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Friday, 12th May, 2023
Further Mathematics/Mathematics (Elective) 2 (Essay) – 09:30am – 12:00pm
2023 WAEC FURTHER MATHEMATICS OBJECTIVES (OBJ) ANSWERS
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2023 WAEC FURTHER MATHEMATICS ESSAY (THEORY) ANSWERS
(No2).
Let V be the volume of the cube and s be the length of a side. We know that V = s^3, so differentiating both sides with respect to time t gives:
dV/dt = 3s^2 ds/dt
We are given that dV/dt = 3 cm^3/s, and s = 6 cm. Substituting these values into the equation above, we get:
3 = 3(6)^2 ds/dt
Solving for ds/dt, we get:
ds/dt = 1/12 cm/s
Therefore, the rate of change of the side of the base when its length is 6 cm is 1/12 cm/s.
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2. Let V be the volume of the cube and s be the length of a side. We know that V = s^3, so differentiating both sides with respect to time t gives:
dV/dt = 3s^2 ds/dt
We are given that dV/dt = 3 cm^3/s, and s = 6 cm. Substituting these values into the equation above, we get:
3 = 3(6)^2 ds/dt
Solving for ds/dt, we get:
ds/dt = 1/12 cm/s
Therefore, the rate of change of the side of the base when its length is 6 cm is 1/12 cm/s.
No 4)
(a) To find the number of terms in the series, we can use the formula for the sum of an arithmetic progression:
Sum = (n/2) * (first term + last term),
where "n" represents the number of terms in the series.
Given: First term (a₁) = -8, Last term (aâ‚™) = 52, and Sum (S) = 286.
Using the formula:
286 = (n/2) * (-8 + 52).
Simplifying the equation:
286 = (n/2) * 44.
Dividing both sides of the equation by 44:
286/44 = n/2.
6.5 = n/2.
Multiplying both sides of the equation by 2:
13 = n.
the number of terms in the series is 13.
(b) To find the common difference (d), we can use the formula:
Last term = First term + (n - 1) * common difference.
Given: First term (a₁) = -8, Last term (aâ‚™) = 52, and number of terms (n) = 13.
Using the formula:
52 = -8 + (13 - 1) * d.
Simplifying the equation:
52 = -8 + 12d.
Adding 8 to both sides of the equation:
60 = 12d.
Dividing both sides of the equation by 12:
5 = d.
the common difference in the arithmetic progression is 5.
2023 WAEC FURTHER MATHS QUESTIONS
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