All practice questions

Question 7061Question →

A meteorological station in northern Nigeria records an annual rainfall of $850\text{ mm}$ concentrated within a 4-month wet season, accompanied by a mean monthly relative humidity dropping below $30\%$ during the dry season and a high annual temperature range of about $10^\circ\text{C}$ . Which climatic region of Nigeria does this station represent, and what primary atmospheric factor accounts for its extended dry season?

Tropical Continental (Sudan) Climate, caused by the prolonged influence of the dry Tropical Continental (cT) air mass.

Tropical Hinterland (Guinea) Climate, caused by the convergence of marine air masses over high-altitude landforms.

Sub-Equatorial Climate, caused by the seasonal subsidence of squall lines along the coast.

Highland (Montane) Climate, caused by rain-shadow effects along the Eastern Borderlands.

Show answer & explanation

Answer: Tropical Continental (Sudan) Climate, caused by the prolonged influence of the dry Tropical Continental (cT) air mass.

Answer

Tropical Continental (Sudan) Climate, caused by the prolonged influence of the dry Tropical Continental (cT) air mass.

The correct response accurately identifies the Tropical Continental (Sudan) climate belt. In northern Nigeria, the Inter-Tropical Discontinuity (ITD) retreats southward rapidly after August, leaving the region under the prolonged influence of the dry, continental air mass (cT) bringing low humidity, sparse rainfall (

500\text{--}1000\text{ mm}

), and higher diurnal/annual temperature ranges.

Step-by-Step Solution

1

Analyze the climatic parameters given in the stem

Annual rainfall of

850\text{ mm}

, short 4-month wet season, low relative humidity (

<30\%

), and high temperature range (

10^\circ\text{C}

).

These statistics define a semi-arid tropical continental regime in northern Nigeria.

2

Match parameters to Nigerian climatic zones

Northern Nigeria (Sudan/Sahel belt) is dominated for 7–8 months of the year by the dry Tropical Continental (cT) air mass originating from the Sahara Desert.

The Inter-Tropical Discontinuity (ITD) remains south of this latitude for most of the year, preventing moisture-laden maritime winds from bringing rain.

Key Concept

Tropical Continental Climate Characteristics and Air Mass Dynamics in Nigeria

Estimated Time:1m 30s

Question 7062Question →

If $y = (2x - 3)^5$ , what is the value of $\frac{dy}{dx}$ at $x = 2$ ?

5

8

10

20

Show answer & explanation

Answer: 10

Answer

10

The derivative of

y = (2x - 3)^5

with respect to

x

requires the chain rule:

\frac{dy}{dx} = 5(2x - 3)^4 \cdot \frac{d}{dx}(2x - 3) = 5(2x - 3)^4 \cdot 2 = 10(2x - 3)^4

. Substituting

x = 2

gives

10(2(2) - 3)^4 = 10(1)^4 = 10

, which makes

10

the correct value.

Step-by-Step Solution

1

Identify the inner function

u(x)

and outer function

f(u)

Let

u = 2x - 3

, so

y = u^5

.

The chain rule states that

\frac{dy}{dx} = \frac{dy}{du} \cdot \frac{du}{dx}

.

2

Differentiate

y

with respect to

u

and

u

with respect to

x

\frac{dy}{du} = 5u^4 = 5(2x - 3)^4

and

\frac{du}{dx} = 2

.

Apply the power rule to both functions.

3

Multiply the derivatives to find

\frac{dy}{dx}

\frac{dy}{dx} = 5(2x - 3)^4 \cdot 2 = 10(2x - 3)^4

.

Combine terms using the chain rule formula.

4

Substitute

x = 2

into the derivative

\frac{dy}{dx}\Big|_{x=2} = 10(2(2) - 3)^4 = 10(1)^4 = 10

.

Evaluate the expression numerically at the target point.

Key Concept

Chain Rule for Differentiation

Estimated Time:45s

Question 7063Question →

If $8^{x - 1} = 32$ , what is the value of $x$ ?

