2024 - JAMB Mathematics Past Questions and Answers - page 7

We are given the equation: \(25^{1 - x} \times 5^{x + 2} \div (\frac{1}{125})^{x} = 625^{-1}\). Start by expressing all numbers in terms of base 5:

• \(25 = 5^2\), so \(25^{1 - x} = 5^{2(1 - x)} = 5^{2 - 2x}\)
• \(125 = 5^3\), so \((1/125)^x = (5^{-3})^x = 5^{-3x}\)
• \(625 = 5^4\), so \(625^{-1} = 5^{-4}\)

Now, the equation becomes: \(5^{2 - 2x} \times 5^{x + 2} \div 5^{-3x} = 5^{-4}\).

Combine the exponents: \(5^{2 - 2x + x + 2 + 3x} = 5^{4 + 2x}\)

Set the exponents equal: 4 + 2x = -4, hence 2x = -8 and x = -4.

The area of a circle is given by \(A = \pi r^2\), where r is the radius. Given r = 4 cm and π = 3.142:

\(A = 3.142 \times 4^2 = 3.142 \times 16 = 50.272\) cm². The closest option is 50.3 cm².

Simplify the expression: \(\frac{2x^3 + 2x}{x} = 2x^2 + 2\)

Integrate term by term:

• \(\int 2x^2 dx = \frac{2x^3}{3}\)
• \(\int 2 dx = 2x\)

Therefore, the integral is: \(\frac{2x^3}{3} + 2x + k\), where k is the constant of integration.

Given 8x^{-2} = 2/25, rewrite as 8 / x^2 = 2 / 25. Cross-multiply:

8 * 25 = 2 * x^2 → 200 = 2x^2

Divide both sides by 2: x^2 = 100. Taking square root: x = 10