2024 - JAMB Mathematics Past Questions and Answers - page 4

The diagram shows a pair of intersecting lines forming angles at the intersection. To find the value of x, we use the property of vertically opposite angles. Since the angles are equal, the value of x is 40^o.

In the diagram above, < CDE = < CED = 15^o (base angles of isosceles triangle)

< ECD = 180^o - (15 + 15)^o = 150^o

But x + 110^o = 150^o (sum of opposite interior angles = opposite exterior angle)

x = 150^o - 110^o = 40^o

0.04945 to 2 significant figures is 0.05

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:

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

\[ 3080 = 49\pi h \]

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

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.

The common ratio \( r \) of a G.P. is the ratio of the second term to the first term:

\[ r = \frac{\sqrt{10} + 2\sqrt{5}}{\sqrt{10} + \sqrt{5}} \]

Rationalize by multiplying numerator and denominator by \( \sqrt{10} - \sqrt{5} \):

\[ r = \frac{(\sqrt{10} + 2\sqrt{5})(\sqrt{10} - \sqrt{5})}{(\sqrt{10} + \sqrt{5})(\sqrt{10} - \sqrt{5})} = \frac{\sqrt{50}}{5} = \sqrt{2} \]

The common ratio is \( \sqrt{2} \).

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

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

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