Solve the quadratic equation: 3x² - 7x - 6 = 0
Mathematics
Question · Medium
Factor it
Short
Express as a single algebraic fraction in its simplest form: 2 / (x - 1) + 3 / (x + 2)
The function f is defined as f(x) = (3x + 4) / 5. Find the inverse function f⁻¹(x).
Line L₁ has equation 2y + 4x = 7. Line L₂ is perpendicular to L₁ and passes through the point (2, 5). What is the equation of L₂?
Question · Hard
Points A, B, and C lie on a circle with centre O. Angle AOC is 110°. If B lies on the major arc AC, what is the size of angle ABC?
In triangle ABC, side b = 8 cm, side c = 11 cm, and angle A = 60°. Calculate the length of side a to 1 decimal place.
The bearing of lighthouse L from ship S is 065°. What is the back bearing of ship S from lighthouse L?
Question · Easy
Vector p = (3, -4) and vector q = (-1, 2). Find the magnitude of the resultant vector 2p + 3q.
Given the 2x2 matrix M = [[4, 2], [3, 2]], find the determinant of M.
A solid cone has a base radius of 5 cm and a vertical height of 12 cm. Taking π = 3.142, calculate its total surface area.
A box contains 6 red cards and 4 black cards. Two cards are drawn at random without replacement. What is the probability that both cards drawn are red?
Find the nth term formula for the quadratic sequence: 3, 8, 15, 24, 35, ...
It is given that y is inversely proportional to the square of x. When x = 3, y = 8. What is the value of y when x = 6?
A rectangle has length 12 cm and width 8 cm, each measured correct to the nearest centimetre. Calculate the upper bound for the perimeter of the rectangle.
The price of a laptop including 15% VAT in Mauritius is Rs 41,400. What was the original price before VAT was added?
Solve the simultaneous equations: y = 2x + 1 and x² + y² = 10 for positive values of x and y.
A cumulative frequency curve for the marks of 80 students gives a lower quartile (Q₁) of 42 marks, a median of 58 marks, an upper quartile (Q₃) of 70 marks and a 90th percentile of 78 marks. What is the interquartile range (IQR)?
A circle has an arc of length 11 cm that subtends an angle of θ at the centre. If the radius of the circle is 14 cm and π = 22/7, find θ in degrees.
Which single transformation is represented by the matrix [[0, -1], [1, 0]]?
Simplify the expression: (2x² - 8) / (x² + 3x + 2)
In a right-angled triangle ABC with hypotenuse AC = 15 cm and angle BAC = 35°, calculate the length of BC correct to 2 decimal places.
The volume of a sphere of radius r is given by V = (4/3)πr³. If the volume of a sphere is 288π cm³, find its radius.
A map of Mauritius is drawn to a representative fraction scale of 1 : 50,000. If two towns are 14 cm apart on the map, what is the actual ground distance in kilometres?
Which of the following points lies in the region defined by the system of linear inequalities: x ≥ 0, y ≥ 0, x + y ≤ 6, and y ≥ 2x?
Two circles touch internally at point T. A tangent line drawn at T is common to both circles. What is the angle between this common tangent and the line connecting the centres of both circles?
In formal English reading comprehension, which sentence most effectively avoids dangling or misplaced modifiers?
English Language
Identify the author's tone in the following passage: 'While the glossy tourism brochures depict pristine shores, a closer look at the lagoon reveals discarded plastic bottles and dying coral bleached by uncontrolled runoff.'
Choose the modal verb construction that expresses a logical deduction about a past event that definitely occurred:
Which of the following sentences correctly uses an inverted conditional structure?
Choose the word which best fills the blank in formal prose: 'The committee members commended the young scholar for her _____ research on marine biodiversity.'
Which sentence demonstrates the correct use of the colon according to formal punctuation standards?
Choose the sentence that correctly distinguishes between 'disinterested' and 'uninterested':
In Cambridge English summary writing, what is the most critical principle when condensing a text to a specific word limit?
Which of the following sentences features an oxymoron?
Choose the reporting verb that implies the speaker made a reluctant admission of truth:
What grammatical function does the gerund phrase in capitals serve in the sentence: 'PRESERVING ENDEMIC ECOSYSTEMS requires long-term international cooperation'?
Choose the dependent preposition that correctly completes the sentence: 'The corporate board agreed to comply _____ all environmental safety directives.'
Which of the following sentences effectively uses an antithesis for rhetorical contrast?
Select the sentence that avoids wordiness and tautology (needless repetition of meaning):
Choose the correct phrase to complete the mixed conditional sentence: 'If she had listened to the advice yesterday, she _____ in trouble now.'
What is the meaning of the word 'UBIQUITOUS' in formal prose?
Which sentence correctly demonstrates the formal placement of a preposition in a relative clause?
What rhetorical effect does a tricolon (rule of three) achieve in persuasive speech?
Which of the following sentences correctly uses the word 'compliment' as opposed to 'complement'?
What is the function of cohesive discourse markers like 'conversely' and 'in contrast' in academic writing?
Choose the sentence that correctly uses the idiom 'in the wake of':
Which of the following extracts demonstrates an appeal to pathos (emotional persuasion)?
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