JAMB Mathematics Past Questions & Answers - Page 4

Intersecting Chords Theorem states that If two chords intersect in a circle, then the products of the measures of the segments of the chords are equal.

⇒ AE * EB = CE * ED

⇒ 6 * $x$ = 4 * ($x$ + 5)

⇒ 6$x$ = 4$x$ + 20

⇒ 6$x$ - 4$x$ = 20

⇒ 2$x$ = 20

∴ $x = \frac{20}{2}$ = 10 units

Area of the composite figure = Area of semi circle + Area of rectangle + Area of triangle

Area of semi circle = $\frac{1}{2}\pi r^2 = \frac{1}{2}\times\pi\times\frac{d^2}{4} = \frac{1}{2}\times\frac{22}{7}\times\frac{42^2}{4} = 693 m^2$

Area of rectangle = l x b = 42 x 60  =2520 m$^2$

Area of triangle = $\frac{1}{2}\times b \times h = \frac{1}{2}\times 36 \times 42 = 756 m^2$

∴ Area of the composite figure = 693 + 2520 + 756 = 3969 m$^2$

$log_2 (6 - x) = 3 - log_2 x$

⇒ $log_2 (6 - x) = 3 log_2 2 - log_2 x$ (since $log_2$ 2 = 1)

⇒ $log_2 (6 - x) = log_2 2^3 - log_2 x$ $(a log$ c = $log$ c$^a)$

⇒ $log_2 (6 - x) = log_2 8 - log_2 x$

⇒$log_2 (6 - x) = log_2 \frac{8}{x}$ ($log$ a - $log$ b = $log \frac{a}{b})$

⇒ $6 - x = \frac{8}{x}$

⇒ $x (6 - x) = 8$

⇒ $6x - x^2 = 8$

⇒ $x^2 - 6x + 8 = 0$

⇒ $x^2 - 4x - 2x + 8 = 0$

⇒ $x (x - 4) - 2(x - 4) = 0$

⇒ $(x - 4)(x - 2) = 0$

⇒ $x - 4 = 0 or x - 2 = 0$

∴ x = 4 or 2

Let number of children's ticket at ₦250.00 each = $x$

∴ Number of adult tickets at ₦520.00 each = 5$x$

Then,

Total amount of money received from children's tickets = 250$x$

Total amount of money received from adult tickets = 520(5$x$)

⇒ 250$x$ + 520(5$x$) = 171,000

⇒ 250$x$ + 2600$x$ = 171,000

⇒ 2850$x$ = 171,000

⇒ $x = \frac{171,000}{2850} = 60$

∴ 60 tickets were sold at ₦250.00 and 300 tickets were sold at ₦520.00

The line: $3y + 6x$ = 48

Divide through by 3

⇒ y + 2$x$ = 16

⇒ y = -2$x$ + 16

∴ The gradient of the line = -2

The points: A(-2, k) and B (4, 8)

m =$\frac{y2 - y1}{x2 - x1} = \frac{8 - k}{4 - (-2)}$

⇒ m =$\frac[8 - k}{4 + 2} = {8 - k}{6}$

Since the line passes through the points

∴ -2 = $\frac{8 - k}{6}$

⇒ $\frac{-2}[1} = \frac{8 - k]{6}$

⇒ 8 - k = -12

⇒ k = 8 + 12

∴ k = 20