Correct Answer: B. small in relation to available resources

Correct Answer: B. \(\frac{x - 6}{12}\)

Explanation

\(\frac{x - 4}{4} - \frac{x - 3}{6}\) = \(\frac{3(x - 4) - 2(x - 3)}{12}\)

= \(\frac{3x -12 - 2x + 6}{12}\)

= \(\frac{3x - 2x - 12 + 6}{12}\)

= \(\frac{x - 6}{12}\)

Correct Answer: A. positive

Correct Answer: A. Human sense of smell is easily fatigued

Correct Answer: C. net income from abroad

Explanation

The British colonial policies contributed to the rise of nationalism in West Africa in many ways. These include:

(i) The crown-colony policy was not acceptable to the nationalists, e.g. both the legislative and executive councils were dominated by British officials. Only illiterate African chiefs were nominated as members of the legislative council.

(ii) The land law was unfavourable to the chiefs and people.

(iii) The whites adopted colour bar and social segregation, e.g. housing estates, recreational facilities, hospital and schools.

(iv) Economic inequalities between 9. the whites and the indigenes especially in commercial enterprises contributed a lot to the rise of nationalism, e.g. granting of loans by banks, the activities of companies like UAC, UTC and P.Z.

(v) There was little or no opportunities for the advancement of the Africans in the public service.

(vi) There was inequality in wages between whites and natives especially in commercial enterprises were.

(vii) Provision of educational facilities through missionaries made the Africans politically conscious.

(viii)There opportunities for the Africans to participate in government through constitutional developments.

Explanation

(a) \(\overrightarrow{AB} = \begin{pmatrix} 4 \\ 5 \end{pmatrix} = 4i + 5j\)

\(\overrightarrow{AC} = \overrightarrow{AB} + \overrightarrow{BC}\)

= \(\begin{pmatrix} 4 \\ 5 \end{pmatrix} + \begin{pmatrix} -3 \\ 5 \end{pmatrix}\)

= \(\begin{pmatrix} 1 \\ 10 \end{pmatrix}\)

(i) Let \(\alpha\) be the angle between \(\overrightarrow{AB}\) and \(\overrightarrow{AC}\).

\(\overrightarrow{AB} \cdot \overrightarrow{AC} = |AB||AC| \cos \alpha\)

\((4i + 5j) \cdot (i + 10j) = (\sqrt{4^{2} + 5^{2}})(\sqrt{1^{2} + 10^{2}}) \cos \alpha\)

\(4 + 50 = (\sqrt{41})(\sqrt{101}) \cos \alpha\)

\(\cos \alpha = \frac{54}{(\sqrt{41})(\sqrt{101})}\)

\(\cos \alpha = 0.8392\)

\(\alpha = 32.94°\)

(ii) \(\overrightarrow{AB} - \overrightarrow{BC} = \begin{pmatrix} 4 \\ 5 \end{pmatrix} - \begin{pmatrix} -3 \\ 5 \end{pmatrix}\)

=\(\begin{pmatrix} 7 \\ 0 \end{pmatrix} = 7i\)

\(\overrightarrow{AB} - \overrightarrow{BC} = 7i\)

Unit vector in the direction of 7i = \(\frac{7i}{7} = i\)

(b) \(\overrightarrow{PQ} = \begin{pmatrix} 2 \\ 8 \end{pmatrix} ; \overrightarrow{PR} = \begin{pmatrix} 11 \\ -12 \end{pmatrix}\)

\(\overrightarrow{QR} = \overrightarrow{QP} + \overrightarrow{PR} \)

= \(-\overrightarrow{PQ} + \overrightarrow{PR}\)

= \(\begin{pmatrix} -2 \\ -8 \end{pmatrix} + \begin{pmatrix} 11 \\ -12 \end{pmatrix}\)

= \(\begin{pmatrix} 9 \\ -20 \end{pmatrix}\)

\(\frac{QM}{MR} = \frac{QP + PM}{MP + PR} = \frac{-PQ + PM}{-PM + PR}\)

\(\frac{QM}{MR} = \frac{3}{7}\)

\(7QM = 3MR\)

\(7(-PQ + PM) = 3(-PM + PR)\)

\(7(-PQ) + 7PM = 3(-PM) + 3(PR)\)

\(7(\begin{pmatrix} -2 \\ -8 \end{pmatrix} - 3(\begin{pmatrix} 11 \\ -12 \end{pmatrix} = -10(PM)\)

\(\begin{pmatrix} -47 \\ -20 \end{pmatrix} = -10(PM)\)

\(PM = \begin{pmatrix} 4.7 \\ 2 \end{pmatrix}\)

Explanation

(a)(i) An array is a collection of elements of the same type stored in a single variable.

OR

An array is a data structure with homogeneous element.

OR An array is a row of values, a column of values or a combination of rows and columns of values.

OR

An array is a data structure consisting of a collection of elements (values or variables) each identified by at least an array index or key.

(i) A syntax error is an error resulting from violation of grammatical rules of a language.

OR

A syntax error is an error from non compliance with the grammar of a language

(b) 10 DIM M (7)

20 PRINT "MULTIPLE OF 3"

30 FOR I = 1 TO 6

40 M() = 3 *I

50 PRINT M(I)

60 NEXT I

70 END

OR

10 FOR I = 1 TO 6

20 M(I) =3 *I

30 PRINT M(I)

40 NEXT I

(c) Converting D5 FA\(_{16}\) to binary

D = 1101

5 = 0101

F = 1111

A = 1010

D5FA\(_{16}\) = 1101010111111010\(_{2}\)

Explanation

*It is the fifth verse of S?ratul F?ti?ah.

*It means: “Thee alone do we worship and from Thee alone we seek for help:

*Man should worship none but Allah.

*In worship, man is not to associate partner(s) with Allah.

*Associating partner(s) with Allah is a major and unpardonable sin.

*Humankind’s source of help is Allah.

*Those who seek help from sources other than Allah are on the wrong path

*Such persons incur Allah’s displeasure.

- It is the last verses of S?ratut –T?n.

- It means: Is Allah not the best of Judges?

- Allah;s judgement is straight and fair.

- Human judgement is full of flaws.

- Those who flout Allah;s regulations are to be punished.

- The law-abiding ones will enjoy unending reward.

- In Allah;s court, there are no lawyers to argue a case.

- One cannot also deny wrong- doing if one indeed committed it.

- It is the opening verse of S?ratul- Qadr

- It means: we have revealed it on the Night of Power.

-The objectof revelation is the Qur;?n.

-It was on the Law?ul-Ma?f?z (Heavenly preserved Tablet).

- It was kept in the <em>Baytul- cIzza

- The revelation began in the year 610 C.E. at Cave Hira.

- The revelation to the Prophet was through the agency of Jibr?l.

- The revelation ended in 632 C.E.

- The compilation of the Qur;?n started in the reign of Caliph Ab?-Bakar.

- It was standardization during the rule of cUthm?n b. cAff?n.

Correct Answer: A. Presence of chloroplasts

Explanation

Kingdom Plantae is characterized by the presence of chloroplasts. Chloroplasts are the site of photosynthesis in plant cells, where light energy is converted into chemical energy. This is not to say that all organisms with chloroplasts belong to the Plantae kingdom, but it is a common feature of this kingdom.