Nutrients lost by trees in leaf-fall can be re-used by the trees because the?

• A. trees are renewable resources
• B. nutrients circulate in the ecosystem
• C. nutrients are inexhaustible
• YD. trees store nutrients

a. In the diagram below, the radius of the sector of circle centre O is 7 cm and ∠MON is 60°. Find, correct toone decimal place, the area of the shaded portion. (take \(\pi = \frac{22}{7})\)

b. The x and y intercepts of a straight line are \(\frac{-3}{4} and \frac{2}{7}\) respectively. Find the equation of the line.

Explanation

a. Area of sector MON = \(\frac{MON}{360} \times\pi r^2\)

= \(\frac{60}{360}\times\frac{22}{7}\times7^2\)

= \(\frac{77}{3}cm^2\)

\(\frac{NT}{7}\) = sin60°

NT = 7sin60° = \(7\times\frac{\sqrt{3}}{2}\) = \(7\times\frac{\sqrt{3}}{2}\)cm.

\(\frac{OT}{9} = cos60^0\)

OT = 7cos60° = \(7\frac{1}{2}\)cm

Area of ?ONT = \(\frac{1}{2}\times OT\times NT\)

= \(\frac{1}{2}\times\frac{7}{2}\times\frac{7\sqrt{3}}{2} = 49\sqrt{3}{8}cm^2\)

Area of shaded portion = Area of sector MON - Area of ?ONT

= \(\frac{77}{3} - \frac{49\sqrt{3}}{8}\) = 25.67 - 10.61 = \(15.06cm^2\) = 15.1\(cm^2\)

b. Given : y = mx + c; hence ; x = \(\frac{ y - c }{ m } = \frac{ y }{ m } - \frac{ c }{ m }\)

x-intercept = \(\frac{ - c }{ m } = \frac{ - 3 }{ 4 }\)

Therefore, m = \(\frac{4}{3}\)c ....................... (1)

But y-intercept, c = \(\frac{2}{7}\)

Therefore, m = \(\frac{4}{3}\times\frac{2}{7} = \frac{8}{21}\)

Equation of straight: y = mx + c

y = \(\frac{8}{21}x + \frac{2}{7}\) OR 21y = 8x + 6 = 8x - 21y = - 6

The highest stage of socialism is

• A. racism
• B. fascism
• C. communism
• D. nazism

There are m boys and 12 girls in a class. What is the probability of selecting at random a girl from the class?

• A. \(\frac{m}{12}\)
• B. \(\frac{12}{m}\)
• C. \(\frac{12}{m+12}\)
• D. \(\frac{12}{m-12}\)

(a)(i) Define the term addition polymerization

(ii) What type of organic compounds undergo addition polymerization

(iii) List two factors which affect the strength of polymers

(b) The diagram below shows some reaction pathways involving ethanol

(i) Write the name and structural of the organic product X

(ii) State the reagent for the conversation indicated as step A.

(iii) What type of reaction will ethanol undergo CH\(_3\)CH\(_2\)COOH during the process of conversation indicated as step B?

(c)(i) Write three balanced equation for the complete combustion of ethanol in :date the volume of oxygen required at s.t.p for the complete combustion of ethanol. (H = 1, C = 12, O = 16, molar volume of gases at s.t.p. = 22.4 dm\(^3\))

(d)( i} State two substances produced when coal is heated in the absence of air

(ii) What name is given to the process in (d)(i) above?

(iii) State the importance of the non-volatile residue of the process named in (d)(iii) to the iron and steel industry.

The following nullifies an Islamic marriage if it is not fulfilled except

• A. proposal and acceptance
• B. conent of parents
• C. marriage feast
• D. payment of dowry

''God has made laughter for me; every one who hears will laugh over me.'' Sarah made the statement above when

• A. Abraham made a great feast on the day Isaac was weaned
• B. Hagar the Egyptian gave birth to Ishmael
• C. she gave birth to Isaac and was full of joy
• D. Abraham sent Hagar and her son away

Choose the option nearest in meaning to the underlined word. Thedisagreement between the two men became obvious during the meeting?

• A. insult
• B. confrontation
• C. passion
• D. insinuation

The deliberate tampering with the boundary of constituencies in order to win more seats is called

• A. devolution
• B. gerontocracy
• C. delimitation
• D. gerrymandering

A ball thrown vertically upward reaches a maximum height of 50 m above the level of projection. Calculate the;

(i) time taken to reach the maximum height,

(ii) speed of the throw. [g = 10 ms\(^{-2}\)]