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 a regular pentagon and a regular hexagon joined along one edge. Find the value of x. [Figure 9]
a = (-3 4) b = (8 -2) Work out 3a-b.
A factory makes batteries. A batch of 2000 batteries are tested and 28 are found to be faulty. The factory makes 125000 batteries. Calculate the nu...
Write 372000000 in standard form.
These are the first five terms of a sequence. 3 8 13 18 23 Find the next term of the sequence.
N=2ˣ×3ʸ×5¹. The lowest common multiple (LCM) of N and 360 is 16200.
The mass of a bag of potatoes is 2.5kg, correct to the nearest 0.1 kg.
The population of a town decreases exponentially at a rate of x% per year. The population of the town on 1 January 2020 was 120000. The population ...
Sketch the graph of each function. Show the value where each graph intersects the y-axis.
The equation of line L is y = x/5 + 3.
A group of 22 students are asked if they study Economics (E) or History (H). The Venn diagram shows the results. [Figure 19]
y is inversely proportional to (x-3)². y = 4 when x = 7.
Solve the equation. 2x+1 / x+4 + 5 = x. You must show all your working and give your answers correct to 2 decimal places.
ABCD is a field. A straight path crosses the field from B to D. [Figure 22]
The diagram shows a shaded area in a large circle, centre O. The radius of the large circle is 10 cm. OAB is a sector of a small circle, centre O. ...
Owen records the mass of each of 250 onions. The histogram shows the results. [Figure 24]
Find the coefficients of x⁴ and x⁵ in the expansion of (1 – 2x)⁵.
A curve for which dy/dx = 3x² - 2/x² passes through (-1, 3). Find the equation of the curve.
The 12th term of an arithmetic progression is 17 and the sum of the first 31 terms is 1023. Find the 31st term.
Solve the equation sin⁻¹(3x) = −π/6, giving the solution in an exact form.
Two points have coordinates A (5, 7) and B (9, −1).
A vacuum flask (for keeping drinks hot) is modelled as a closed cylinder in which the internal radius is r cm and the internal height is h cm. The ...
The diagram shows a pyramid OABC with a horizontal triangular base OAB and vertical height OC. Angles AOB, BOC and AOC are each right angles. Unit ...
The function f is such that f(x) = a²x² – ax + 3b for x ≤ 1/(2a), where a and b are constants.
(a) [Figure 1] In Fig. 1, OAB is a sector of a circle with centre O and radius r. AX is the tangent at A to the arc AB and angle BAX = α. (b) [Figu...
The diagram shows part of the curve y = 1/16 (3x – 1)², which touches the x-axis at the point P. The point Q (3, 4) lies on the curve and the tange...
Find the set of values of k for which the equation 2x² + 3kx + k = 0 has distinct real roots.
In the expansion of (1/ax + 2ax²)⁵, the coefficient of x is 5. Find the value of the constant a.
The diagram shows a water container in the form of an inverted pyramid, which is such that when the height of the water level is h cm the surface o...
In the diagram, AB = AC = 8 cm and angle CAB = 2/7 π radians. The circular arc BC has centre A, the circular arc CD has centre B and ABD is a strai...
The diagram shows the graphs of y = tan x and y = cos x for 0 ≤ x ≤ π. The graphs intersect at points A and B. [Figure 5.1]
Relative to an origin O, the position vectors of the points A and B are given by OA = 2i + 3j + 5k and OB = 7i + 4j + 3k.
The function f is defined for x ≥ 0 by f(x) = (4x + 1)³ᐟ².
The functions f and g are defined for x ≥ 0 by f : x → 2x² + 3, g: x → 3x + 2.
The point A (2, 2) lies on the curve y = x² – 2x + 2.
The diagram shows the curve y = f(x) defined for x > 0. The curve has a minimum point at A and crosses the x-axis at B and C. It is given that dy/d...
Solve the equation 2 ln(2x) – ln(x + 3) = ln(3x + 5).
Given that tan 2θ cot θ = 8,
Solve the inequality |2x – 5| < |x + 3|.
Find the gradient of the curve x² sin y + cos 3y = 4 at the point (2, ½π).
It is given that a is a positive constant such that ∫[0 to a] (1 + 2x + 3e³ˣ) dx = 250.
The polynomial p(x) is defined by p(x) = ax³ + bx² – 17x – a, where a and b are constants. It is given that (x + 2) is a factor of p(x) and that th...
The diagram shows part of the curve y = 2 cos 2x cos(2x + ⅙π). The shaded region is bounded by the curve and the two axes.
A particle of mass 0.4 kg is projected with a speed of 12 m s⁻¹ up a line of greatest slope of a smooth plane inclined at 30° to the horizontal.
A particle P of mass 1.6 kg is suspended in equilibrium by two light inextensible strings attached to points A and B. The strings make angles of 20...
A particle of mass 0.6 kg is placed on a rough plane which is inclined at an angle of 21° to the horizontal. The particle is kept in equilibrium by...
A car of mass 900 kg is moving on a straight horizontal road ABCD. There is a constant resistance of magnitude 800 N in the sections AB and BC, and...
A particle P moves in a straight line starting from a point O and comes to rest 35 s later. At time t s after leaving O, the velocity v m s⁻¹ of P ...
Two particles of masses 1.2 kg and 0.8 kg are connected by a light inextensible string that passes over a fixed smooth pulley. The particles hang v...
A small ball is projected with speed 15 m s¯¹ at an angle of 60° above the horizontal. Find the distance from the point of projection of the ball a...