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.
Answer only one of the following two alternatives. EITHER [Figure: A diagram showing a curve y = ln(x+1) - lnx. A tangent line and a normal line a...
Answer only one of the following two alternatives. OR A curve has equation y = xe^x. The curve has a stationary point at P.
The universal set & and the sets A and B shown in the Venn diagram below are such that n(A) = 15, n(B) = 20, n(A' ∩ B) = 6 and n(E) = 30. In the Ve...
On the grid below, draw on the same axes, for 0° ≤ x ≤ 180°, the graphs of y = sinx and y = 1 + cos 2x. [Figure 2.1]
It is given that 2x – 1 is a factor of the expression 4x³ + ax² – 11x + b and that the remainder when the expression is divided by x + 2 is 25. Fin...
It is given that A = (3 -2 / 1 -5) , B = (1 -4 2 / -3 0 5) and C = (4 / 2 / -7)
Four boys and three girls are to be seated in a row. Calculate the number of different ways that this can be done if
The length of a rectangular garden is xm and the width of the garden is 10m less than the length.
In the diagram AD and BE are arcs of concentric circles centre O, where OA = 6cm and AB = 8 cm. The area of the region ABED is 32 cm². The triangle...
A particle travels in a straight line so that, t s after passing through a fixed point O, its velocity, vms⁻¹, is given by v = 12cos (t/3).
It is given that f(x) = 2x² – 12x + 10.
The diagram shows part of the curve y = x³ – 9x² + 24x + 2 cutting the y-axis at the point P. The curve has a minimum point at Q. [Figure 10.1]
Answer only one of the following two alternatives. EITHER [Figure 11.1 (EITHER)] In the diagram above OA = a, OB = b, OS = (3/5)OA and OT = (7/5)OB...
It is given that a = (4 3), b = (-1 2) and c = (21 2).
Find the inverse of the matrix (2 -1 -1 1.5).
Show that cotθ + sinθ / (1 + cosθ) = cosecθ.
Given that logₐ pq = 9 and logₐ p²q = 15, find the value of
The line x – 2y = 6 intersects the curve x² + xy + 10y + 4y² = 156 at the points A and B. Find the length of AB.
[Figure 6.1] Using sin15° = √2/4 (√3 - 1) and without using a calculator, find the value of sinθ in the form a + b√2, where a and b are integers.
Solutions to this question by accurate drawing will not be accepted. [Figure 7.1] The vertices of the trapezium ABCD are the points A(−5, 4), B(8, ...
[Figure 8.1] The diagram shows an isosceles triangle OBD in which OB = OD = 18 cm and angle BOD = 1.5 radians. An arc of the circle, centre O and r...
Using the axes below, sketch for 0 ≤ x ≤ π, the graphs of y = sin 2x and y = 1+cos2x.
A function f is such that f(x) = 4x³ + 4x² + ax + b. It is given that 2x – 1 is a factor of both f(x) and f'(x).
Answer only one of the following two alternatives. EITHER A curve is such that y = 5x² / (1 + x²)
Solve the equation |7x + 5| = |3x – 13|.
The total surface area, A cm², of a solid cylinder with radius r cm and height 5 cm is given by A = 2πr² + 10πr. Given that r is increasing at a ra...
Solve the inequality 4x(4 – x) > 7.
Find the coefficient of x⁵ in the expansion of (2 – x)⁸.
A 4-digit number is formed by using four of the six digits 2, 3, 4, 5, 6 and 8; no digit may be used more than once in any number. How many differe...
Given that 2ˣ⁻³ / 8²ʸ⁻³ = 16ˣ⁻ʸ, show that 3x + 2y = 6.
Find d/dx (tan 4x).
The variables x and y are related in such a way that when lg y is plotted against lg x a straight line graph is obtained as shown in the diagram. T...
A plane, whose speed in still air is 420kmh⁻¹, travels directly from A to B, a distance of 1000km. The bearing of B from A is 230° and there is a w...
The acceleration, a ms⁻², of a particle, t s after passing through a fixed point O, is given by a = 4 – 2t, for t > 0. The particle, which moves in...
Solve 4sinx + 9cosx = 0 for 0° < x < 360°.
Answer only one of the following alternatives. EITHER The point A(0, 10) lies on the curve for which dy/dx = e⁻ˣ/⁴. The point B, with x-coordinate ...
Answer only one of the following alternatives. OR The diagram shows part of the curve y = 8 + e⁻ˣ/³ crossing the y-axis at P. The normal to the cur...
The diagram shows the graph of y = a sin(bx) + c for 0 ≤ x ≤ 2π, where a, b and c are positive integers.
Find the set of values of k for which the curve y = (k + 1)x² – 3x + (k + 1) lies below the x-axis.
Show that (1 + sin θ / cos θ) + (cos θ / (1 + sin θ)) = 2 sec θ.
The sets A and B are such that A = {x: cos x = 1/2, 0° ≤ x ≤ 620°}, B = {x: tan x = √3, 0° ≤ x ≤ 620°}.
Find ∫(9 + sin 3x)dx.
The function f(x) = ax³ + 4x² + bx – 2, where a and b are constants, is such that 2x – 1 is a factor. Given that the remainder when f(x) is divided...
Find how many different 4-digit numbers can be formed from the digits 1, 3, 5, 6, 8 and 9 if each digit may be used only once.
On the grid below, sketch the graph of y = |(x - 2)(x + 3)| for -5 ≤ x ≤ 4, and state the coordinates of the points where the curve meets the coord...
Differentiate 4x³ln(2x + 1) with respect to x.
Solutions to this question by accurate drawing will not be accepted. The points A(-3, 2) and B(1, 4) are vertices of an isosceles triangle ABC, whe...
It is given that the matrix A = [[2, 3], [4, 1]].
The function f is such that f(x) = 3x² – 1 for –10 ≤ x ≤ 8. Find the range of f.
Find the set of values of x for which x² < 6 – 5x.