Correct Answer: A. calcium tetraoxsulphate (VI).

Explanation

Water hardness is primarily caused by the presence of dissolved mineral ions, especially divalent cations like calcium (Ca²⁺) and magnesium (Mg²⁺). These ions react with soap to form scum and can lead to scale buildup in pipes and appliances.

Let's break down the options:

• A. calcium tetraoxsulphate (VI): This is Calcium sulfate (CaSO₄). Calcium sulfate is a dissolved salt that contributes to permanent hardness in water.

• B. Magnesium tetraoxosulphate (VI): This is Magnesium sulfate (MgSO₄). Magnesium sulfate is also a dissolved salt that contributes to permanent hardness in water.

• C. Calcium hydrogen trioxocarbonate(IV): This is Calcium bicarbonate (Ca(HCO₃)₂). Calcium bicarbonate is a dissolved salt that contributes to temporary hardness in water.

• D. Magnesium hydrogen trioxcocarbonate (IV): This is Magnesium bicarbonate (Mg(HCO₃)₂). Magnesium bicarbonate is also a dissolved salt that contributes to temporary hardness in water.

All four options represent compounds that cause hardness in water. However, the question asks to identify *a* cause, and all options are valid. In a multiple-choice setting, if only one answer can be selected, there might be an implicit preference for a common example or a specific type of hardness. Calcium salts are very common contributors to hardness. Calcium sulfate is a well-known cause of permanent hardness.

The final answer is A

Correct Answer: A. potasium dioxonitrate (III)

Correct Answer: D. Chief Justice of Nigeria

Explanation

The Judicial Service Commission is vested with the power to recommend suitable persons for the appointment of the Chief justice of Nigeria.

Correct Answer: D. land, seas and vegetation

Correct Answer: D. Rock

Explanation

Parent materials are the weathered rock or sediment from which the soil was formed.

Explanation

Sources of farm power are: (i) Man (ii) Animal (iii) Machines (iv) Wind (v) Water (vi) Sun (vii) Electricity

Discussion (i) Man: (i) human labour is used with traditional tools. (ii) It involved many more people than all other sources power. (iii) output is very low. (iv) easily fatigued. (v) most intelligent source of power used for precision jobs. (vi) coorrdinates other forms of farm power. (vii) human can die. (viii) human labour can be hired. (ix) human labour may ed or unskilled. (x) high incidence of pests and diseases may limit its use.

ii. Animal: (i) animals such as cattle, horses, donkeys and buffaloes are used. (ii) used to carry people, draw ploughs, transport load e.g. farm produce, fertilizers, chemicals, e.t.c. (iii) the output is lower than the machines. (iv) gets tired easily. (v) should be properly maintained and red. (vi) constitute cheap source of power. (vii) has to be directed to perform its job - not intelligent source (viii).can eat up crops. (ix) animals can die (x) animal power can be hired. (xi) high incidence of pests diseases may limit its use e.g. the incidence of tse-tse fly in the south.

iii. Machines: (i) mechanical power is derived from machines and engines. (ii) It can also be used to operate ploughs, planters, harvesters, and other farm implements (iii) used in traction, grinding, food processing and others. (iv) their use is the bedrock of mechanised agriculture by which many hectares of land are cultivated i.e they facilitate the cultivation of large hectares of land. (v) examples machines are tractors, generators, water pumps, bulldozers (vi) They are costly to maintain. (vii) they must be controlled and they need skill for use. (viii) they reduce farm drugery i.e they make farm work less tedious. (ix) they are costly to purchase. (x) they can breakdown and hold up farm work. (xi) they make operations timely. (xii) it can destroy soil structure.

iv. Wind (i) The force of the wind can be converted into electricity through windmills. converts wind power to mechanical power. (iii) it is used in winnowing i.e separation of chaff from grains. (iv) the supply is erratic and is subject to weather conditions. (v) its efficiency is highly variable. (vi) used for drying.

v. Water(i) It is derived from rivers, streams or dams. (ii) It is also used in hydro-electric power station to drive the turbine that generate electricity. (iii) water used in transportation e.g. logs, farmer's goods etc. (iv) it is used to operate steam engines. (v) The use of water can be limited by adverse weather conditions.

vi. Sun: (i) solar energy is converted in electrical energy by solar panels installed in buildings. (ii) radiation, light and heat reaching the earth's surface com from the sun. (iii) It is also used in processing farm produce e.g. drying of items such as melon, maize, cocoa, meat, fish (iv) it is used in heating of farm stead. (v) the electrical energy so converted is used for different farming activities (vi) its efficiency is highly dependent on the degree of solar radiation/ intensity. (vii) it can be erratic. (viii) it is a neat source of energy. (ix) it is a cheap source of energy.

vii Electricity: (i) can be generated from various sources, e generators hydro-electricity. (ii) it is a very clean or neat source of energy. (iii) it is very versatile. (iv) land is used in performing several farming activities, including driving other machines, drying, refridgeration, feedmilling etc (v) it is a very efficient source of farm power. (vi) it must be controlled. (vii) it is expensive. (viii) it is usual reliable. (ix) it could be dangerous if carelessly handled.

Correct Answer: C. Valentine

Explanation

(a) \(y = 4x^{3}\)

\(\frac{\mathrm d y}{\mathrm d x} = 12x^{2}\)

\(12x^{2} = 108 \implies x^{2} = 9\)

\(\therefore x = \pm 3\)

When x = -3, \(y = 4(-3^{3}) = -108\)

When x = 3, \(y = 4(3^{3}) = 108\)

\(\therefore P = (-3, -108) ; Q = (3, 108)\)

(b)(i) \(\sin (A - B) = \sin A \cos B - \sin B \cos A\)

\(\sin 15 = \sin (45 - 30) = \sin 45 \cos 30 - \sin 30 \cos 45\)

= \((\frac{\sqrt{2}}{2})(\frac{\sqrt{3}}{2}) - (\frac{1}{2})(\frac{\sqrt{2}}{2})\)

= \(\frac{\sqrt{6} - \sqrt{2}}{4}\)

\(\cos (A - B) = \cos A \cos B + \sin A \sin B\)

\(\cos 15 = \cos (45 - 30) \)

= \(\cos 45 \cos 30 + \sin 45 \sin 30\)

= \((\frac{\sqrt{2}}{2})(\frac{\sqrt{3}}{2}) + (\frac{\sqrt{2}}{2})(\frac{1}{2})\)

= \(\frac{\sqrt{6} + \sqrt{2}}{4}\)

(b)(ii) \(\tan \theta = \frac{\sin \theta}{\cos \theta}\)

\(\tan 15 = \frac{\sqrt{6} - \sqrt{2}}{4} \div \frac{\sqrt{6} + \sqrt{2}}{4}\)

= \(\frac{\sqrt{6} - \sqrt{2}}{\sqrt{6} + \sqrt{2}}\)

Ratinalizing, we have

\((\frac{\sqrt{6} - \sqrt{2}}{\sqrt{6} + \sqrt{2}})(\frac{\sqrt{6} - \sqrt{2}}{\sqrt{6} - \sqrt{2}}) = \frac{6 - 2\sqrt{3} - 2\sqrt{3} + 2}{6 - 2}\)

= \(\frac{8 - 4\sqrt{3}}{4}\)

= \(2 - \sqrt{3}\)

Correct Answer: A. nature of man's creation

Correct Answer: C. operating system