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.
The 7th and 10th terms of an arithmetic progression are 158 and 149 respectively.
Find the coefficient of x² in the expansion of (x - 3/x) (x + 2/x)⁵.
f(x) = x²+2x-3 for x≥-1 Given that the minimum value of x² + 2x-3 occurs when x =-1, explain why f(x) has an inverse.
A curve has equation y = ln(3x²-5) / (2x+1) for 3x² > 5.
Find the number of ways in which 12 people can be put into 3 groups containing 3, 4 and 5 people respectively.
A curve has equation y = (2x-1)√4x+3.
The polynomial p(x) = 6x³ +ax²+bx+2, where a and b are integers, has a factor of x-2.
In this question all lengths are in centimetres and all angles are in radians. [Figure 11.1] The diagram shows the rectangle ADEF, where AF = DE = ...
[Figure 12.1] The diagram shows the velocity-time graph of a particle P that travels 2775 m in 90s, reaching a final velocity of V ms⁻¹.
Solve the inequality (x-8)(x−10) > 35.
Find the value of x such that 4^(x+1) / 2^(x-1) = 32^(2/3) x 8^(1/3).
Find the equation of the perpendicular bisector of the line joining the points (12, 1) and (4, 3), giving your answer in the form y = mx+c.
Solve the simultaneous equations. log3 (x+y) = 2 2log3 (x + 1) = log3 (y+2)
Find the exact value of ∫₄² (x+1)² / x² dx.
A geometric progression has a first term of 3 and a second term of 2.4. For this progression, find
DO NOT USE A CALCULATOR IN THIS QUESTION. In this question lengths are in centimetres. [Figure 8.1: A diagram showing a triangle ABC with angle A =...
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...