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.
Differentiate with respect to x
Find the first 3 terms of the expansion, in ascending powers of x, of (1 + 3x)6.
Find the set of values of k for which the equation x2 + (k – 2)x + (2k – 4) = 0 has real roots.
Copy the Venn diagram [Figure 4(a)] above and shade the region that represents (A ∩ B) U C.
Solve the equation 3x(x² + 6) = 8 – 17x2.
Given that log8p=x and log8q = y, express in terms of x and/or y
The function f is defined by f(x) = (2x + 1)² - 3 for x = -1/2.
Solve the equation (23 – 4x) (4x + 4) = 2.
Variables x and y are related by the equation y = 5x + 2 – 4e⁻ˣ. Find dy/dx
Solve 4 sinx = cosx for 0° <x<360°,
Answer only one of the following two alternatives. EITHER A curve has equation y = ln x / x², where x > 0.
OR A curve is such that dy/dx = 6 cos(2x + π/2) for -π/4 <= x <= 5π/4. The curve passes through the point (π/4, 5).
Find the coordinates of the points of intersection of the curve y² + y = 10x - 8x² and the line y + 4x + 1 = 0.
The expression 6x³ + ax² − (a + 1)x + b has a remainder of 15 when divided by x + 2 and a remainder of 24 when divided by x + 1. Show that a = 8 an...
Given that OA = ( -17 / 25 ) and OB = ( 4 / 5 ) find
Variables x and y are such that, when y² is plotted against secx, a straight line graph passing through the points (2.4, 1.6) and (1.3, 3.8) is obt...
The diagram shows part of the curve y = 6 - 3/x which passes through the point A where x = 3. The normal to the curve at the point A meets the x-ax...
On the same diagram, sketch the curves y = cosx and y=1+cos2x for 0≤x≤2π.
The table shows values of the variables p and v which are related by the equation p = kvⁿ, where k and n are constants. ν 10 50 110 230 p 1412 151 ...
Given that A = ( 4 3 / 1 2 ) and B = ( -2 0 / 1 4 ), find
The diagram shows a sector OXY of a circle centre O, radius 3cm and a sector OAB of a circle centre O, radius 8 cm. The point X lies on the line OA...
A music student needs to select 7 pieces of music from 6 classical pieces and 4 modern pieces. Find the number of different selections that she can...
A particle moves in a straight line such that its displacement, xm, from a fixed point O at time tseconds is given by x = 12{ln(2t+3)}. Find
Answer only one of the following two alternatives. EITHER The diagram shows part of a curve for which dy/dx = 8 cos 2x. The curve passes through th...
Answer only one of the following two alternatives. OR A curve is such that dy/dx = 6e³ˣ – 12. The curve passes through the point (0, 1).
The variables x and y are related so that, when y/x² is plotted against x³, a straight line graph passing through (3, 9) and (7, 1) is obtained. Ex...
In a singing competition there are 8 contestants. Each contestant sings in the first round of this competition.
It is given that x − 1 is a factor of f(x), where f(x) = x³ – 6x² + ax + b.
Given that sinx = p and cosx = 2p, where x is acute, find the exact value of p and the value of cosecx.
Given that a curve has equation y = x² + 64√x, find the coordinates of the point on the curve where d²y/dx² = 0.
The line y = x + 4 intersects the curve 2x² + 3xy − y² + 1 = 0 at the points A and B. Find the length of the line AB.
Solutions to this question by accurate drawing will not be accepted. [Figure showing quadrilateral ABCD with coordinates A(−1, 5), B(–2, 6), C(4, 1...
Given that A = (2 3 / 1 -5) and B = (7 4 / 2 8), calculate 2A,
A particle starts from rest and moves in a straight line so that, t seconds after leaving a fixed point O, its velocity, v ms⁻¹, is given by v = 4 ...
In this question, (1 / 0) is a unit vector due east and (0 / 1) is a unit vector due north. A lighthouse has position vector (27 / 48) km relative ...
Answer only one of the following two alternatives.
Find ∫ (2+5x - 1/(x-2)²) dx.
Copy the diagram and shade the region which represents the set A ∪ (B ∩ C').
The volume V cm³ of a spherical ball of radius r cm is given by V = (4/3)πr³. Given that the radius is increasing at a constant rate of 1/π cm s⁻¹,...
The diagram shows a right-angled triangle ABC in which the length of AB is 16/√2, the length of BC is 7√3 and angle BCA is θ. [Figure 4]
Solve the equation 2x³ - 3x² - 11x + 6 = 0.
The diagram shows part of the line y = 12 – 2x. The point Q(x, y) lies on this line and the points P and R lie on the coordinate axes such that OPQ...
Sketch the graph of y = |3x + 9| for -5 < x < 2, showing the coordinates of the points where the graph meets the axes.
Write down the first 4 terms, in ascending powers of x, of the expansion of (1 – 3x)⁷.
Given that y = (x+2) / (4x+12)½, show that dy/dx = k(x+4) / (4x+12)³/², where k is a constant to be found.
Given that logₚ X = 6 and logₚ Y = 4, find the value of
Solve, for 0 < x < 3 radians, the equation 4 sin x – 3 = 0, giving your answers correct to 2 decimal places.
Answer only one of the following two alternatives. EITHER It is given that f(x) = 4x² + kx + k.
Answer only one of the following two alternatives. OR The functions f, g and h are defined, for x ∈ R, by f(x) = x² + 1, g(x) = 2x - 5, h(x) = 2ˣ.
Show that (1 / (1 - cosθ)) + (1 / (1 + cosθ)) = 2cosec²θ.