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.
8 Solve the equation 4 sin²(2α-π/3) = 1 for -π/2 < α < π/2. Give your answers in terms of π.
9 (a) Solve the following simultaneous equations. ex+y × e3x-2y = 1 x²y = 256
10 In this question, all distances are in metres and time, t, is in seconds. A particle P is at a fixed point O at time t = 0. The velocity, v, of ...
11 The tangent to the curve y = (3x-1)¹/² at the point where x = 3 meets the coordinate axes at the points A and B. The point with coordinates (a, ...
12 (a) It is given that y = (ln 3x) / x² for x > 0. Find dy/dx. Give your answer in the form (A+B ln 3x) / x³, where A and B are integers. (b) Henc...
The diagram shows the graph of y = a sinbx+c for -360°≤x≤ 360°, where a, b and c are constants. Find the values of a, b and c. [Figure 1.1]
Given that log₃r+2log₉s = 8, find the value of rs.
Given that y = tan(x/2), find the exact value of dy/dx when x = π/3.
A team of 8 people is to be formed from 6 teachers, 5 doctors and 4 police officers.
DO NOT USE A CALCULATOR IN THIS QUESTION. In this question, all lengths are in centimetres. The diagram shows the trapezium ABCD. The lengths of AB...
In this question, all lengths are in metres and all angles are in radians. The diagram shows a circle with centre O and radius 5. The points A, B, ...
The line y = 3x-2 intersects the curve 2x²-xy+y² = 2 at the points A and B. The point C with coordinates (k, 7/8) lies on the perpendicular bisecto...
A curve has equation y = (3x²-5)^(1/2) / (x+4).
In this question, all distances are in metres and time, t, is in seconds.
10 (a) The first 3 terms of an arithmetic progression are 3 sin 2x, 5 sin 2x, 7 sin2x.
11 (a) Given that y = x²lnx, find dy/dx.
On the axes, sketch the graph of y=|4x-6|, showing the points where the graph meets the axes.
Write 3+4x-2x² in the form a+b(x+c)², where a, b and c are integers.
Use algebra to show that the equation 5x(x-3) = 5x-26 has no real solutions.
There are 3 women, 2 men and 4 children in a choir.
Variables x and y are such that y = cosx sin²x. Use differentiation to find the approximate change in y as x increases from 3 to 3+h, where h is sm...
It is given that y = mx² + x/2 + n, where m and n are non-zero constants. It is also given that 3(d²y/dx²) = (dy/dx)² - y for all values of x. Find...
In an arithmetic progression, the sum of the first 30 terms is -1065. The sum of the next 20 terms is -2210. Find the first term and the common dif...
The functions f and g are defined by f(x) = 3x²/(4x-1) for x < 0 and g(x) = 1/x² for x < 0.
Show that (tanx+secx)² can be written as (1+sinx)/(1-sinx).
In this question all lengths are in centimetres. The diagram shows a rectangle ABCD with BC = x. The area of the rectangle is 400 cm². Two identica...
The diagram shows a triangle OBC. OA : OB = 4 : 7 and OD : OC = 4 : 7. OB = b and OC = c. The point P is the point of intersection of AC and BD suc...
On the axes, sketch the graph of y = (2x-5) (x+3)(1-x), stating the intercepts with the coordinate axes.
Evaluate ∫(from π/4 to π/2) cos(x/2) dx. You must show all your working.
Determine whether the equation (4x+1)(3x+2)/(5x-3) = x+1 has two distinct real roots, two equal roots or no real roots.
The polynomial p is such that p(x) = 6x³ +x² - 12x+5.
A curve has equation y = 5e^(2x−1)+e. The tangent to the curve at the point where x = 1 cuts the x-axis at the point P. Find the equation of the ta...
Show that sin³x (cosec x / cotx) can be written as sin²x tanx.
Find the number of different ways the 9 letters of the word POLYMATHS can be arranged when
An experiment was carried out and values of y for certain values of x were recorded. The table shows the values recorded. x 15 30 45 60 75 y...
The diagram shows part of the curve y = 32x-4x² - 48 and the line AB. The curve and the line AB meet the x-axis at A and meet again at the point B(...
The functions f and fg are defined by f(x) = e^(x²+3) for x < 0 fg(x) = e^(2x) for x > 3/2
In the binomial expansion of (2 + x/a)^n, the first three terms in increasing powers of x are b + abx + (9/8)abx². Find the values of the constants...
Calculators must not be used in this paper.
Point A has coordinates (3, -1). A circle has equation (x-4)² + (y+3)² = 5.
Solve the equation x¹ᐟ³ - x¹ᐟ⁶ = 2.
Solve the equation 5|2x-1|+8 = 23.
A curve has equation y = ((x²-1)/(x²+1))⁴.
Solutions to this question by accurate drawing will not be accepted.
Write down the set of values of x for which log₅(12x-4) exists.
The point A with x-coordinate 2 lies on the curve y = √4x+1. The diagram shows part of this curve and the tangent to the curve at A. Find the area ...
Given that 0 < θ < π/2, show that sinθ/√cosec²θ-1 + 1/√1+tan²θ can be written as secθ.
An arithmetic progression has common difference d. The 3rd term of this progression is 10.
In this question n ≥ 6. Use an algebraic method to show that ⁿC₅ - ⁿ⁻¹C₅ can be written as ⁿ⁻¹C₄.
The diagram shows the graph of y = |f(x)|, where f is a cubic polynomial. Find expressions for the two possible functions f(x). Write each expressi...