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.
Given that A = (2 -1 / 3 5 / 7 4) and B = (1 -2 4 / -2 3 0), calculate 2BA.
Solve the following equations to find p and q. 8^(q-1) × 2^(2p+1) = 4⁷ 9^(p-4) × 3^q = 81
The figure shows part of the graph of y = a + b sin cx. [Figure 6.1]
A cone, of height 8 cm and base radius 6cm, is placed over a cylinder of radius r cm and height h cm and is in contact with the cylinder along the ...
Solutions to this question by accurate drawing will not be accepted. Two points A and B have coordinates (–3, 2) and (9, 8) respectively.
Solve the following equations.
A particle is moving in a straight line such that its velocity, v ms⁻¹, t seconds after passing a fixed point O is v = e^(2t) - 6e^(-2t) - 1.
Sets E, A and B are such that n(E) = 26, n(A ∩ B) = 7, n(A ∪ B) = 3 and n(B) = 15. Using a Venn diagram, or otherwise, find. It is given that E = {...
Given that (p^(1/2)q^(1/3)r^(2/3))/(p^(-1/5)(qr)^(3/2)) = p^a q^b r^c , find the value of each of the integers a, b and c.
By using the substitution y = log₃x, or otherwise, find the values of x for which 3 (log₃x)² + log₃x⁵ – log₃9 = 0.
Find the first 3 terms in the expansion of (2x² - 1/(3x))⁵, in descending powers of x.
Find the equation of the normal to the curve y = (1/2)ln(3x + 2) at the point P where x = -1/3.
Matrices X, Y and Z are such that X = ((2, 3), (4, -1), (6, 5)), Y = (1 -1 0) and Z = ((0, -1), (5, 3)). Write down all the matrix products which a...
The diagram shows part of the graph of y = 2 cos (x - π/6). The graph intersects the y-axis at the point A, has a maximum point at B and intersects...
The diagram shows a sector AOB of the circle, centre O, radius 12cm, together with points C and D such that ABCD is a rectangle. The angle AOB is θ...
Do not use a calculator in this question. The polynomial p(x) is ax³ - 4x² + bx + 18. It is given that p(x) and p'(x) are both divisible by 2x-3.
The diagram shows part of the velocity-time graph for a particle, moving at vms⁻¹ in a straight line, ts after passing through a fixed point. The p...
The variables x and y are such that when lny is plotted against x, a straight line graph is obtained. This line passes through the points x = 4, ln...
Solve the equation |4x-3|=x.
Without using a calculator, find the integers a and b such that a/(√3+1) + b/(√3-1) = √3-3.
Solve the equation 2lgx - lg((x+10)/2) = 1.
The number of bacteria, N, present in a culture can be modelled by the equation N = 7000+2000e-0.05t, where t is measured in days. Find
The curve with equation y = x³ + 2x²-7x+2 passes through the point A (-2, 16). Find
Prove that cosx/(1+tanx) - sinx/(1+cotx) = cosx - sinx.
3 cm P x cm R 8 S 14 cm [Figure 7]
The function f(x) is given by f(x) = (3x³-1)/(x³+1) for 0 ≤ x ≤ 3.
The line y = kx – 4, where k is a positive constant, passes through the point P (0, -4) and is a tangent to the curve x² + y² - 2y = 8 at the point...
The town of Cambley is 5 km east and p km north of Edwintown so that the position vector of Cambley from Edwintown is (5000 / 1000p) metres. Manjit...
Mr and Mrs Coldicott have 5 sons and 4 daughters. All 11 members of the family play tennis. Six members of the family enter a tennis competition wh...
On the Venn diagram below, draw sets X and Y such that n(X∩ Y) = 0.
The graph of y = a sin(bx) + c has an amplitude of 4, a period of π/3 and passes through the point (π/12, 2). Find the value of each of the constan...
Find, in ascending powers of x, the first 3 terms in the expansion of (2 - x²/4)⁵.
Given that y = ln(3x² + 2) / (x² + 1), find the value of dy/dx when x = 2, giving your answer as a + b ln14, where a and b are fractions in their s...
When lgy is plotted against x, a straight line is obtained which passes through the points (0.6, 0.3) and (1.1, 0.2).
Functions f and g are defined, for x > 0, by f(x) = lnx, g(x) = 2x² + 3.
A polynomial p(x) is ax³ + 8x² + bx + 5, where a and b are integers. It is given that 2x - 1 is a factor of p(x) and that a remainder of -25 is obt...
The diagram shows a river which is 120m wide and is flowing at 4 ms⁻¹. Points A and B are on opposite sides of the river such that B is 50m downstr...
The diagram shows the displacement-time graph of a particle P which moves in a straight line such that, ts after leaving a fixed point O, its displ...
The diagram shows an isosceles triangle ABC, where AB = AC = 5cm. The arc BEC is part of the circle centre A and has length 6.2cm. The point D is t...
Solve 2 cot(φ + 35°) = 5 for 0° ≤ φ ≤ 360°.
If z = 2 + √3 find the integers a and b such that az² + bz = 1 + √3.
Solve the equation 2x^1.5 + 6x^-0.5 / x^0.5+ 5x^-0.5 = x.
Solve the inequality |3x - 1| > 3 + x.
Solve the simultaneous equations log2(x + 4) = 2log2y, log2 (7y - x) = 4.
Naomi is going on holiday and intends to read 4 books during her time away. She selects these books from 5 mystery, 3 crime and 2 romance books. Fi...
The volume of a closed cylinder of base radius x cm and height h cm is 500 cm³.
The gradient of the normal to a curve at the point with coordinates (x, y) is given by √x / (1 - 3x).
The matrix A is (2 1 / 4 3).
Find d/dx (x ln x).
Without using a calculator, solve the equation 6c³ - 7c² + 1 = 0.