2

\frac{8}{3}

5

\frac{2}{3}

Show answer & explanation

Answer: $\frac{8}{3}$

Answer

The value of

x

is

\frac{8}{3}

.

To solve

8^{x - 1} = 32

, rewrite both sides using a base of

2

:

(2^3)^{x - 1} = 2^5

. Applying the index law

(a^m)^n = a^{mn}

yields

2^{3x - 3} = 2^5

. Since the bases are identical, set the exponents equal to each other:

3x - 3 = 5

. Solving for

x

gives

3x = 8

, so

x = \frac{8}{3}

.

Step-by-Step Solution

1

Express both numbers as powers of a common base,

2

.

8 = 2^3

and

32 = 2^5

, so

(2^3)^{x - 1} = 2^5

.

Exponential equations with different bases are easiest to solve by expressing terms with the same base.

2

Apply the law of indices

(a^m)^n = a^{mn}

to simplify the left-hand side.

2^{3(x - 1)} = 2^5

, which expands to

2^{3x - 3} = 2^5

.

Multiplying the inner exponent by the outer exponent removes parentheses.

3

Equate the exponents since the bases are equal.

3x - 3 = 5

.

If

a^P = a^Q

for

a > 0

and

a \neq 1

, then

P = Q

.

4

Solve the linear equation for

x

.

3x = 5 + 3 \implies 3x = 8 \implies x = \frac{8}{3}

.

Isolate

x

by adding

3

to both sides and dividing by

3

.

Key Concept

Solving Exponential Equations using Base Conversion

Estimated Time:1m 0s

Question 7064Question →

If $\frac{2\sqrt{3} - \sqrt{5}}{\sqrt{3} + \sqrt{5}} = a + b\sqrt{15}$ , where $a$ and $b$ are rational numbers, what is the value of $a - b$ ?

-7

7

-4

-2

Show answer & explanation

Answer: $-7$

Answer

-7

Rationalizing

\frac{2\sqrt{3} - \sqrt{5}}{\sqrt{3} + \sqrt{5}}

by multiplying top and bottom by

(\sqrt{3} - \sqrt{5})

yields

\frac{11 - 3\sqrt{15}}{-2} = -\frac{11}{2} + \frac{3}{2}\sqrt{15}

. Comparing this with

a + b\sqrt{15}

gives

a = -\frac{11}{2}

and

b = \frac{3}{2}

. Computing

a - b

gives

-\frac{11}{2} - \frac{3}{2} = -7

.

Step-by-Step Solution

1

Multiply the numerator and denominator by the conjugate of the denominator

(\sqrt{3} - \sqrt{5})

\frac{(2\sqrt{3} - \sqrt{5})(\sqrt{3} - \sqrt{5})}{(\sqrt{3} + \sqrt{5})(\sqrt{3} - \sqrt{5})}

Rationalizing the denominator requires using the difference of squares.

2

Expand the numerator and simplify the denominator

Numerator:

2(3) - 2\sqrt{15} - \sqrt{15} + 5 = 11 - 3\sqrt{15}

. Denominator:

3 - 5 = -2

.

Multiply terms using FOIL and replace

(\sqrt{3})^2

with

3

and

(\sqrt{5})^2

with

5

.

3

Divide the numerator by the denominator to express in standard form

a + b\sqrt{15}

\frac{11 - 3\sqrt{15}}{-2} = -\frac{11}{2} + \frac{3}{2}\sqrt{15}

Separate the rational term and the surd coefficient.

4

Equate coefficients to find

a

and

b

, then compute

a - b

a = -\frac{11}{2}, b = \frac{3}{2} \implies a - b = -\frac{11}{2} - \frac{3}{2} = -\frac{14}{2} = -7

Calculate the target expression

a - b

using the derived rational values.

Key Concept

Rationalization of Binomial Denominators and Equating Surd Coefficients

Question 7065Question →

What is the numerical value of the expression $\log_2(\log_3 81) + \log_5\left(\frac{1}{125}\right) + 4^{\log_2 3}$ ?

