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.
Solve the equation 5 sin x – 3 cos x = 0, for 0° ≤ x ≤ 360°,
Answer only one of the following two alternatives. OR A particle moves in a straight line so that, at time t s after passing a fixed point O, its v...
Sets A and B are such that n(A) = 15 and n(B) = 7. Find the greatest and least possible values of
The function f is such that f(x) = 4x³ – 8x² + ax + b, where a and b are constants. It is given that 2x - 1 is a factor of f(x) and that when f(x) ...
Variables t and N are such that when lgN is plotted against lgt, a straight line graph passing through the points (0.45, 1.2) and (1, 3.4) is obtai...
Six-digit numbers are to be formed using the digits 3, 4, 5, 6, 7 and 9. Each digit may only be used once in any number. Find how many of these six...
A particle moves in a straight line such that its displacement, x m, from a fixed point O at time t s, is given by x = 3 + sin 2t, where t ≥ 0.
The diagram shows part of the graph y = p + 3tan3x passing through the points (−π/12, −5), (0, p) and (q, 1). Find the value of p and of q.
The coefficient of x² in the expansion of (1 + x/5)ⁿ, where n is a positive integer, is 3/5.
Find ∫ (eˣ + 1)² dx and hence evaluate ∫₂⁰ (eˣ + 1)² dx.
Solve 1 + cot² x = 8 sin x for 0° ≤ x ≤ 360°.
Answer only one of the following two alternatives. [Figure 10.2 OR]
Show that (1 / (tan θ + cot θ)) = sin θ cos θ.
Find the coordinates of the points where the line 2y = x − 1 meets the curve x² + y² = 29.
Express logₓ 2 in terms of a logarithm to base 2.
A curve has equation y = (3x² + 15)². Find the equation of the normal to the curve at the point where x = 2.
Variables x and y are such that, when y² is plotted against 2ˣ, a straight line graph is obtained. This line has a gradient of 5 and passes through...
Given that (3 + x)⁵ + (3 - x)⁵ = A + Bx² + Cx⁴, find the value of A, of B and of C.
Show that ((4 - √x) / √x)² can be written in the form px⁻¹ + q + rx^(1/2), where p, q and r are integers to be found.
The line CD is the perpendicular bisector of the line joining the point A (−1, –5) and the point B (5,3).
Given that y = x sin 4x, find dy/dx.
Solve 2 sec² x = 5 tan x + 5, for 0° < x < 360°.
Answer only one of the following two alternatives. EITHER A curve has equation y = e⁻ˣ (Acos2x + Bsin2x). At the point (0, 4) on the curve, the gra...
Solve the equation |4x - 5| = 21.
Given that the straight line y = 3x + c is a tangent to the curve y = x² + 9x + k, express k in terms of c.
Without using a calculator, find the value of cosθ, giving your answer in the form (a+b√3)/c where a, b and c are integers. [Figure: A triangle wit...
Given that y = 1/(x² + 3), show that dy/dx = -kx / (x² + 3)², where k is a constant to be found.
The functions f and g are defined, for x ∈R, by f : x → 2x + 3, g : x → x² – 1. Find fg(4).
Solutions to this question by accurate drawing will not be accepted. The points A(1, 4), B(3, 8), C(13, 13) and D are the vertices of a trapezium i...
Given that tan x = p, find an expression, in terms of p, for cosec²x.
In the diagram OA = a, OB = b and AP = (2/5)AB. [Figure: A diagram showing vectors O, A, B, P, X. O is the origin. Vector OA is 'a', vector OB is '...
The table shows experimental values of two variables x and y. x | 1 | 2 | 3 | 4 | 5 y | 3.40 | 2.92 | 2.93 | 3.10 | 3.34 It is known that x and y a...
It is given that A = ( (3, 2), (1, -5) ) and B = ( (1, 4), (-2, 3) ).
Solve 5^(2x+3) / 25^(2x) = 25^(2-x) / 125^x.
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.