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.
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.
Express lga + 3lgb – 3 as a single logarithm.
Shade the region corresponding to the set given below each Venn diagram.
Solve the equation 16^(3x-2) = 8^(2x).
On the diagram above, sketch the curve y = 1 + 3sin2x for 0° ≤ x ≤ 180°. [Figure 5.1]
The curves y = x² and 3y = −2x² + 20x – 20 meet at the point A. [Figure 6.1]
The points A and B have coordinates (–2, 15) and (3, 5) respectively. The perpendicular to the line AB at the point A (–2, 15) crosses the y-axis a...
The matrices A, B and C are given by A = (2 1 / 1 3 / 2 5), B = (2 1 3 4 / 1 5 6 7) and C = (9 10). Write down, but do not evaluate, matrix product...
A body moves in a straight line such that, t s after passing through a fixed point O, its displacement from O is s m. The velocity v ms⁻¹ of the bo...
(a) A curve is such that dy/dx = ae^(1-x) - 3x², where a is a constant. At the point (1, 4), the gradient of the curve is 2.
(a) The function f is such that f(x) = 2x² – 8x + 5.
Find the value of k for which the x-axis is a tangent to the curve y = x² + (2k + 10)x + k² + 5.
The coefficient of x³ in the expansion of (2 + ax)⁵ is 10 times the coefficient of x in the expansion of (1 + (ax/3))⁴. Find the value of a.
The figure shows the graph of y= k+ m sin px for 0 ≤ x ≤ π, where k, m and p are positive constants. [Figure 3.1]
You must not use a calculator in Question 4. In the triangle ABC, angle B = 90°, AB = 4+ 2√2 and BC = 1 + √2 .
Show that 2x – 1 is a factor of 2x³ – 5x² + 10x – 4.
The figure shows the graph of a straight line with lg y plotted against x. The straight line passes through the points A (5,3) and B (15,5). [Figur...