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.
Do not use a calculator in this question. [Figure 2.1] The diagram shows the triangle ABC where angle B is a right angle, AB = (4 + 3√2) cm, BC = (...
Find the first 4 terms in the expansion of (2 + x²)⁶ in ascending powers of x.
Given that the matrix X = [2 -4; k 0], find X² in terms of the constant k.
The curve y = xy + x² – 4 intersects the line y = 3x – 1 at the points A and B. Find the equation of the perpendicular bisector of the line AB.
The polynomial f(x) = ax³ – 15x² + bx – 2 has a factor of 2x – 1 and a remainder of 5 when divided by x – 1.
The point A, where x = 0, lies on the curve y = ln(4x² + 3)/(x – 1). The normal to the curve at A meets the x-axis at the point B.
It is given that f(x) = 3e²ˣ for x ≥ 0, g(x) = (x + 2)² + 5 for x ≥ 0.
[Figure 9.1] The diagram shows parts of the line y = 3x + 10 and the curve y = x³ – 5x² + 3x + 10. The line and the curve both pass through the poi...
Solve 4 sin x = cosec x for 0° ≤ x ≤ 360°.
Given that the graph of y = (2k+ 5)x² + kx + 1 does not meet the x-axis, find the possible values of k.
Show that tan θ + cot θ / cosec θ = sec θ.
Find the inverse of the matrix (4 2 / 5 3) and hence solve the simultaneous equations 4x+2y-8 = 0, 5x + 3y - 9 = 0.
The diagram shows a circle, centre O, radius 12 cm. The points A, B and C lie on the circumference of this circle such that angle AOB is 1.7 radian...
(a) A security code is to be chosen using 6 of the following: • the letters A, B and C • the numbers 2, 3 and 5 • the symbols * and $. None of the ...
A particle moves in a straight line such that its displacement, x m, from a fixed point O after t s, is given by x = 10ln(t² + 4) – 4t.
In the diagram AB = 4a, BC = b and DC = 7a. The lines AC and DB intersect at the point X. Find, in terms of a and b,
(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...