Show answer & explanation

Answer: 8

Answer

8

Evaluating each term individually: the nested logarithm

\log_2(\log_3 81) = \log_2 4 = 2

; the reciprocal log argument

\log_5(1/125) = -3

; and the exponential log power

4^{\log_2 3} = (2^{\log_2 3})^2 = 3^2 = 9

. Combining these gives

2 - 3 + 9 = 8

.

Step-by-Step Solution

1

Evaluate the first component

\log_2(\log_3 81)

2

Since

81 = 3^4

, the inner expression

\log_3 81 = 4

, and subsequently

\log_2 4 = 2

.

2

Evaluate the second component

\log_5\left(\frac{1}{125}\right)

-3

Since

\frac{1}{125} = 5^{-3}

, applying the power law of logarithms gives

-3

.

3

Evaluate the third component

4^{\log_2 3}

9

Rewrite

4

as

2^2

to obtain

(2^{\log_2 3})^2 = 3^2 = 9

using the fundamental identity

a^{\log_a b} = b

.

4

Sum the results of the three components

8

Calculate

2 + (-3) + 9 = 8

.

Key Concept

Properties of logarithms including change of power, negative exponents, and logarithm exponentiation identities

Question 7066Question →

A coastal African nation faces two distinct environmental challenges: the illegal dumping of imported toxic electronic waste along its shoreline, and the ecological degradation of an expansive coastal wetland that serves as a critical habitat for endangered migratory birds. Which pair of international agreements specifically provides the regulatory frameworks to address these two challenges, respectively?

The Basel Convention and the Ramsar Convention

The Montreal Protocol and the Kyoto Protocol

The CITES Treaty and Agenda 21

The Paris Agreement and the Basel Convention

Show answer & explanation

Answer: The Basel Convention and the Ramsar Convention

Answer

The Basel Convention and the Ramsar Convention

The option selecting the Basel Convention and the Ramsar Convention is correct because the Basel Convention directly targets international movements and dumping of hazardous e-waste, while the Ramsar Convention provides international standards for preserving wetland ecosystems.

Step-by-Step Solution

1

Analyze the first environmental challenge in the stem

The issue involves transboundary movement and dumping of toxic electronic waste.

The Basel Convention on the Control of Transboundary Movements of Hazardous Wastes and Their Disposal (1989) is the global treaty designed to prevent and control the transfer of toxic materials from developed to developing countries.

2

Analyze the second environmental challenge in the stem

The issue involves the degradation of a coastal wetland providing habitat for migratory birds.

The Ramsar Convention on Wetlands of International Importance (1971) specifically targets the protection, sustainable management, and preservation of wetland ecosystems and waterfowl habitats.

3

Match the identified treaties in the correct sequence

The correct sequence is Basel Convention followed by Ramsar Convention.

The question requires matching the treaties to hazardous waste regulation first and wetland habitat preservation second.

Key Concept

Scope and mandates of global environmental conventions

Question 7067Question →

The East African Highlands support one of the highest rural population densities on the African continent. Which physical factor is primarily responsible for attracting and sustaining this dense settlement despite the rugged terrain?

Highly fertile soils derived from weathered volcanic deposits

Extensive flat floodplains suitable for large-scale mechanized wheat farming

High annual temperatures that naturally eradicate agricultural pests

Abundant subsurface petroleum deposits driving industrial urbanization

Show answer & explanation

Answer: Highly fertile soils derived from weathered volcanic deposits

Answer

Highly fertile soils derived from weathered volcanic deposits

Weathered volcanic rocks in the East African Highlands produce exceptionally fertile soils rich in essential minerals, enabling continuous crop production and supporting high rural population densities despite steep slopes.

Step-by-Step Solution

1

Identify the main physical characteristics and economic baseline of the East African Highlands

The region features high elevation, steep relief, and an economy centered on intensive smallholder agriculture.

Understanding land use helps distinguish physical environmental factors from industrial or urban drivers.

2

Analyze how volcanic geology impacts agricultural carrying capacity

Weathering of volcanic ash and basalt yields mineral-rich soils that retain high fertility under continuous cultivation.

