a – b, where a and b are constants.

The diagram shows a semicircle with diameter AB, centre O and radius r. The point C lies on the circumference and angle AOC = θ radians. The perime...

The equation of a curve is y = 3 cos 2x and the equation of a line is 2y + 3x/π = 5.

Functions f and g are defined by f : x ↦ 3x – 2, x ∈ R, g : x ↦ (2x + 3)/(x – 1), x ∈ R, x ≠ 1.

The position vectors of points A and B, relative to an origin O, are given by OA = (6, -2, -6) and OB = (3, k, -3), where k is a constant.

The curve C₁ has equation y = x² – 4x + 7. The curve C₂ has equation y² = 4x + k, where k is a constant. The tangent to C₁ at the point where x = 3...

(a) In an arithmetic progression, the sum of the first ten terms is equal to the sum of the next five terms. The first term is a. (b) The sum to in...

The diagram shows part of the curve y = √(4x + 1) + 9/√(4x + 1) and the minimum point M. [Figure 11.1]

Show that ln(x³ – 4x) – ln(x² – 2x) = ln(x + 2).

Solve the inequality |3x – 5| < |x + 3|.

Find the equation of the normal to the curve x² ln y + 2x + 5y = 11 at the point (3, 1).

Find ∫ tan² 3x dx.

The polynomial p(x) is defined by p(x) = 5x³ + ax² + bx – 16, where a and b are constants. It is given that (x – 2) is a factor of p(x) and that th...

The diagram shows the curve with equation y = (8 + x³)/(2 - 5x). The maximum point is denoted by M.

Show that 2 cosec 2θ cot θ = cosec² θ.

The polynomial p(x) is defined by p(x) = 4x³ + (k + 1)x² – mx + 3k, where k and m are constants. Given that (x + 1) is a factor of p(x), express m ...

Solve the equation |4 + 2x| = |3 – 5x|.

Find the exact coordinates of the stationary point of the curve with equation y = 3x / ln x

Find the exact value of ∫(from 0 to π/2) (4 sin 2x + 2 cos²x)dx. Show all necessary working.

Find the quotient and remainder when 2x³ + x² – 8x is divided by (2x + 1).

The diagram shows the curve with parametric equations x = 3t - 6e⁻²ᵗ, y = 4t eᵗ, for 0 ≤ t ≤ 2. At the point P on the curve, the y-coordinate is 1....

Express 4 sin θ + 4 cos θ in the form R sin(θ + α), where R > 0 and 0° < α < 90°.

Find the exact coordinates of the stationary point of the curve with equation y = 3x / ln x.

Find the quotient and remainder when 2x³ + x2 – 8x is divided by (2x + 1).

The diagram shows the curve with parametric equations x = 3t - 6e⁻²ᵗ, y = 4teᵗ, for 0 ≤ t ≤ 2. At the point P on the curve, the y-coordinate is 1. ...

Use the trapezium rule with 3 intervals to estimate the value of 3 ∫ |2ˣ – 4|dx. 0

Showing all necessary working, solve the equation ln(2x – 3) = 2lnx – ln(x – 1). Give your answer correct to 2 decimal places.

Find the gradient of the curve x³ + 3xy² – y³ = 1 at the point with coordinates (1, 3).

By first expressing the equation cot θ – cot(θ + 45°) = 3 as a quadratic equation in tan θ, solve the equation for 0° < θ < 180°.

Differentiate 1 with respect to θ. sin²θ

By first expanding sin(2x + x), show that sin 3x = 3 sin x – 4 sin³ x.

The diagram shows the curves y = 4 cos ½x and y = 1/(4-x) for 0 ≤ x < 4. When x = a, the tangents to the curves are perpendicular.

Let f(x) = (16-17x) / ((2 + x)(3 - x)²).

The diagram shows a set of rectangular axes Ox, Oy and Oz, and four points A, B, C and D with position vectors **OA** = 3**i**, **OB** = 3**i** + 4...

Throughout this question the use of a calculator is not permitted. The complex number (√3) + i is denoted by u.

Find the coefficient of x³ in the expansion of (3 – x)(1 + 3x)⅓ in ascending powers of x.