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 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.
For –1 ≤ x ≤ 1 it is given that x = 2−3sinθ and y = 3cot²θ. Find y in terms of x.
The line y = 4x-3 meets the curve y = 3+5x-2x² at the points A and B.
The diagram shows the shaded region ABCD. The lines AC and BD each have a length of 12 cm. The lines AC and BD bisect each other at the point O. Th...
Find the exact value of the term independent of x in the expansion of (2+3/x)¹⁰ (1-4x²)².
Variables x and y are such that when eʸ is plotted against x³, a straight-line graph is obtained. This line passes through the points (1, 13.5) and...
A 6-character password is to be formed from the following characters. Letters b f g k m (5 characters) Numbers 3 5 7 9 (4 characters) Symbols * ! @...
In this question lengths are in centimetres and time, t, is in seconds. A particle P is moving in a straight line with a speed of 26 in the directi...
Given that y = x cos 2x, find dy/dx.
An arithmetic progression has first term t and common difference 1.5. The 4th, 8th and 20th terms of this arithmetic progression form the 1st, 2nd ...
It is given that f(x) = ln(2x+5) for x > a, where a is a constant. It is also given that g(x) = x² +1 for x ∈ R.
The diagram shows parts of the graphs of y = 2+5eˣ and y = 4-3e²ˣ. Find the area of the shaded region. Give your answer in the form a+b ln3, where ...
Solve the equation tan²2x-4 tan2x = 0 for 0° ≤ x ≤ 180°.
The points A, B and C have position vectors a = beginpmatrix 2 1 3 endpmatrix, b = beginpmatrix 4 -1 5 endpmatrix and c = beginpmatrix k ...
A curve C has equation y = 3x² - 12x + 10.
Which of the following is the correct expansion of (2x - y)³?
Given that y = (3x-1)⁴, find dy/dx.
The equation eˣ - 3x = 0 has a root α in the interval $[0, 1]$.
Solve the inequality |2x - 3| leqslant 5.
The nth term of an arithmetic series is uₙ = 5n - 2. (a) Write down the first three terms of the series. (b) Find the sum of the first 20 terms of ...
Solve the equation 2 tan² θ - 3 sec θ = 0 for 0^(°) leqslant θ < 360^(°). Give your answers to one decimal place where appropriate.
A particle P moves in a straight line such that its velocity v m/s at time t seconds is given by v = 6t² - 10t + 3. The particle is initially at th...
The curve C has equation y = 3x² - 4x + 1. The line L has equation y = x - 1. (a) Find the coordinates of the points of intersection of C and L. (b...
A circle C has equation x² + y² - 6x + 8y - 24 = 0. (a) Find the coordinates of the centre of C and the radius of C. (b) The point P(7, 3) lies on ...
The curve C has equation y=x/(x+2). The line L has equation y=x-2.