2024 - JAMB Mathematics Past Questions and Answers - page 1

To convert the base-ten number 27 to base three, we repeatedly divide by 3 and record the remainders.

1. 27 ÷ 3 = 9, remainder 0
2. 9 ÷ 3 = 3, remainder 0
3. 3 ÷ 3 = 1, remainder 0
4. 1 ÷ 3 = 0, remainder 1

Reading the remainders from bottom to top gives \(1000_3\).

Therefore, the correct conversion is \(27_{10} = 1000_3\).

The number of arrangements of MATHEMATICIAN can be found using permutations with repeated letters.

The word has 13 letters.

• M appears 2 times
• A appears 3 times
• T appears 2 times
• I appears 2 times
• C, E, N each appear once

The formula is:

Evaluating gives:

So the number of arrangements is 129,729,600.

First find the diagonal of the floor:

Next, find the space diagonal of the room:

The cosine of the angle with the floor is:

The determinant of the left-hand side is:

The determinant of the right-hand side is:

Equate both sides:

Solve for x:

Total Surface Area of an open cylinder is:

Convert units:

Length = 50 cm = 0.5 m

Compute areas:

Curved surface area:

Area of base:

Total:

Multiply numerator and denominator by the conjugate:

Expand:

Thus:

Mean:

Squared deviations:

• 25
• 16
• 1
• 9
• 25

Sum = 76

Variance:

Standard deviation:

Using the chain rule:

Let \(u = 2x + 1\).

Then \(y = u^3\).

Differentiate:

Use the quadratic formula:

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

Thus the solutions are:

Volume formula:

Substitute:

Rounded:

\(1.62 \text{ cm}^3\)