Explanation

(a) Two functions of a cultivator are: (i) For soil pulverisation (breaking the large clods of soil) (ii) For turning an burying of weeds.

(b)(i) Five tools or implements for land preparation are: (1) Plough (2) Spade (3) Harrow (4) Ridger (5) Hoe

(ii) Five tools/implements for planting are: (1) Planter (2) Hand trowel (3) Matchet (4) Hoe (5) Digger

(iii) Five tool implements for Harvesting are: (i) Combined harvester (2) Hoe (3) Sickle (4) Harvesting knives (5)Cassava puller

(iv) Five tools/implements for crop processing are: (1) sheller (2) thresher (3) grader (4) grinder and miller (5) grater

(c) Four reasons why farmers cultivate small holdings are: (i) Lack of finance to increase production (ii) Poor storage and processing facilities (iii) Problems of diseases and pests (iv) Problems of inadequate land (i. e land tenure system

Correct Answer: B. paradox

Correct Answer: B) persists until the environment changes

Explanation

The question is asking about a true climax community. A climax community is a stable and self-sustaining group of plants and animals that live in a particular environment. The question is asking which of the options is true about a climax community. Option A says that a climax community changes from year to year, but this is incorrect. A climax community is stable and doesn't change significantly unless the environment changes. Option B is correct. A climax community persists until the environment changes. This means that the group of plants and animals living in a specific environment will remain relatively stable until something happens to the environment that disrupts the balance. Option C says that a climax community is the first stage in plant succession, but this is incorrect. A climax community is the final stage in plant succession, after a series of changes in the plant community over time. Option D says that a climax community consists of the tallest trees and small animals, but this is incorrect. A climax community can include a variety of plant and animal species, not just the tallest trees and small animals. Option E says that a climax community is in a state of perturbation, but this is incorrect. A climax community is stable, not in a state of perturbation. In summary, the correct answer to the question is Option B. A climax community persists until the environment changes.

Correct Answer: C. Na2CO3 and CH3COONa

Correct Answer: B. paradox

Correct Answer: D. Tornado

Correct Answer: C) Yam and palm oil are complimentary goods

Explanation

This question is asking about the relationship between yam and palm oil. The question is asking whether yam and palm oil are substitute goods or complimentary goods. Substitute goods are goods that can be used to replace each other, while complimentary goods are goods that are used together.

In this case, yam and palm oil are used together, so they are complimentary goods. This means that when someone buys yam, they are likely to buy palm oil as well, and vice versa.

It's important to note that just because two goods are used together doesn't mean they are always complimentary goods. It depends on the specific situation and the preferences of the buyers.

For example, if someone is allergic to palm oil, then yam and palm oil would not be complimentary goods for them. They would use a substitute good instead, like a different type of oil.

It's also worth noting that the other options in the question are not correct. Yam is not a substitute good for palm oil, and palm oil is not a substitute good for yam. Yam and beans are not related in this question.

Understanding the difference between substitute goods and complimentary goods is an important concept in economics. It helps us understand how buyers make decisions about what to buy and how much to buy.

Explanation

(a)(i) Mean = \(\frac{\sum fx}{\sum f} = \frac{167}{32}\)

= \(5.21875 \approxeq 5.22\)

(ii) By inspection, the average of the numbers in the 16th and 17th position give the median

= \(\frac{5 + 5}{2} = 5\)

(iii) Mode = 7 marks having the largest frequency.

(b) Students who scored at least 8 marks = Those who scored 8, 9, 10.

Total number of students that scored at least 8 = 3 + 2 + 1 = 6.

\(%age = \frac{6}{32} \times 100% = 18.75%\)

Explanation

(a) From a displacement - time graph, the following can be deduced

(i) Uniform velocity

(ii) Instantaneous velocity

(iii) Initial displacement

(b) The force would remain the same Gram =

\(F_2 = \frac{Gmm}{r^2}\)

F\(_2\) = \(\frac{G2m \times 2m}{(2r)^2}\)

=\(\frac{G4m^2}{4r^2}\)

= \(\frac{Gm^2}{r^2}\)

= \(\frac{Gmm}{r^2}\)

\(F_1 = F_2\)

(c)Factors that affect maximum height of a bullet include

(i) Initial velocity / speed

(ii) Acceleration due to gravity

(iii) Angle of projection

(iv) Air resistance

(d)Practical examples of mechanical resonance include:

(i) Shattering of glass due to high pitch note.

(ii) Throwing of 2 paper rider from a vibrating stretched string

(iii) Collapse of a bridge by matching soldiers

(iv) Car bodies rattle (at very high speed)

(e)

acceleration = g sin \(\theta\) – \(\mu\) cos \(\theta\)

a =10 x sin 30 – 0.3 x 10 x cos30

=10 x 0.5 –0.3 x 10 x 0.8660

= 5 – 2.598

= 2.4m/s\(^2\)

Distance covered, s = \(\frac{4}{\sin30}\)

= \(\frac{4}{0.5}\)

= 8m

Using S = Ut + \(\frac{1}{2}\)at\(^2\)

8 =\(\frac{1}{2}\) x 2.4 x r\(^2\)

8 = 1.2\(t^2\)

\(r^2\) = \(\frac{8}{1.2}\)

= 2.58s

Correct Answer: A)

\(\cfrac{3n + 1}{2}\)