2024 - JAMB Mathematics Past Questions and Answers - page 5

w = \(\frac{v(2 + cn)}{1 - cn}\)

2v + cnv = w(1 - cn)

2v + cnv = w - cnw

2v - w = -cnv - cnw

Multiply through by negative sign:

-2v + w = cnv + cnw

-2v + w = n(cv + cw)

n = \(\frac{-2v + w}{cv + cw}\)

n = \(\frac{1}{c} \frac{-2v + w}{v + w}\)

Re-arrange:

n = \(\frac{1}{c} \frac{w - 2v}{v + w}\)

We are given a point \(B\) such that its distance from Y is always twice its distance from X. This means the ratio of the distances from B to X and from B to Y is 1:2.

Let d_X represent the distance from B to X, and d_Y represent the distance from B to Y. According to the given condition, we have:

\( d_Y = 2 \cdot d_X \)

This suggests that point B lies on a locus where the distance to Y is always twice the distance to X. This condition is satisfied by a specific geometric construction, which is the perpendicular bisector of the line segment XY. The perpendicular bisector divides the segment XY into two equal parts and places any point on it equidistant from X and Y, satisfying the given ratio of distances.

For a geometric progression: S_∞ = a / (1 - r)

-1/10 = -1/8 / (1 - r)

Multiply both sides: -1/10 (1 - r) = -1/8

-(1 - r)/10 = -1/8

1 - r = 10/8 = 5/4

r = 1 - 5/4 = -1/4

The range = largest number - smallest number = 11 - 2 = 9

The problem states that y varies directly as √x. Thus:

\( y = k \sqrt{x} \)

Given y = 3 when x = 16:

3 = k \sqrt{16} = 4k

k = \frac{3}{4}

Now, when x = 64:

y = \frac{3}{4} \sqrt{64} = \frac{3}{4} \times 8 = 6

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:

Using the chain rule:

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

Then \(y = u^3\).

Differentiate:

Start with:

Multiply all terms by 12:

Simplify:

The function given is y = -3 - 2x + x². To find the minimum value, differentiate with respect to x:

dy/dx = -2 + 2x

Set dy/dx = 0 to find the critical point:

-2 + 2x = 0 → x = 1

Therefore, the value of x that gives the minimum value is 1.

∑f = 2 + 2 + 8 + 4 + 4 = 20