2024 - JAMB Mathematics Past Questions and Answers - page 6

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.

Multiply each score by the number of students:

• 0 x 4 = 0
• 1 x 3 = 3
• 2 x 7 = 14
• 3 x 8 = 24
• 4 x 6 = 24
• 5 x 2 = 10

Total = 0 + 3 + 14 + 24 + 24 + 10 = 75

The locus of a point that is equidistant from two intersecting straight lines is the angle bisector of the two lines. It divides the angle between the two lines into two equal parts.

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)

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

Rewrite the equation:

Slope = \(\frac{7}{4}\)

Perpendicular slope:

Using point-slope form for point (-3, 1):

Simplifying:

Multiply by 7:

Final Answer: 4x + 7y + 5 = 0

For the committee to include 2 females, we must select 3 males so that the total number of members is 5.

Number of ways = \(^4C_3 \times ^3C_2\)

= \(\frac{4!}{(4-3)! 3!} \times \frac{3!}{(3-2)! 2!} \)

= 4 x 3

= 12 ways

The volume of a cylinder is given by:

\[ V = \pi r^2 h \]

Where \(V\) is volume, \(r\) is radius, and \(h\) is height.

Given diameter = 14 m, so radius \( r = 7 \, m \)

Substitute values:

\[ 3080 = \pi \times 7^2 \times h \]

\[ 3080 = 49\pi h \]

\[ h = \frac{3080}{49\pi} \approx 20 \, m \]

Compute total goals by summing products of goals and frequencies:

\(0*4 + 1*3 + 2*15 + 3*16 + 4*1 + 5*0 + 6*1 = 0 + 3 + 30 + 48 + 4 + 0 + 6 = 91\)

Total number of goals = 91

Mean = (Σ frequency x marks) / Σ frequency = 3

Compute Σ frequency = (2y-2)+(y-1)+(3y-4)+(3-y)+(6-2y) = 3y-4

Compute Σ (frequency x marks) = 1*(2y-2) + 2*(y-1) + 3*(3y-4) + 4*(3-y) + 5*(6-2y) = 9y - 12

Set mean = 3: (9y - 12)/(3y - 4) = 3 ⇒ 9y - 12 = 9y - 12 (true for y = 2)

Therefore, y = 2