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.
The first and second terms of an arithmetic progression are tanθ and sinθ respectively, where 0 < θ < ½π. For parts (b)(i) and (b)(ii), the first a...
The curve with equation y = 2x – 8x¹⁄² has a minimum point at A and intersects the positive x-axis at B. The diagram shows the curve with equation ...
The equation of a circle is (x−6)² + (y+a)² = 18. The line with equation y = 2a−x is a tangent to the circle.
The diagram shows a symmetrical plate ABCDEF. The line ABCD is straight and the length of BC is 2 cm. Each of the two sectors ABF and DCE is of rad...
A function f is such that f'(x) = 6(2x−3)² − 6x for x ∈ R.
The equation of a curve is y = (5−2x)³/² + 5 for x < 5/2.
A curve has equation y = 2 tanx-5 sin x for 0 < x < π. Find the x-coordinate of the stationary point of the curve. Give your answer correct to 3 si...
A curve has equation x²lny+y² + 4x = 9. Find the gradient of the curve at the point (2, 1).
Sketch on the same diagram the graphs of y = |3x-8|and y = 5-x.
Show that 3 tan 2θ+ tan(θ+45°) = tan²θ+8 tanθ+1 1-tan²θ
A curve has equation y = 1+e2x 1+3x . The curve has exactly one stationary point P.
The diagram shows the curve with equation y = √sin2x+sin²2x for 0 < x < π. The shaded region is bounded by the curve and the straight lines x = π a...
The polynomial p(x) is defined by p(x) = 9x³ + 6x² +12x+k, where k is a constant.
Solve the inequality |5x+7|>|2x-3|.
Use logarithms to solve the equation 6^(2x−1) = 5e^(3x+2). Give your answer correct to 4 significant figures.
The diagram shows the curve with equation y = 8e¯ˣ – e^(2x). The curve crosses the y-axis at the point A and the x-axis at the point B. The shaded ...
A curve is defined by the parametric equations x = 4 cos²t, y = √3 sin 2t, for values of t such that 0 < t < π/2. Find the equation of the normal t...
The polynomial p(x) is defined by p(x) = 9x³ +18x² +5x+4.
The diagram shows the curve with equation y = ln(2x+1) / (x+3). The curve has a maximum point M. [Figure 6.1]
Prove that 2 sin θ cosec 2θ ≡ sec θ.
The diagram shows the curve with equation y = 8e⁻ˣ – e²ˣ. The curve crosses the y-axis at the point A and the x-axis at the point B. The shaded reg...
The diagram shows the curve with equation y = (ln (2x+1))/(x+3). The curve has a maximum point M.
Prove that 2 sinθ cosec 2θ = secθ.
Expand (3+x)(1-2x)⁻¹ in ascending powers of x, up to and including the term in x², simplifying the coefficients.
Solve the equation ln(x-5) = 7-lnx. Give your answer correct to 2 decimal places.
The variables x and y satisfy the equation aʸ = bx, where a and b are constants. The graph of y against lnx is a straight line passing through the ...
The complex number u is given by u = -1-i√3.
The equation of a curve is y = e^(sinx) / cos²x for 0 ≤ x ≤ 2π. Find dy/dx and hence find the x-coordinates of the stationary points of the curve.
By sketching a suitable pair of graphs, show that the equation cosec(1/2)x = eˣ - 3 has exactly one root, denoted by α, in the interval 0 < x < π.
On a single Argand diagram sketch the loci given by the equations |z-3+2i|= 2 and |w-3+2i|=|w+3-4i| where z and w are complex numbers.
Use the substitution u = 1-sinx to find the exact value of integral from π/6 to (3/2)π of (sin(2x) / sqrt(1-sinx)) dx. Give your answer in the form...
The equations of two straight lines l₁ and l₂ are l₁: r = i-2j+3k + λ(2i-j+ak) and l₂: r = -i-j-k + μ(3i-2j-2k), where a is a constant. The lines l...
Given that 2x = tany, show that dy/dx = 2 / (1+4x²).
In a field there are 300 plants of a certain species, all of which can be infected by a particular disease. At time t after the first plant is infe...
Sketch the graph of y = |x-2a|, where a is a positive constant.
Express (6x²-9x-16) / (2x²-5x-12) in partial fractions.
The variables x and y satisfy the equation a^(2y−1) = b^(x−y), where a and b are constants.
The equation of a curve is ye^(2x) + y²e^x = 6. Find the gradient of the curve at the point where y = 1.
It is given that the equation e^(2x) = 5 + cos 3x has only one root. Show by calculation that this root lies in the interval 0.7 < x < 0.8 .
The diagram shows the curve y = xe^(-ax), where a is a positive constant, and its maximum point M. [Figure 6.1]
Show that cos⁴θ - sin⁴θ ≡ cos 2θ.
The points A, B and C have position vectors OA =−2i+j+4k, OB = 5i+2j and OC = 8i+5j-3k, where O is the origin. The line l₁ passes through B and C.
The complex numbers z and ω are defined by z = 1-i and ω =-3+3√3i.
By writing y = sec³θ as (1/cos³θ) show that dy/dθ = 3 sin θ sec⁴θ.
Solve the equation 8³⁻⁶ˣ = 4×5⁻²ˣ. Give your answer correct to 3 decimal places.
Find the exact coordinates of the stationary point of the curve y = e²ˣ sin2x for 0 ≤ x ≤ ½π.
The square roots of 24-7i can be expressed in the Cartesian form x+iy, where x and y are real and exact. By first forming a quartic equation in x o...
The variables x and y satisfy the equation ky = eᶜˣ, where k and c are constants. The graph of ln y against x is a straight line passing through th...
Express (6x² - 2x + 2) / ((x-1)(2x+1)) in partial fractions.
On an Argand diagram shade the region whose points represent complex numbers z which satisfy both the inequalities|z-4-3i|<2 and arg(z-2-i) > ¾π.