2024 - JAMB Mathematics Past Questions and Answers - page 5

The function given is y = -3 - 2x + x². To find the minimum value, differentiate with respect to x:

dy/dx = -2 + 2x

Set dy/dx = 0 to find the critical point:

-2 + 2x = 0 → x = 1

Therefore, the value of x that gives the minimum value is 1.

The external radius is 11 cm and the thickness of the metal is 10 cm. Hence, the internal radius is 11 - 10 = 1 cm. The surface area of the metal is:

Surface area = 2π x (external radius + internal radius) x height

Substituting values gives the area as 21π cm².

Formula for sum of interior angles of a polygon with n sides:

Sum = (n - 2) x 180°

Set (n - 2) x 180° = 1080°:

(n - 2) = 1080 / 180 = 6

n = 6 + 2 = 8

The polygon has 8 sides.

∑f = 2 + 2 + 8 + 4 + 4 = 20

Derivative using the chain rule:

1. Let u = 4x³ - 2x

2. du/dx = 12x² - 2

3. d/dx [log(u)] = 1/u x du/dx = (12x² - 2) / (4x³ - 2x)

Convert each number to base 10:

243₆ = 2x6² + 4x6 + 3 = 99

243₅ = 2x5² + 4x5 + 3 = 73

Difference = 99 - 73 = 26

2^x+y = 2⁴ ⇒ x + y = 4 ... (1)

4^x-y = 2²^x-y = 2²(x-y) = 2⁻⁵ ⇒ 2x - 2y = -5 ... (2)

Solving (1) and (2) simultaneously gives x = 3/4 and y = 13/4

The range = largest number - smallest number = 11 - 2 = 9

0.0014 x 0.011 = 0.0000154

In standard form: 1.54 x 10⁻⁵

Given: P = N525, A = N588, t = 3 years. Find r.

Simple interest formula: A = P + (P x r x t) / 100

Substitute values: 588 = 525 + (525 x r x 3) / 100

63 = (525 x r x 3) / 100

6300 = 525 x r x 3

r = 6300 / (525 x 3) = 4%