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 |2x + 10| = 7.
The expression x³ + ax² – 15x + b has a factor x – 2 and leaves a remainder of 75 when divided by x + 3. Find the value of a and of b.
A number, N₀, of fish of a particular species are introduced to a lake. The number, N, of these fish in the lake, t weeks after their introduction,...
Students take three multiple-choice tests, each with ten questions. A correct answer earns 5 marks. If no answer is given 1 mark is scored. An inco...
Find the set of values of m for which the line y = mx – 2 cuts the curve y = x² + 8x + 7 in two distinct points.
A 4-digit number is formed by using four of the seven digits 1, 3, 4, 5, 7, 8 and 9. No digit can be used more than once in any one number. Find ho...
A rectangular sheet of metal measures 60 cm by 45 cm. A scoop is made by cutting out squares, of side x cm, from two corners of the sheet and foldi...
Solve the equation lg(5x + 10) + 2 lg 3 = 1 + lg(4x + 12),
A plane, whose speed in still air is 250 kmh⁻¹, flies directly from A to B, where B is 500 km from A on a bearing of 060°. There is a constant wind...
Solutions to this question by accurate drawing will not be accepted. The diagram shows a quadrilateral ABCD in which A is the point (1, 4) and B is...
Solve the equation 5 sin x – 3 cos x = 0, for 0° ≤ x ≤ 360°,
Answer only one of the following two alternatives. EITHER The functions f and g are defined, for x > 1, by f(x) = (x + 1)² - 4, g(x) = (3x + 5) / (...
OR A particle moves in a straight line so that, at time t s after passing a fixed point O, its velocity is v m s⁻¹, where v = 6t + 4 cos 2t. Find
Solve the equation lg(5x + 10) + 2lg3 = 1 + lg(4x + 12),
A plane, whose speed in still air is 250kmh⁻¹, flies directly from A to B, where B is 500km from A on a bearing of 060°. There is a constant wind o...
Solutions to this question by accurate drawing will not be accepted. [Figure showing a quadrilateral ABCD on a Cartesian plane. Point A is (1,4), P...
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.