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.
A bag contains only red counters, blue counters and green counters. The ratio of the number of red counters to the number of blue counters is 3 : 4...
The diagram shows a solid cylinder. The cylinder has diameter 9 cm and height 16 cm. Work out the total surface area of the cylinder. Give your ans...
Make t the subject of the formula r = 5t – 3.
Solve the inequality 4x – 7 < 11.
Describe fully the single transformation that maps triangle A onto triangle B.
Simplify (8a³)¹/³.
Given that y = 2x³ – 3x² + 5x – 1. Find dy/dx.
Here are two similar triangles. The area of triangle ABC is 20 cm². The area of triangle PQR is 45 cm². The length of BC is 8 cm. Work out the leng...
Solve 2x² – 5x – 3 = 0. Show your working clearly. Give your answers correct to 3 significant figures.
The equation of a curve is y = x³ – 6x² + 9x – 2. Find the coordinates of the turning points of the curve.
Simplify fully (4x² - 9)/(2x² - 13x + 15)
The curve C has equation y = 2x³ - 9x² + 12x. The point P lies on C and has x-coordinate 2. (a) Find dy/dx. (b) Find an equation of the tangent to ...
The circle C has equation x² + y² - 6x + 8y - 24 = 0. (a) Find the coordinates of the centre of C and the exact radius of C. (b) The point P(8, -10...
Given that the coefficient of x³ in the expansion of (2 - 1/4x)ⁿ is 280, find the value of the positive integer n.
The functions f and g are defined by f(x) = (2x+3)/(x-1), x ∈ ℝ, x ≠ 1 g(x) = 2x² - 3, x ∈ ℝ (a) Find the range of f. (b) Find f⁻¹(x). (c) Solve t...
[Figure 1] Figure 1 shows a sketch of part of the curve with equation y = x(x-2)(x-4). The curve crosses the x-axis at the origin O and at the poin...
Solve, for 0 ≤ θ < 360^(°), the equation 4 sin²θ = 5 - 4 cosθ
The polynomial P(x) is given by P(x) = x³ - 4x² - 7x + 10. (a) Show that (x-1) is a factor of P(x). (b) Hence, or otherwise, factorise P(x) complet...
Sketch the curve with equation y = x(x-3)², showing the coordinates of the points where the curve crosses or touches the coordinate axes.
Which of the following expressions is equivalent to 1/2 ln(9x²)?
The function f is defined by f(x) = 3x² - 6x + 5, x ∈ ℝ, x ≥ 1.
A curve C has equation y = (2x+3)e^{-x}.
The curve C has equation cos(y) = x² sin(x).
Using the substitution u = tan x, find the exact value of ∫_(π/6)^(π/3) 1/(1 - sin² x) dx.
Given that θ is small and measured in radians, use the small angle approximations to show that (cos(3θ) - 1)/(θ sin(2θ)) ≈ -9/2.
Show that (cos 2θ)/(sin θ cos θ) ≡ cot θ - tan θ.
The population of a species of insects in a laboratory is modelled by the equation P = (800e^(0.1t))/(1 + 4e^(0.1t)), t ≥ 0, where P is the populat...
Figure 1 shows a sketch of the curve with equation y = 2x ln x, x > 0.
The curve C has equation y = 2x + cot x, 0 < x < π.
Water is leaking from a cylindrical tank. The depth of the water in the tank at time t minutes is h cm. The rate at which the depth of water is cha...
(a) Express (2x + 7) / ((x + 2)(2x + 1)) in partial fractions. (b) Hence find ∫ (2x + 7) / ((x + 2)(2x + 1)) dx.
The curve C has equation y = x²(3-x). The point P lies on C and has x-coordinate $1$. (a) Find the equation of the tangent to C at P. The normal to...
A curve C has equation y = x²-10x+26. The line L has equation y = -3x+c, where c is a constant.
Figure 1 shows a sketch of the curve C with equation y = f(x), where f(x) = (x+1)(x-2)(x-4). The curve C crosses the x-axis at x=-1, x=2 and x=4. T...
Given that x²-12x+k = (x-p)²+5, where k and p are constants. Find the value of k and the value of p.
Figure 2 shows a sketch of the curve C with equation y = 1/2x²-3x+8. The points P and Q lie on C such that the tangent to C at P is parallel to the...
I am unable to extract the questions, mark schemes, model answers, and examiner report traps because the Pearson Edexcel IAL Question Paper, Mark S...
A function f is defined by f(x) = (x^2 - 2x + 1) / (x - 3), x ∈ ℝ, x ≠ 3. (a) Express f(x) in the form Ax + B + C / (x - 3), where A, B and C are ...
(a) Show that 3cos(2θ) - sin(2θ) ≡ Rcos(2θ + α), where R > 0 and 0 < α < π/2, giving the value of R and α to 3 decimal places. (b) Hence solve, for...
A curve C has equation y = x e^(2x). (a) Find dy/dx. (b) Find the exact coordinates of the stationary point of C. (c) Determine the nature of this...
Using the substitution u = 1 + cos x, find the exact value of ∫(from π/2 to π) [sin(x) / (1 + cos x)^2] dx.
The curve C has equation x^2 + 2xy - 3y^2 + 16 = 0. (a) Show that dy/dx = (x + y)/(3y - x). (b) Find the equation of the normal to the curve C at t...
Given that the general solution of the differential equation (x + 1) dy/dx = y(x^2 - 1) is y = A(x - 1)e^(x^2/2), where A is an arbitrary constant....
A curve has parametric equations x = t^2 + 1, y = 2ln(t + 1), t > -1 (a) Find dy/dx in terms of t. (b) Find the equation of the normal to the curve...
A curve C has equation y = x³ - 6x² + 5x - 2.
The 5th term of an arithmetic series is 18 and the 10th term is 33. Find the first term and the common difference of the series.
The first three terms of an arithmetic series are 2x, x+4, and 2x-5 respectively.
The binomial expansion of (1 + px)ⁿ, where n is a positive integer, is 1 - 12x + 54x² + ...
Figure 1 shows a sketch of the curve C with equation y = f(x). The curve C passes through the origin O and touches the x-axis at the point (3, 0). ...
Figure 1 shows a sketch of the curve C with equation y = f(x). The curve C passes through the origin O and touches the x-axis at the point (3, 0). ...