NECO 2023 Mathematics Questions and Answers (Essay & Objective)
Wednesday, 2nd August 2023
Mathematics (Objective) – 10:00am – 11:45am
Mathematics (Essay) – 12:00pm – 2:30pm
(i) P = k * Q² / Z³
where k is the constant of proportionality. To find the value of k, we can plug in the given values (P=5, Q=3, and Z=1) into the equation:
5 = k * 3² / 1³
Solving for k gives us k = 5/9. So, the relationship between P, Q, and Z is:
P = (5/9) * Q² / Z³
(ii) To find Z when P=3 and Q=5, we substitute these values into the equation we derived:
3 = (5/9) * 5² / Z³
Solving this equation for Z gives us Z = ((5/9) * 25 / 3)^(1/3). Computing this results in approximately Z = 1.88 (rounded to the nearest hundredth).
(I) To find the number of sides in the polygon, we can use the formula for the sum of interior angles of a regular polygon, which is (n-2) * 180°, where ‘n’ is the number of sides. Given that the sum is 1440°, we can set up an equation: (n-2) * 180° = 1440°. Solving for ‘n’, we get n = 10. So, the polygon has 10 sides.
(ii) To find the size of each exterior angle of a regular polygon, we can use the formula: exterior angle = 360° / n, where ‘n’ is the number of sides. Substituting ‘n’ with 10, we get the exterior angle as 36°.
To calculate the principal amount, we can use the formula:
Principal = Interest / (Rate * Time)
Given the interest (Interest) is N29,880.00, the rate (Rate) is 3% (0.03 as a decimal), and the time (Time) is 15 years.
Principal = 29880 / (0.03 * 15) = 29880 / 0.45 = N66,400.00
So, the principal amount that will earn N29,880.00 in 15 years at 3% per annum simple interest is N66,400.00.
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