2024 - JAMB Mathematics Past Questions and Answers - page 1

We are tasked with solving the inequality:

\( \frac{x+2}{4} - \frac{2x-3}{3} < 4 \)

First, we multiply both sides of the inequality by 12 (the least common multiple of 4 and 3) to eliminate the fractions:

\( 12 \times \left( \frac{x+2}{4} - \frac{2x-3}{3} \right) < 12 \times 4 \)

Which simplifies to:

\( 3(x+2) - 4(2x-3) < 48 \)

Now, distribute and simplify:

\( 3x + 6 - 8x + 12 < 48 \)

\( -5x + 18 < 48 \)

Subtract 18 from both sides:

\( -5x < 30 \)

Divide both sides by -5 (and reverse the inequality sign):

\( x > -6 \)

We are given the equation:

\[ \frac{x}{a + 1} + \frac{y}{b} = 1 \]

Subtract \(\frac{x}{a + 1}\) from both sides:

\[ \frac{y}{b} = 1 - \frac{x}{a + 1} \]

Multiply both sides by b:

\[ y = b \left(1 - \frac{x}{a + 1}\right) \]

Simplify:

\[ y = \frac{b(a + 1 - x)}{a + 1} \]

To find the cosine of the angle a diagonal of the room makes with the floor, we first need to determine the length of the room's diagonal and the diagonal on the floor.

Let's denote the length, width, and height of the room as l = 12m, w = 9m, and h = 8m respectively.

1. The diagonal of the floor (d_f) can be found using the Pythagorean theorem:

d_f = \[\sqrt{l^2 + w^2} = \sqrt{12^2 + 9^2} = \sqrt{144 + 81} = \sqrt{225} = 15m\]

1. The diagonal of the room (d_r) can be found using the Pythagorean theorem, with the floor diagonal and height:

d_r = \[\sqrt{d_f^2 + h^2} = \sqrt{15^2 + 8^2} = \sqrt{225 + 64} = \sqrt{289} = 17m\]

Now, let \[\theta\] be the angle between the room's diagonal and the floor. The cosine of this angle can be found using the adjacent side (floor diagonal) and the hypotenuse (room diagonal):

cos(\[\theta\]) = \(rac{d_f}{d_r}\) = \[\frac{15}{17}\]

The word "LEADER" has 6 letters. The letter E appears twice.

To find the number of arrangements, we use the formula for permutations with repetitions:

In "LEADER":

• Total letters: 6
• 'E' appears twice

Thus, the total number of arrangements is 360.

Volume of a cylinder:

Given:

• V = 3080 m³
• Diameter = 14 m → r = 7 m
• π = \(\frac{22}{7}\)

Substitute:

Depth = 20 m

Total surface area of a cuboid:

Substitute:

Total surface area = 592 cm²

Formula for curved surface area:

\(CSA = 2\pi r h\)

Given \(CSA = 110\), \(h = 5\):

\(110 = 2 \times \frac{22}{7} \times r \times 5\)

\(110 = \frac{220}{7} r\)

\(r = \frac{110 \times 7}{220} = 3.5\) cm

Substitute \(x = 2\) into both equations:

\(y = 4p + q\)

\(y = 8 - 1 = 7\)

Equate:

\(4p + q = 7\)

Solve for p:

\(p = \frac{7 - q}{4}\)

0.04945 to 2 significant figures is 0.05

Convert each number to base 10:

243₆ = 2x6² + 4x6 + 3 = 99

243₅ = 2x5² + 4x5 + 3 = 73

Difference = 99 - 73 = 26