# WAEC May/June Further Mathematics (Obj/Essay) Answers 2023 Expo runz

Get free 2023 WAEC May/June Further Maths (Obj & Essay) questions and answers for school candidates. Our WAEC May/June Free Further Mathematics Questions and Answers EXPO Room will be available on Friday, 12th May, 2023 . This is a chance for students to access practice questions and answers to aid their preparation for the upcoming exam. Please note that our service is only meant to provide educational support and not to encourage exam malpractice.

Friday, 12th May, 2023
Further Mathematics/Mathematics (Elective) 2 (Essay) – 09:30am – 12:00pm

## 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 (aₙ) = 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 (aₙ) = 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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