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 velocity-time graph represents the motion of a particle travelling in a straight line. [Figure 5.1]
A = ((x+3), -x; (2x), (x-3)). Given that A does not have an inverse, find the exact values of x.
The variables x, y and u are such that y = tan u and x = u³ + 1.
The diagram shows a right-angled triangle ABC with AB = 8cm and angle ABC = π/2 radians. The points D and E lie on AC and BC respectively. BAD and ...
Find the number of different ways the televisions can be arranged.
Solutions to this question by accurate drawing will not be accepted. The points A and B have coordinates (p, 3) and (1, 4) respectively and the lin...
Show that (cosec θ - cot θ) / sin θ = 1 / (1 + cos θ)
Given that ∫₀ᵃ e^(2x) dx = 50, find the exact value of a. You must show all your working.
Given that y = sinx / lnx², find an expression for dy/dx.
Find the values of k for which the equation (k-1)x²+kx-k = 0 has real and distinct roots.
Given that x-2 is a factor of ax³-12x²+5x+6, use the factor theorem to show that a = 4.
A circle has diameter x which is increasing at a constant rate of 0.01 cm s⁻¹. Find the exact rate of change of the area of the circle when x = 6 cm.
Express 5x² - 15x+1 in the form p(x+q)² +r, where p, q and r are constants.
State the order of the matrix `(0 1 4 8; 5 8 1 6)`.
Solve 1g(x² -3) = 0.
In the binomial expansion of `(a - x/2)^6`, the coefficient of x³ is 120 times the coefficient of x⁵. Find the possible values of the constant a.
Solve `6 sin²x - 13 cosx = 1` for `0° ≤ x ≤ 360°`.
Find the unit vector in the direction of `5i – 15j`.
The velocity, v ms⁻¹, of a particle travelling in a straight line, t seconds after passing through a fixed point O, is given by v = 4/(t+1)³.
(a) The functions f and g are defined by `f(x) = 5x-2` for `x > 1`, `g(x) = 4x²-9` for `x > 0`. (b) The function h is defined by `h(x) = √(x²-1)` f...
The diagram shows the graph of a cubic curve y = f(x). [Figure X.X]
Write down the period of 2 cos x/3 - 1.
The radius, r cm, of a circle is increasing at the rate of 5 cms⁻¹. Find, in terms of π, the rate at which the area of the circle is increasing whe...
DO NOT USE A CALCULATOR IN THIS QUESTION. Find the positive solution of the equation (5+4√7)x²+(4-2√7)x-1 = 0, giving your answer in the form a+b√7...
Find the equation of the tangent to the curve y = ln(3x²-1) / (x+2) at the point where x = 1. Give your answer in the form y = mx+c, where m and c ...
The line y = 5x+6 meets the curve xy = 8 at the points A and B.
The diagram shows an isosceles triangle OAB such that OA = OB and angle AOB = θ radians. The points C and D lie on OA and OB respectively. CD is an...
Show that 3/(2x-3) + 3/(2x+3) can be written as 12x / (4x²-9).
An arithmetic progression has a second term of -14 and a sum to 21 terms of 84. Find the first term and the 21st term of this progression.
Show that 1/(sec θ - 1) - 1/(sec θ + 1) = 2 cot² θ.
A curve is such that d²y/dx² = 5 cos 2x. This curve has a gradient of 3/4 at the point (-π/12, 5π/4). Find the equation of this curve.
On the axes below, sketch the graph of y=|(x-2)(x+1)(x+2)| showing the coordinates of the points where the curve meets the axes.
The volume, V, of a sphere of radius r is given by V = 4/3 πr². The radius, r cm, of a sphere is increasing at the rate of 0.5 cms⁻¹. Find, in term...
Find the first 3 terms in the expansion of (4-x/16)⁶ in ascending powers of x. Give each term in its simplest form.
Find how many different 5-digit numbers can be formed using the digits 1, 2, 3, 5, 7 and 8, if each digit may be used only once in any number.
f: x → (2x+3)² for x > 0 Find the range of f.
The diagram shows the straight line 2x+y=-5 and part of the curve xy+3 = 0. The straight line intersects the x-axis at the point A and intersects t...
Given that y = (x²-1)√5x+2, show that dy/dx = (Ax²+Bx+C) / (2√5x+2) where A, B and C are integers.
The diagram shows a triangle OAB such that OA = a and OB = b. The point P lies on OA such that OP = 3/4 OA. The point Q is the mid-point of AB. The...
A particle P moves in a straight line such that its displacement, xm, from a fixed point O at time ts is given by x = 10 sin2t-5. Find the speed of...
Solve tan 3x = -1 for -π/2 ≤ x ≤ π/2 radians, giving your answers in terms of π.
Variables x and y are such that, when √y is plotted against 1/x, a straight line graph passing through the points (0.5, 9) and (3, 34) is obtained....
Write 9x²-12x+5 in the form p(x-q)² +r, where p, q and r are constants.
DO NOT USE A CALCULATOR IN THIS QUESTION. p(x) = 15x³ +22x² - 15x+2
In an examination, candidates must select 2 questions from the 5 questions in section A and select 4 questions from the 8 questions in section B. F...
The vectors a and b are such that a = αi+j and b = 12i+βj.
Find the values of k for which the line y = kx-7 and the curve y = 3x² +8x+5 do not intersect.
Solve the simultaneous equations 10^(x+2y) = 5, 10^(3x+4y) = 50, giving x and y in exact simplified form.
Expand (2-x)⁵, simplifying each coefficient.
A particle travels in a straight line. As it passes through a fixed point O, the particle is travelling at a velocity of 3 ms⁻¹. The particle conti...