FURTHER MATHEMATICS WAEC ANSWERS 2023
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OBJ FURTHER MATHEMATICS
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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!!!
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FURTHER MATHEMATICS QUESTION 1
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FURTHER MATHEMATICS QUESTION 2
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FURTHER MATHEMATICS QUESTION 3
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FURTHER MATHEMATICS QUESTION 4
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