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.
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...
Solve the equation x³ + 1 = 6/x³.
A circle with centre C has the equation x²+y² - 10x-4y+24 = 0.
Find ∫₀^(π/2) sin θ dθ.
The polynomial p is such that p(x) = 3x³ − 7x² + ax + b, where a and b are integers. It is given that p'(-1) = 21 and that x-2 is a factor of p(x).
When ln y is plotted against x³, a straight line passing through the points (2,5) and (-8,25) is obtained.
A geometric progression has a 4th term of 8k⁶/27 and a 6th term of 32k¹⁰/243, where k is a constant. The common ratio of this geometric progression...
It is given that y = ln(3x² + 16) / (x+2).
It is given that f(x) = 2ln(3x-4), for x > a, and that f⁻¹ exists.
The diagram shows the shape OABCDEF. AOF is a straight line. OAB and OEF are sectors of a circle with centre O and radius r. Angle BOA = angle EOF....
The diagram shows the triangle OAB, where OA = a and OB = b. The point P lies on OA such that OP = (3/4)OA. The point Q lies on AB such that AQ = (...
A curve is such that its gradient at the point (x, y) is given by (5x-2)³ᐟ². The curve passes through the point (2, 32/5). Find the coordinates of ...
A curve has equation y = x²+2x-3.
In this question, k is a constant. It is given that 2x² + (3k-2)x+k = 0 has roots that are real and distinct. Find the set of possible values of k.
A sports club has the following members. 5 runners, 4 swimmers, 3 gymnasts
The coordinates of points A, B, C and D are as follows. A(-4,3) B(6, -9) C(15,10) D(14, -1) The line L has equation y = 11x-75. The perpendicular b...
Given that y = x² tan(x/2), use calculus to find the approximate change in y as x increases from π/3 to π/3 + h, where h is small.