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 3 sec² (2θ + π/6) = 4 for -π/2 < θ < π/2, giving your answers in terms of π.
The polynomial p(x) is such that p(x) = ax³ + bx² +cx-5, where a, b and c are integers. It is given that p'(0) = 12. It is also given that p(x) has...
A 6-digit number is to be formed using the digits 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9. Each digit can be used only once in any 6-digit number. A 6-digi...
It is given that f : x → (3x+1)²−4 for x ≥ a, and that f⁻¹ exists. (i) Find the least possible value of a. (ii) Using this value of a, write down t...
Solve the equation 12x^(3/2) - 5x^(3/4) - 11 = 0 for x > 0. Give your answer correct to one decimal place.
In this question all lengths are in centimetres and all angles are in radians. [Figure 10.1] The diagram shows a badge which consists of a minor se...
[Figure 11.1] In the triangle OAB, OA = a_and OB = b. The mid-point of the line OB is X, and the mid-point of the line AB is Y. The lines OY and AX...
A curve has equation y = √(5x-2) / (x-3).
A straight line passes through the points (4, 23) and (-8, 29). Find the point of intersection, P, of this line with the line y = 2x+5.
Find the non-zero value of k for which the line y=-2x-6k-1 is a tangent to the curve y = x(x+2k).
DO NOT USE A CALCULATOR IN THIS QUESTION. A cylinder has base radius (2+ √3)m and volume π(16+9√3)m³. Find the exact value of its height, giving yo...
Find the equation of the normal to the curve y = x³ - 7x² + 12x - 5 at the point (1, 1).
Find the exact value of ∫₂³ ((x+2)² / x) dx.
A particle is travelling in a straight line. Its displacement, s metres, from the origin at time t seconds is given by s = 1.5e^(2t) + 2e^(-2t) - t.
A curve has equation y = xsin 2x.
An arithmetic progression has twelve terms. The sum of the first three terms is -36 and the sum of the last three terms is 72. Find the first term ...
By writing cotx and tanx in terms of cosx and sinx, show that sinx/(1-cotx) + cosx/(1-tanx) = sinx + cosx.
The curve y = acos bx+c, where a, b and c are integers, passes through the points (-π/6,-2) and (π/2, 1). The curve has a period of 2π/3.
It is given that y = f(x), where f(x) = (2x-5)(x-1)2.
In this question, all lengths are in centimetres and all angles are in radians. [Figure X.X] The diagram shows a circle with centre O and radius 12...
The function f is such that f(x) = 4ln(3x-2), for x > a, where a is as small as possible.
Show that (1+cot²θ)/cot²θ = sec²θ.
Find, in descending powers of x, the first 3 terms in the expansion of (x + 2/x²)¹⁰. Simplify each term as far as possible.
It is given that y = ln(3x²-1)/(x+2), for x > 1/√3. When x = 1, y is increasing at the rate of h units per second. Find, in terms of h, the corresp...
The tangent to the curve y = e^(2x+5)^(1/2) at the point where x = 2 meets the x-axis at the point X and the y-axis at the point Y. Find the coordi...
The diagram shows part of the curve y = 4/(2x+1) and the straight line 2y = 6x+1. Find the area of the shaded region, giving your answer in the for...
The first 3 terms of an arithmetic progression are 2 tan 2x, 5 tan 2x, 8 tan2x. Find the values of x, where -180° ≤ x ≤ 180°, for which the sum to ...
Solve the following simultaneous equations. y/x = 3/2 y^4/x^5 = 27/16
Variables x and y are related by the equation y = x√1+2x.
DO NOT USE A CALCULATOR IN THIS QUESTION. The polynomial p is defined by p(x) = ax³ −3x² – 3x+b, where a and b are constants.
Use a graphical method to solve the inequality |2x-8|>4.
DO NOT USE A CALCULATOR IN THIS QUESTION. Write (5-√3)(√6+ √2)⁻² in the form a+b√3, where a and b are constants.
A class of 10 students includes Abby and Ben.
Solve the equation cot²2θ+3 cosec 2θ = 9 for -90° ≤ θ ≤ 90°.
In this question time is measured in seconds.
The diagram shows part of the curve y = x-x²/4 and the line y =-4. The curve and the line intersect at the point A.
In this question i is a unit vector in the positive x-direction and j is a unit vector in the positive y-direction. Time is in seconds and distance...
A metal tank is in the shape of a cuboid with a square base of side xm and an open top. The tank has a volume of 5 m³. Given that x can vary, and t...
On the axes, sketch the graph of y = (1-x)(x - 5)(2x-5), stating the intercepts with the axes.
The polynomial p is such that p(x) = 2x³ + ax² + 13x+b, where a and b are integers. It is given that x+2 is a factor of p(x). When p(x) is divided ...
The sum of the first two terms of a geometric progression is 9. The sum to infinity of this geometric progression is 25.
Show that 2x²+5x+3 can be written in the form 2(x+a)²+b, where a and b are constants to be found.
Write 5lg a – 4lg b – 3 as a single base 10 logarithm.
Solve the equation |2x²+x-10|= 5.
The point A has coordinates (-2, 4). The point B has coordinates (6, 10). The point C has coordinates (12, 2).
On the axes, sketch the graph of y = 5 ln(4x+3). State the intercepts with the axes. State the equation of any asymptote.
A curve y = f(x) is such that f'(x) = (2x+5)⁻½. The curve has gradient ²⁄₃ at the point (2, 2).
Show that ∫(from π/2 to 3π/2) ((sinθ+cosθ)² + (sinθ−cosθ)²)dθ = kπ, where k is an integer to be found.
Solve the equation (n-4) n+1C5 = n+2C7.
A curve has equation y = e^(x²)/(x-2) for x < 2.