Which of the following is the correct expansion and simplification of (2x - 3)(x + 5)?
Mathematics
Question · Easy
Why a balance sheet balances
Short
Solve the linear equation for x: (2x + 5) / 3 = x - 1
Question · Medium
Simplify using the laws of indices: (3a²b³)² ÷ (9ab⁴)
Factorise completely the quadratic expression: x² - 7x + 12
Solve the simultaneous equations: 2x + y = 13 and x - y = 2
Factor it
Make r the subject of the formula: V = πr²h, where r > 0.
Find the gradient of the line segment joining the points A(2, 3) and B(6, 11).
A straight line passes through the point (0, -4) and has a gradient of 3. What is the equation of the line?
A 10-metre ladder rests against a vertical wall. The base of the ladder is 6 metres away from the wall on level ground. How high up the wall does the ladder reach?
In a right-angled triangle PQR, angle Q = 90°, PQ = 5 cm, and QR = 12 cm. What is the value of sin ∠PRQ?
Question · Hard
Two similar triangles have corresponding side lengths in the ratio 3 : 5. If the area of the smaller triangle is 36 cm², what is the area of the larger triangle?
A sector of a circle of radius 7 cm has an angle of 60° at the centre. Taking π = 22/7, calculate the area of the sector.
A solid metal cylinder has a radius of 3 cm and a height of 10 cm. Taking π = 3.142, calculate its total surface area.
A bag contains 5 red balls, 4 blue balls, and 3 green balls. A ball is drawn at random. What is the probability that the ball drawn is NOT blue?
The table below shows the distribution of marks scored by 25 pupils: Marks (1, 2, 3, 4, 5) with frequencies (3, 6, 8, 5, 3). What is the median mark?
A sum of Rs 20,000 is placed in a fixed deposit paying 5% compound interest per annum. What is the total amount accumulated at the end of 2 years?
Solve the double inequality for integer values of x: -3 ≤ 2x - 1 < 7
The speed-time graph of a Metro Express train shows that it accelerates uniformly from rest to 20 m/s in 10 seconds, cruises at 20 m/s for 30 seconds, and decelerates uniformly to rest in 10 seconds. What is the total distance travelled?
Express the value of (4.8 × 10⁵) ÷ (1.6 × 10⁻²) in standard scientific form.
In a universal set ξ of 50 students, 28 study Computer Science (set C) and 24 study Art (set A). If 8 students study neither subject, how many students study both Computer Science and Art?
A net force of 150 N is applied to an object with a mass of 25 kg on a frictionless surface. What is the acceleration produced?
Science
A 2 kg stone is dropped from a cliff 45 metres high. Taking g = 10 m/s² and ignoring air resistance, what is its kinetic energy just before hitting the ground?
Two resistors of resistances 6 Ω and 12 Ω are connected in parallel across a 12 V battery. What is the total current drawn from the battery?
A light ray travels from air (refractive index n = 1.0) into glass with an angle of incidence of 30°. If the refractive index of the glass is 1.5, what can be stated about the angle of refraction?
What is the liquid pressure at a depth of 8 metres in a freshwater swimming pool? (Density of water = 1,000 kg/m³, g = 10 N/kg)
Which of the following electromagnetic waves has the highest frequency and shortest wavelength?
An atom of an element has 11 protons, 12 neutrons, and 11 electrons. What is its mass number and electron configuration?
Which of the following pairs of elements will react to form an ionic compound via electron transfer?
What is the general trend in reactivity of Group 1 alkali metals (Li, Na, K) as you go down the group?
When dilute hydrochloric acid (HCl) reacts with sodium hydroxide (NaOH), what are the products formed in this neutralisation reaction?
Which coefficients balance the chemical equation for the complete combustion of propane: C₃H₈ + x O₂ -> y CO₂ + z H₂O?
A piece of zinc metal is placed into an aqueous solution of copper(II) sulfate (CuSO₄). What observation will be made?
Which separation method is best suited for separating a mixture of miscible liquids with different boiling points, such as ethanol (78°C) and water (100°C)?
Which of the following cellular structures is present in plant cells but absent in animal cells?
What happens to the structure and activity of an enzyme when it is heated to 80°C, well above its optimum temperature?
How are human alveoli structurally adapted to maximise the rate of gas exchange in the lungs?
Which of the following factors can act as a limiting factor for photosynthesis on a cold, overcast winter morning in Mauritius?
During the human female menstrual cycle, which hormone triggers ovulation (the release of a mature egg from the ovary)?
In an ecological pyramid of energy, why does only approximately 10% of energy transfer from one trophic level to the next?
What is the phenomenon called when non-biodegradable pesticides like DDT become increasingly concentrated in tissues of organisms at higher trophic levels?
Choose the sentence with correct subject-verb agreement:
English
Which of the following sentences represents a third conditional expressing regret about an unfulfilled past situation?
Choose the correct preposition: 'The student was disqualified _____ entering the national science fair due to late submission.'
Convert into the passive voice: 'The Ministry should implement strict environmental regulations.'
Choose the sentence that correctly reports the direct command: '"Do not touch the laboratory equipment without permission," warned the science teacher.'
Identify the word closest in meaning to 'METICULOUS' in the sentence: 'The researcher conducted a meticulous audit of the coral reef ecosystem.'
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