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 the coefficient of x² in the expansion of (2 + px)⁶ is 60, find the value of the positive constant p.
Matrices A and B are such that A = ( (3a, 2b), (-a, b) ) and B = ( (-a, b), (2a, 2b) ) where a and b are non-zero constants.
The point P lies on the line joining A(-2, 3) and B(10,19) such that AP:PB = 1:3.
The table shows experimental values of variables x and y. | x | 2 | 2.5 | 3 | 3.5 | 4 | |---|---|-----|---|-----|---| | y | 18.8 | 29.6 | 46.9 | 7...
Find how many different 4-digit numbers can be formed using the digits 1, 2, 3, 4, 5 and 6 if no digit is repeated.
Solve 2 cos 3x = cot 3x for 0° ≤ x ≤ 90°.
The position vectors of points A and B relative to an origin O are a and b respectively. The point P is such that OP = μOA. The point Q is such tha...
On each of the Venn diagrams below shade the region which represents the given set. (A∩B) ∪ C' A' ∩ (B∪C)
Solve the inequality 9x² + 2x - 1 < (x + 1)².
Solve the following simultaneous equations. log2(x + 3) = 2 + log2y log2(x + y) = 3
The functions f and g are defined for real values of x by f(x) = √x - 1 - 3 for x > 1, g(x) = (x - 2) / (2x - 3) for x > 2.
The number of bacteria B in a culture, t days after the first observation, is given by B = 500 + 400e^(0.2t).
Calculate the coordinates of the points where the line y=x+2 cuts the curve x² + y² = 10.
A particle moving in a straight line passes through a fixed point O. The displacement, x metres, of the particle, t seconds after it passes through...
Given that y = x² / (2 + x²), show that dy/dx = kx / (2 + x²)², where k is a constant to be found.
Integers a and b are such that (a + 3√5)² + a - b√5 = 51.
Prove that sec x cosec x - cot x = tan x.
The diagram shows a sector OPQ of a circle with centre O and radius x cm. Angle POQ is 0.8 radians. The point S lies on OQ such that OS = 5cm. The ...
The diagram below shows part of the curve y = 3x - 14 + 32/x² cutting the x-axis at the points P and Q. [Figure 12.1]
Find the range of values of k for which the equation kx² + k = 8x - 2xk has 2 real distinct roots.
A curve, showing the relationship between two variables x and y, passes through the point P(-1,3). The curve has a gradient of 2 at P. Given that d...
Show that √sec²θ-1 + √cosec²θ-1 = sec θ cosec θ.
6 books are to be chosen from 8 different books.
Variables x and y are such that y = (x - 3)ln(2x² + 1).
It is given that 𝓔 = {x : 1 < x < 12, where x is an integer} and that sets A, B, C and D are such that A = {multiples of 3}, B = {prime numbers}, ...
Two variables, x and y, are such that y = Axᵇ, where A and b are constants. When lny is plotted against lnx, a straight line graph is obtained whic...
Find the equation of the tangent to the curve y = (2x-1) / √(x²+5) at the point where x = 2.
You are not allowed to use a calculator in this question. The diagram shows the graph of y = √4+x, which meets the y-axis at the point A and the li...
The diagram shows two circles, centres A and B, each of radius 10cm. The point B lies on the circumference of the circle with centre A. The two cir...
A function f is such that f(x) = x² + 6x + 4 for x≥0.
The line 2x - y + 1 = 0 meets the curve x² + 3y = 19 at the points A and B. The perpendicular bisector of the line AB meets the x-axis at the point...
It is given that f(x) = 4x³ – 4x² – 15x + 18.
Find, in the simplest form, the first 3 terms of the expansion of (2 – 3x)⁶, in ascending powers of x.
Relative to an origin O, points A, B and C have position vectors (5/4), (-10/12) and (-6/-18) respectively. All distances are measured in kilometre...
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.