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.
In the diagram OP = 2b, OS = 3a, SR = b and PQ = a. The lines OR and QS intersect at X. [Figure 9.1: A diagram showing vectors OP, OS, SR, PQ. Line...
The number, b, of bacteria in a sample is given by b = P+Qe^(2t), where P and Q are constants and t is time in weeks. Initially there are 500 bacte...
Show that sinx tanx / (1-cosx) = 1+ secx.
The diagram shows the graph of the cubic function y = f(x). The intercepts of the curve with the axes are all integers. [Figure 1.1]
Given that `√xy(zy)² / (xz)⁻³√z = xᵃyᵇzᶜ`, find the exact values of the constants a, b and c.
Write `3+2lg a-4lg b` as a single logarithm to base 10.
Solve the equation `cot(2x+π/3)-√3 = 0`, where `-π < x < π` radians. Give your answers in terms of π.
Find the possible values of the constant c for which the line `y = c` is a tangent to the curve `y = 5 sin(x/3) + 4`.
DO NOT USE A CALCULATOR IN THIS QUESTION. The polynomial `p(x) = 10x³ + ax² -10x+b`, where a and b are integers, is divisible by `2x+1`. When `p(x)...
[Figure 7.1] The diagram shows triangle OAC, where `OA = a`, `OB = b` and `OC = c`. The point B lies on the line AC such that `AB:BC = m:n`, where ...
A 5-digit number is made using the digits 0, 1, 4, 5, 6, 7 and 9. No digit may be used more than once in any 5-digit number. Find how many such 5-d...
The diagram shows a circle, centre O, radius 12cm, and a rectangle ABCD. The diagonals AC and BD intersect at O. The sides AB and AD of the rectang...
The diagram shows the graph of the curve `y = 1/(x+2)² + 3/(x+2)` for `x > -2`. The points A and B lie on the curve such that the x-coordinates of ...
(a) The diagram shows the velocity-time graph for a particle P, travelling in a straight line with velocity vms⁻¹ at a time t seconds. P accelerate...
[Figure showing a Cartesian coordinate plane with x from -6 to 6 and y from 0 to 20.]
Expand (2-3x)⁴, evaluating all of the coefficients.
Show that (1/(secx-1)) + (1/(secx+1)) = 2 cotx cosecx.
Find the x-coordinates of the stationary points on the curve y = 3 lnx+x² - 7x, where x > 0.
Solve the following simultaneous equations. ex + ey = 5, 2ex-3ey = 8
It is given that d²y/dx² = e^(2x) + 1/((x+1)²) for x > -1.
Variables x and y are such that when √y is plotted against log₂(x+1), where x > -1, a straight line is obtained which passes through (2,10.4) and (...
Find the equation of the normal to the curve y = x³+x²-4x+6 at the point (1, 4).
The first three terms of an arithmetic progression are x, 5x-4 and 8x +2. Find x and the common difference.
The diagram shows the graph of y = a sinbx+c, where a, b and c are integers. Find the values of a, b and c.
On the axes, draw the graph of y = |3x²+13x-10|, stating the coordinates of the points where the graph meets the axes.
Write √(9p²q)×r⁻³ / ((2p)⁻¹q⁻¹√r) in the form kpᵃqᵇrᶜ, where k, a, b and c are constants.
Solve the equation 3 sin(2x+π/4) = √3 cos(2x+π/4), for 0 ≤ x ≤ π.
Find the vector with magnitude 200 in the direction of (7 -24).
A group of 15 people includes 3 brothers. A team of 6 people is to be chosen from this group. The three brothers must not be separated. Find the nu...
The diagram shows a circle, centre O, radius 10cm. The points A and B lie on the circumference of the circle. The tangent at A and the tangent at B...
A function f(x) is such that f(x) = ln(2x+3)+ln4, for x > a, where a is a constant.
Show that 1/(2x+1) - 1/((2x+1)²) + 4/(4x-1) = (24x²+14x+4) / ((2x+1)²(4x-1))
The first three terms of an arithmetic progression are lgx, lgx³, lgx⁹, where x > 0.
A particle P moves in a straight line such that, t seconds after passing through a fixed point O, its displacement, s metres, is given by s = (2t+1...
The first three terms, in descending powers of x, of the expansion of (ax+3)(1-b/x)⁵ can be written as 32x⁵-160x⁴+cx³, where a, b and c are constan...
Solve the following simultaneous equations. x+5y=-4 3y-xy = 6
Solve the equation 4e^(2x-3) = 7e^(5-x).
In this question a and b are constants. The normal to the curve y = ax⁻³ + 3x - 2 at the point where x = 1 has equation y = -1/4 x + b. Find the va...
Solve the equation log₃(11x-8) = 1 + 2/logₓ3 given that x > 1.
DO NOT USE A CALCULATOR IN THIS QUESTION. Find the x-coordinates of the points of intersection of the curves y = x³-2x²-4x-16 and y = 7x³-7x²-17x-4.
A 4-digit code is to be formed using 4 different numbers selected from 2, 3, 4, 5, 6, 7, 8 and 9. Find how many possible codes there are if the cod...
Show that sinx / (1-cosx) + (1-cosx) / sinx = 2 cosecx.
In this question all lengths are in centimetres. The volume of a cylinder with radius r and height h is πr²h and its curved surface area is 2πrh. T...
In this question all lengths are in centimetres. The diagram shows triangle ABC which has area 2√5/3 cm². Angle A is acute. [Figure 9.1]
A geometric progression has third term 4.5 and sixth term 15.1875. Find the first term and the common ratio.
The coordinates of points A and B are (-5,6) and (4, – 6) respectively. The point C lies on the line AB, between A and B, such that AC/CB = 1/2.
[Figure 1.0] The diagram shows the graph of the cubic polynomial y = f(x).
The function g is defined by g(x) = 5 sin(3x/4) - 2 for all values of x.
When ln (y+2) is plotted against x² a straight line graph is obtained. The line passes through the points (2.25, 9.37) and (4.75, 3.92). Find y in ...
It is given that the first four terms, in ascending powers of x, in the expansion of (1 - x/2)^n can be written in the form 1-8x+px²+qx³, where n, ...