# FURTHER MATHEMATICS WAEC ANSWERS 2023

======================================================

OBJ FURTHER MATHEMATICS

1-10:##########

11-20:##########

21-30:##########

31-40:##########

41-50:##########

**Solving/Typing……**

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.

3. To solve this problem:

(a) We know that the inverse function of f(x) is given by:

x = f^(-1)(y)

Therefore, we need to solve the given equation for y to find the inverse function:

y = -6x^(1/4)

So the function f(x) is:

f(x) = y = -6x^(1/4)

(b) We need to find the value of x such that f(x) = 5. Substituting the function f(x) from part (a), we get:

-6x^(1/4) = 5

Dividing both sides by -6, we get:

x^(1/4) = -5/6

Raising both sides to the fourth power, we get:

x = (-5/6)^4 = 0.4823

Therefore, the value of x for which f(x) = 5 is approximately 0.4823.

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.

Complete!!!

======================================================

FURTHER MATHEMATICS QUESTION 1

**Solving/Typing……**

**Answers loading….**

======================================================

FURTHER MATHEMATICS QUESTION 2

**Solving/Typing……**

**Answers loading….**

======================================================

FURTHER MATHEMATICS QUESTION 3

**Solving/Typing……**

**Answers loading….**

======================================================

FURTHER MATHEMATICS QUESTION 4

**Solving/Typing……**

**Answers loading….**

======================================================

END