2024 - JAMB Mathematics Past Questions and Answers - page 2

\(\sin 45 = \frac{1}{\sqrt{2}}\)

\(\sin 30 = \frac{1}{2}\)

Therefore:

\(\sin 45 + \sin 30 = \frac{1}{\sqrt{2}} + \frac{1}{2} = \frac{\sqrt{2} + 1}{2} = \frac{1 + \sqrt{2}}{2}\)

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.

Use the quadratic formula:

Here, \(a = 3\), \(b = -4\), \(c = -5\).

Thus the solutions are:

To find the median, we first organise the data from the table:

Listing all data points:

• 3 appears 2 times → 3, 3
• 6 appears 3 times → 6, 6, 6
• 5 appears 4 times → 5, 5, 5, 5
• 2 appears 6 times → 2, 2, 2, 2, 2, 2

Ordered list:

2, 2, 2, 2, 2, 2, 3, 3, 5, 5, 5, 5, 6, 6, 6

There are 15 values. The median is in position:

The 8th value is 3.

Arc length formula:

Given θ = 30°, r = 12 cm

Substitute:

For two lines to be parallel, their slopes must be equal. The slope of the first line is 5 (from p = 5x + 3), and the slope of the second line is w (from p = wx + 5). Therefore:

\(5 = w\)

Hence, the value of w is 5.

Rewrite the expression:

\(a^2 - 4a + 4 - b^2 = (a - 2)^2 - b^2\)

Apply difference of squares:

\((a - 2 - b)(a - 2 + b)\)

Apply logarithmic rules:

• Power rule: 3 log₁₀2 = log₁₀8
• Product rule: log₁₀1.5 + log₁₀8 = log₁₀12
• Quotient rule: log₁₀12 - log₁₀0.3 = log₁₀(12/0.3) = log₁₀40

The integral of each term:

• ∫cos4x dx = sin4x / 4
• ∫sin3x dx = -cos3x / 3

Therefore:

∫(cos4x + sin3x) dx = (1/4) sin4x - (1/3) cos3x + C

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.