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.
A shop sells two makes of coffee, Café Premium and Café Standard. Both coffees come in two sizes, large jars and small jars. Of the jars on sale, 6...
The random variable X has the distribution N(μ, σ²), where μ = 1.5σ. A random value of X is chosen. Find the probability that this value of X is gr...
Hebe attempts a crossword puzzle every day. The number of puzzles she completes in a week (7 days) is denoted by X.
if digits are not repeated,
The following histogram represents the lengths of worms in a garden. [Figure X.X]
The coefficient of x² in the expansion of (2 + x/2)⁶ + (a + x)⁵ is 330. Find the value of the constant a.
The equation of a curve is y = x² – 6x + k, where k is a constant.
A company producing salt from sea water changed to a new process. The amount of salt obtained each week increased by 2% of the amount obtained in t...
The function f is such that f(x) = a + b cos x for 0 ≤ x ≤ 2π. It is given that f(π/3) = 5 and f(π) = 11.
The diagram shows a three-dimensional shape. The base OAB is a horizontal triangle in which angle AOB is 90°. The side OBCD is a rectangle and the ...
The diagram shows points A and B on a circle with centre O and radius r. The tangents to the circle at A and B meet at T. The shaded region is boun...
The function f is defined by f : x → 7 – 2x² – 12x for x ∈ R.
Points A and B have coordinates (h, h) and (4h + 6, 5h) respectively. The equation of the perpendicular bisector of AB is 3x + 2y = k. Find the val...
A curve is such that dy/dx = √(4x + 1) and (2, 5) is a point on the curve.
Solve the equation 2 cos x + 3 sin x = 0, for 0° ≤ x ≤ 360°.
The diagram shows part of the curve y = x/2 + 6/x. The line y = 4 intersects the curve at the points P and Q. [Figure 18]
Solve the equation 3e2x – 82ex + 27 = 0, giving your answers in the form k ln 3.
The variables x and y satisfy the equation y = A × Blnx, where A and B are constants. The graph of In y against Inx is a straight line passing thro...
Without using a calculator, find the exact value of ∫₂⁰ 4e⁻ˣ(e³ˣ + 1) dx.
The diagram shows the curve with equation y = 5 ln x / (2x + 1) and has a maximum point M. The curve crosses the x-axis at the point P. [Figure 4]
The parametric equations of a curve are x = 2 cos 2θ + 3 sin θ, y = 3 cos θ for 0 < θ < ½π.
The cubic polynomial f(x) is defined by f(x) = x³ + ax² + 14x + a + 1, where a is a constant. It is given that (x + 2) is a factor of f(x).
Express 5 cos θ – 2 sin θ in the form Rcos(θ + α), where R > 0 and 0 < α < ½π. Give the value of α correct to 4 decimal places.
Solve the inequality |3x-2| < |x + 5|.
A curve has equation y = 3 ln(2x + 9) – 2 lnx.
Find the quotient when x⁴ – 2x³ + 8x² – 12x + 13 is divided by x² + 6 and show that the remainder is 1.
Solve the equation 2ln(2x) – ln(x + 3) = 4 ln 2.
A curve has equation y³ sin 2x + 4y = 8. Find the equation of the tangent to the curve at the point where it crosses the y-axis.
It is given that ∫ (1 + e^(x/2))² dx from 0 to a = 10, where a is a positive constant.
Show that 2 cosec² 2x(1 – cos 2x) = sec²x.
A curve has equation y³ sin 2x + 4y = 8.
It is given that ∫₀ᵃ (1 + e½ˣ)² dx = 10, where a is a positive constant.
Show that 2 cosec²2x(1 – cos 2x) = sec²x.
Showing all necessary working, solve the equation ln(x⁴ – 4) = 4 ln x – In 4, giving your answer correct to 2 decimal places.
Given that sin(x – 60°) = 3 cos(x – 45°), find the exact value of tan x.
A curve has equation y = e³ˣ / tan(x/2). Find the x-coordinates of the stationary points of the curve in the interval 0 < x < π. Give your answers ...
The polynomial x⁴ + 2x³ + ax + b, where a and b are constants, is divisible by x² − x + 1. Find the values of a and b.
Let I = ∫(from 1/4 to 3/4) √((x)/(1-x)) dx.
In a certain chemical reaction the amount, x grams, of a substance is decreasing. The differential equation relating x and t, the time in seconds s...
Showing all working and without using a calculator, solve the equation z² + (2√6)z + 8 = 0, giving your answers in the form x + iy, where x and y a...
The positive constant a is such that ∫(from 0 to a) x e^(-x/2) dx = 2.
Let f(x) = (12x² + 4x - 1) / ((x−1)(3x + 2)).
The point P has position vector 3i – 2j + k. The line l has equation r = 4i + 2j + 5k + μ(i + 2j + 3k).
Showing all necessary working, solve the equation 3|2x – 1| = 2x, giving your answers correct to 3 significant figures.
Showing all necessary working, solve the equation cot θ + cot(θ + 45°) = 2, for 0° < θ < 180°.
In the diagram, the tangent to a curve at the point P with coordinates (x, y) meets the x-axis at T. The point N is the foot of the perpendicular f...
Show that (2 sin x - sin 2x) / (1 - cos 2x) = sin x / (1 + cos x)
The equation of a curve is x²(x + 3y) – y³ = 3.
The diagram shows a triangle ABC in which AB = AC = a and angle BAC = θ radians. Semicircles are drawn outside the triangle with AB and AC as diame...
Throughout this question the use of a calculator is not permitted. The complex numbers −3√3 + i and √3 + 2i are denoted by u and v respectively.