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.
Four parts in a play are to be given to four of the girls chosen from the seven girls in a drama class. Find the number of different ways in which ...
In the diagram, ABC is an arc of the circle centre O, radius 5 cm, and angle AOC is 1.5 radians. AD and CE are diameters of the circle and DE is a ...
Vectors i and j are vectors parallel to the x-axis and y-axis respectively. Given that a = 2i + 3j, b = i – 5j and c = 3i + 11j, find
A = \( \begin{pmatrix} 2 & -1 \\ 1 & -3 \end{pmatrix} \) and B = \( \begin{pmatrix} 0 & -2 \\ 3 & -5 \end{pmatrix} \). Find (BA)⁻¹.
Differentiate x⁴(√sinx) with respect to x.
On the axes below, sketch the graph of y = |(x + 3)(x-5)| showing the coordinates of the points where the curve meets the x-axis. y X
Find ∫√2x - 1 dx.
In this question all lengths are in centimetres. The volume of a cone of height h and base radius r is given by V = ⅓πr²h. It is known that sin (π/...
On the Venn diagrams below, shade the region indicated. E A B C (A∩B)∪C E A B C (A'∪B)∩C
Write down the amplitude of 4 sin 3x-1.
The polynomial p(x) = (2x-1)(x+k)-12, where k is a constant.
The first 3 terms, in ascending powers of x, in the expansion of (2+bx)^8 can be written as a + 256x + cx². Find the value of each of the constants...
A particle P is moving with a velocity of 20ms⁻¹ in the same direction as (3/4).
The diagram shows the curve y = 3x²-2x+1 and the straight line y = 2x+5 intersecting at the points P and Q. Showing all your working, find the area...
Solve log₃x+log₉x = 12.
It is given that f(x) = 5e^x -1 for x ∈ R. It is given also that g(x) = x²+4 for x ∈ R.
In this question all lengths are in centimetres. A closed cylinder has base radius r, height h and volume V. It is given that the total surface are...
When lg y is plotted against x² a straight line graph is obtained which passes through the points (2, 4) and (6, 16).
It is given that y = (x²+1)(2x-3)^(1/2).
(a) On the Venn diagrams below, shade the region indicated. [Figure 1.1] (b) E = {x : 0° ≤ x ≤ 360°} P = {x: cos2x = 0.5} Q = {x: sinx = 0.5} Find...
Do not use a calculator in this question. Find the coordinates of the points of intersection of the curve y = (2x+3)²(x-1) and the line y = 3 (2x+3).
The number, B, of a certain type of bacteria at time t days can be described by B = 200e²ᵗ +800e⁻²ᵗ.
Given that (pr²) ^(1/2) √qr / q²(pr²)^(-1) can be written in the form p^a q^b r^c, find the value of each of the constants a, b and c.
The diagram shows the right-angled triangle OAB. The point C lies on the line OB. Angle OAB = π/2 radians and angle AOB = θ radians. AC is an arc o...
Find the number of different arrangements of the books if there are no restrictions.
A pilot wishes to fly his plane from a point A to a point B on a bearing of 055°. There is a wind blowing at 120kmh⁻¹ from the west. The plane can ...
When eʸ is plotted against 1/x, a straight line graph passing through the points (2, 20) and (4, 8) is obtained.
The diagram shows the curve y = 4+2cos 3x intersecting the line y = 5 at the points P and Q. [Figure 9.1]
The diagram shows an open container in the shape of a cuboid of width x cm, length 4x cm and height h cm. The volume of the container is 800 cm³. [...
The normal to the curve y = (x-2)(3x+1)^(1/2) at the point where x = 7/3, meets the y-axis at the point P. Find the exact coordinates of the point P.
Find the values of x for which x(6x + 7) ≥ 20.
Two variables x and y are such that y = In x / x³ for x > 0.
Sketch the graph of y = |5x-3| on the axes below, showing the coordinates of the points where the graph meets the coordinate axes.
Without using a calculator, express (√5-3)² / (√5+1) in the form p√5+q, where p and q are integers.
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.