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.
(i) Find ∫(10e²ˣ + e⁻²ˣ)dx.
A curve has equation y = 4x + 3 cos 2x. The normal to the curve at the point where x = π/4 meets the x- and y-axes at the points A and B respective...
Solve 2cos3x = sec 3x for 0° ≤ x ≤ 120°.
Write log₂₇x as a logarithm to base 3.
The diagram shows the graph of y = |f(x)| passing through (0, 4) and touching the x-axis at (2, 0). Given that the graph of y = f(x)is a straight l...
Find the matrix A if 4A +5 [4 0 -1; 3 -2 5] = [52 -8 19; 31 2 65].
The diagram shows a circle, centre O, radius 8 cm. The points P and Q lie on the circle. The lines PT and QT are tangents to the circle and angle P...
There are twenty numbered balls in a bag. Two of the balls are numbered 0, six are numbered 1, five are numbered 2 and seven are numbered 3, as sho...
A particle P is projected from the origin O so that it moves in a straight line. At time t seconds after projection, the velocity of the particle, ...
The four points O, A, B and C are such that OA = 5a, OB = 15b, OC = 24b-3a.
Find ∫e^(4x+3) dx.
Find the set of values of x for which 4x² + 19x-5 ≤ 0.
The relationship between experimental values of two variables, x and y, is given by y = Abˣ, where A and b are constants.
The Venn diagram above shows the sets A, B and C. It is given that n(A ∪ B ∪ C) = 48, n(A) = 30, n(B) = 25, n(C) = 15, n(A ∩ B) = 7, n(B ∩ C) = 6, ...
The universal set contains all the integers from 0 to 12 inclusive. Given that A = {1, 2, 3, 8, 12}, B = {0, 2, 3, 4, 6} and C = {1, 2, 4, 6, 7, 9,...
The table shows the number of passengers in Economy class and in Business class on 3 flights from London to Paris. The table also shows the departu...
Do not use a calculator in this question. [Figure 3.1] The diagram shows the right-angled triangle ABC, where AB = (6 + 3√5)cm and angle B = 90°. T...
A river, which is 80m wide, flows at 2ms⁻¹ between parallel, straight banks. A man wants to row his boat straight across the river and land on the ...
Solve the simultaneous equations 2x² + 3y² = 7xy, x + y = 4.
Solve 6ˣ⁻² = 1/4.
In the expansion of (1 + 2x)ⁿ, the coefficient of x⁴ is ten times the coefficient of x². Find the value of the positive integer, n.
The graph of y = x² - 6x + 10 cuts the y-axis at A. The graphs of y = x² - 6x + 10 and y = x + 10 cut one another at A and B. The line BC is perpen...
Solutions by accurate drawing will not be accepted. [Figure 9.1] The line y = mx + 4 meets the lines x = 2 and x = -1 at the points P and Q respect...
The function f is defined by f:x↔|sinx| for 0° ≤x≤ 360°. On the axes below, sketch the graph of y = f(x). [Figure 10.1]
[Figure 11.1] The diagram shows a cuboid of height h units inside a right pyramid OPQRS of height 8 units and with square base of side 4 units. The...
Show that x = -2 is a root of the polynomial equation 15x³ + 26x² - 11x − 6 = 0.
Find the value of k for which the curve y = 2x² – 3x + k
Solve the equation 16^(3x−1) = 8^(x+2) .
Find the equation of the normal to the curve y = ln(2x² – 7) at the point where the curve crosses the positive x-axis. Give your answer in the form...
Given the matrices A = [[1, 2], [3, 0]] and B = [[3, 0], [1, 2]], find A² - 2B.
Do not use a calculator in this question.
The function f is defined by f(x) = 2 - √x+5 for -5 ≤ x < 0.
The diagram shows a river with parallel banks. The river is 75 m wide and is flowing with a speed of 2.4 ms⁻¹. A speedboat travels in a straight li...
Solutions to this question by accurate drawing will not be accepted. Three points have coordinates A(-8, 6), B(4, 2) and C(-1, 7) . The line throug...
Show that 2cosx cotx + 1 = cotx + 2cosx can be written in the form (a cosx - b)(cosx - sinx) = 0, where a and b are constants to be found.
Given that f(x) = 4x³ + kx + p is exactly divisible by x + 2 and f'(x) is exactly divisible by 2x-1, find the value of k and of p.
The diagram shows a circle, centre O, radius r cm. The points A and B lie on the circle such that angle AOB = 2θ radians. [Figure 11.1]
The universal set & is the set of real numbers and sets X, Y and Z are such that X= {integer multiples of 5}, Y = {integer multiples of 10}, Z = {π...
The first 3 terms in the expansion of (2 - 1/(4x))^5 are a + b/x + c/x². Find the value of each of the integers a, b and c.
Vectors a, b and c are such that a = [[2],[y]], b = [[1],[3]] and c = [[-5],[5]]
Do not use a calculator in this question. Find the positive value of x for which (4 + √5)x² + (2 - √5)x - 1 = 0, giving your answer in the form (a ...
Show that (1 - cos θ)(1 + sec θ) = sin θ tan θ.
Show that d/dx (e^(3x) √4x + 1) can be written in the form (e^(3x) (px+q)) / √4x + 1, where p and q are integers to be found.
The diagram shows part of the graph of y = 1 - 2cos 3x, which crosses the x-axis at the point A and has a maximum at the point B.
Variables x and y are such that when lgy is plotted against x², the straight line graph shown above is obtained.
A curve passes through the point (2, -4/3) and is such that dy/dx = (3x + 10)^(-1/2).
The diagram shows a badge, made of thin sheet metal, consisting of two semi-circular pieces, centres B and C, each of radius x cm. They are attache...
Find the values of x for which (x - 4)(x + 2) > 7.
[Figure 2(a) showing an empty rectangle labelled E for a Venn diagram.] It is given that the elements of set E are the letters of the alphabet, the...
The diagram shows 3 circles with centres A, B and C, each of radius 5 cm. Each circle touches the other two circles. Angle BAC is θ radians. [Figur...