Cambridge Past Paper Questions
Browse 23,045questions from 25 years of O-Level & A-Level exams. Click any question to practice.
Text, images and sound are represented as binary to be processed by a computer.
A computer game is programmed to use artificial intelligence (AI) to create the movements and actions of the computer-controlled characters in the ...
Tick (✔) one box to complete this sentence. The result of the arithmetic operation 4 ^ 2 is A 2 B 8 C 16 D 42
This pseudocode algorithm is intended to input a first name from a user and search for it in a two-dimensional (2D) array. If the name is found, th...
A program is written that will only accept values between –99.99 and +99.99, inclusive. The program is to be tested. The table, when completed, sho...
This flowchart represents an algorithm. [Figure 5.1]
Consider the logic expression: X = (J XOR NOT K) NAND NOT L
A database table WATERFOWL stores some details of a range of birds found in the UK that live on or near water. The length and wingspan dimensions a...
A program is required to test the fairness of the random number generator. The one-dimensional (1D) array RandomNumber[] is used to store 100000 ra...
Give three ways of creating a maintainable program.
Four descriptions of programming techniques and five programming techniques are given. Draw one line from each description to the relevant techniqu...
Tick (✔) one box to identify the most appropriate data type to store 'M' A integer B char C real D Boolean
Tickets for a theme park are booked online. An adult ticket costs $12.99 and a child ticket costs $7.99. A booking fee of $1.99 is added to the tot...
A program has been written in pseudocode to input five numbers between 1 and 900 inclusive and store the highest number and the lowest number enter...
The flowchart represents an algorithm. [Figure 6.1]
An algorithm has been written in pseudocode to: • input a whole number between 1 and 255 inclusive • convert the input to an 8-bit binary number • ...
A school has set up a database table EquipmentLoan to record details of school equipment loaned to students. EquipmentID Description N...
The variables Name, Age and Found are used in a computer program. Name holds the name of a person. Age holds the age of a person as a whole number....
A number game has two players. Random whole numbers are generated for each player. The numbers are compared and players are given points based on t...
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.
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,
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...