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 diagram shows the graph of the curve y= (e^(4x)+3)/8. The curve meets the y-axis at the point A. The normal to the curve at A meets the x-axis ...
A, B and C are subsets of the same universal set.
The variables x and y are such that y = ln(3x-1) for x > 1/3.
A 7-character password is to be selected from the 12 characters shown in the table. Each character may be used only once. Characters Upper-case let...
Do not use a calculator in this question. It is given that x + 4 is a factor of p(x) = 2x³ + 3x² + ax - 12. When p(x) is divided by x - 1 the remai...
The function f is defined by f(x) = 1/(2x-5) for x > 2.5.
In the diagram AOB and DOC are sectors of a circle centre O. The angle AOB is x radians. The length of the arc AB is 40 cm and the radius OB is 16 ...
An experiment was carried out recording values of y for certain values of x. The variables x and y are thought to be connected by the relationship ...
Express 5x² - 14x - 3 in the form p(x+q)² + r, where p, q and r are constants.
A particle moves in a straight line such that its displacement, s metres, from a fixed point O at time t seconds, is given by s = 4 + cos3t, where ...
Solve 10 cos²x + 3 sinx = 9 for 0° < x < 360°.
In this question all lengths are in metres. A water container is in the shape of a triangular prism. The diagrams show the container and its cross-...
Show that cos θ cot θ + sin θ = cosec θ.
On the Venn diagram below, shade the region that represents A ∩ B΄. E A B
It is given that x + 3 is a factor of the polynomial p(x) = 2x³ + ax² – 24x + b. The remainder when p(x) is divided by x − 2 is -15. Find the remai...
Find the coordinates of the points where the line 2y - 3x = 6 intersects the curve x²/4 + y²/9 = 5.
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.