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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**

**2023 WAEC FURTHER MATHEMATICS OBJECTIVES (OBJ) ANSWERS**

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**2023 WAEC FURTHER MATHEMATICS ESSAY (THEORY) ANSWERS**

**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**

**2023 WAEC FURTHER MATHS QUESTIONS**

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