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.
Show that cosec θ / (cot θ + tan θ) = cos θ.
It is given that y = A(10^bx), where A and b are constants. The straight line graph obtained when lgy is plotted against x passes through the point...
(a) A 5-digit number is to be formed from the seven digits 1, 2, 3, 5, 6, 8 and 9. Each digit can only be used once in any 5-digit number. Find the...
(a) Given that A = [-3 1; -1 2; 4 5], B = [-2 0; 1 3] and C = AB, (b) The matrix X = [5 -12; 4 -7]
The diagram shows a circle, centre O, radius 8 cm. The points A, B, C and D lie on the circumference of the circle such that AB is parallel to DC. ...
The curve y = f(x) passes through the point (1/2, 7/2) and is such that f'(x) = e^(2x-1).
Find the equation of the curve which passes through the point (2, 17) and for which dy/dx = 4x³ + 1.
The variables x and y are such that y = ln(x² + 1).
Given that y = 7 cos 10x – 3, where the angle x is measured in degrees, state the period of y,
Given that a is a constant, expand (2 + ax)⁴, in ascending powers of x, simplifying each term of your expansion.
Four cinemas, P, Q, R and S each sell adult, student and child tickets. The number of tickets sold by each cinema on one weekday were P: 90 adult, ...
On each of the Venn diagrams below shade the region which represents the given set. [Figure 7.1]
A football club has 30 players. In how many different ways can a captain and a vice-captain be selected at random from these players?
The curve 3x² + xy - y² + 4y – 3 = 0 and the line y = 2(1 – x) intersect at the points A and B.
The table shows values of the variables t and P. t: 1, 1.5, 2, 2.5 P: 4.39, 8.33, 15.8, 30.0
Prove that sinx(cotx + tanx) = secx.
A particle moves in a straight line so that, t seconds after passing a fixed point O, its displacement, sm, from O is given by s = 1 + 3t - cos 5t.
Solve |5x + 3| = |1 - 3x|.
Without using a calculator, express ( (1 + √5) / (3 - √5) ) ^-2 in the form a + b√5, where a and b are integers.
Without using a calculator, factorise the expression 10x³ – 21x² + 4.
The point P lies on the curve y = 3x² – 7x + 11. The normal to the curve at P has equation 5y + x = k. Find the coordinates of P and the value of k.
Show that d/dx [0.4x⁵ (0.2 - ln 5x)] = kx⁴ ln 5x, where k is an integer to be found.
Show that the roots of px² + (p - q)x - q = 0 are real for all real values of p and q.
Given that a⁷ = b, where a and b are positive constants, find,
Solutions to this question by accurate drawing will not be accepted. The points A and B are (-8, 8) and (4, 0) respectively.
A function f is defined, for x ≤ 3/2, by f(x) = 2x² - 6x + 5.
Solve the equation 4 sin(3x - π/4) = 3 for 0 ≤ x ≤ π/2 radians,
The diagram shows part of the curve y = x³ + 4x² – 5x + 5 and the line y = 5. The curve and the line intersect at the points A, B and C. The points...
The function g is defined, for x > -1/2, by g(x) = 3/(2x + 1).
Solve the equations y − x = 4, x² + y² – 8x – 4y – 16 = 0.
Find the equation of the perpendicular bisector of the line joining the points (1, 3) and (4, −5). Give your answer in the form ax + by + c = 0, wh...
Diagrams A to D show four different graphs. In each case the whole graph is shown and the scales on the two axes are the same. [Figure A, B, C, D]
The curve y = a + b sin cx has an amplitude of 4 and a period of π/3. Given that the curve passes through the point (π/12, 2), find the value of ea...
The population, P, of a certain bacterium t days after the start of an experiment is modelled by P = 800e^(kt), where k is a constant.
Write (log₂p)(log₃2) + log₃q as a single logarithm to base 3.
Find the inverse of the matrix ( (4 -2) (-5 3) )
Given that p = 2i – 5j and q = i – 3j, find the unit vector in the direction of 3p – 4q.
Find the first 3 terms in the expansion of ( 2x - 1/(16x) )⁸ in descending powers of x.
The diagram shows part of the graph of y = 16x + 27/x², which has a minimum at A. [Figure 11.1]
A curve is such that d²y/dx² = (2x - 5)⁻^(1/2). Given that the curve has a gradient of 6 at the point (9/2, 2/3), find the equation of the curve.
It is given that y = 1+tan3x.
Find the values of k for which the line y = 1-2kx does not meet the curve y = 9x² - (3k + 1)x + 5.
The variables x and y are such that when eʸ is plotted against x², a straight line graph passing through the points (5, 3) and (3, 1) is obtained. ...
A particle P moves so that its displacement, x metres from a fixed point O, at time t seconds, is given by x = ln (5t + 3).
The first three terms in the expansion of (3 - 1/(9x))⁵ can be written as a + b/x + c/x². Find the value of each of the constants a, b and c.
Find the coordinates of the stationary point of the curve y = (x+2)/√(2x-1).
A population, B, of a particular bacterium, t hours after measurements began, is given by B = 1000e^(t/4).
Solve 3 cos²θ + 4 sinθ = 4 for 0° ≤ θ ≤ 180°.
Solve lgx = 3.
Do not use a calculator in this question. All lengths in this question are in centimetres. [Figure showing a triangle ABC with angle B = 60 degrees...