High agricultural productivity allows small areas of land to feed dense rural populations, overriding slope limitations.

Key Concept

Physical factors influencing population density: Volcanic soil fertility and carrying capacity

Question 7068Question →

The political map of East Africa comprises both coastal states and landlocked territories whose international trade depends heavily on transit corridors through neighboring ports. Which of the following groups consists EXCLUSIVELY of landlocked countries located within East Africa?

Uganda, Rwanda, and South Sudan

Kenya, Tanzania, and Uganda

Ethiopia, Somalia, and Eritrea

Zambia, Malawi, and Mozambique

Show answer & explanation

Answer: Uganda, Rwanda, and South Sudan

Answer

Uganda, Rwanda, and South Sudan are all landlocked countries situated in East Africa.

The group comprising Uganda, Rwanda, and South Sudan contains exclusively landlocked states in East Africa. None of these three nations border an ocean or sea, relying on neighboring coastal countries for port access.

Step-by-Step Solution

1

Analyze the geographical location and coastal access of each nation in the options.

Identify whether each country has direct access to an ocean or sea.

A landlocked nation is completely enclosed by land without direct outlet to a sea or ocean.

2

Evaluate the option containing Uganda, Rwanda, and South Sudan.

Uganda relies on Kenyan and Tanzanian ports, Rwanda relies on Tanzanian and Kenyan corridors, and South Sudan relies on Sudan or Kenya for maritime routes.

None of these three sovereign states possess a maritime coastline.

Key Concept

Political Divisions and Landlocked States of East Africa

Estimated Time:1m 0s

Question 7069Question →

The sum to infinity of a geometric progression (G.P.) with positive terms is $18$ , and the sum of its first two terms is $16$ . What is the first term of the progression?

Show answer & explanation

Answer: 12

Answer

The first term of the progression is 12.

Using the sum to infinity formula

S_{\infty} = \frac{a}{1 - r} = 18

, we express the first term as

a = 18(1 - r)

. Combining this with the sum of the first two terms

S_2 = a(1 + r) = 16

yields

18(1 - r)(1 + r) = 16 \implies 18(1 - r^2) = 16

. Solving for

r

gives

r^2 = \frac{1}{9}

, so

r = \frac{1}{3}

for a sequence with positive terms. Substituting

r = \frac{1}{3}

back into

a = 18(1 - r)

gives

a = 12

.

Step-by-Step Solution

1

Express the sum to infinity in terms of the first term

a

and common ratio

r

.

a = 18(1 - r)

The sum to infinity formula for a convergent G.P. is

S_{\infty} = \frac{a}{1 - r}

.

2

Write the expression for the sum of the first two terms.

a(1 + r) = 16

The sum of the first two terms is

T_1 + T_2 = a + ar = a(1 + r)

.

3

Substitute

a = 18(1 - r)

into the sum of the first two terms equation.

18(1 - r^2) = 16

Applying the difference of two squares identity

(1 - r)(1 + r) = 1 - r^2

.

4

Solve for the common ratio

r

.

r = \frac{1}{3}

Rearranging gives

1 - r^2 = \frac{8}{9} \implies r^2 = \frac{1}{9}

. Since all terms are positive,

r

must be positive.

5

Calculate the first term

a

.

a = 12

Substitute

r = \frac{1}{3}

into

a = 18(1 - r)

to get

a = 18 \times \frac{2}{3} = 12

.

Key Concept

Geometric Progression sum to infinity and partial sums

Estimated Time:1m 30s

Question 7070Question →

What is the solution set for the linear inequality $\frac{1 - 4x}{3} \le \frac{x + 7}{2}$ ?

x \ge -\frac{19}{11}

x \le -\frac{19}{11}

x \ge \frac{19}{11}

x \le \frac{23}{5}

Show answer & explanation

Answer: $x \ge -\frac{19}{11}$

Answer

x \ge -\frac{19}{11}

Multiplying the inequality by 6 clears denominators to give

2(1 - 4x) \le 3(x + 7)

. Expanding gives

2 - 8x \le 3x + 21

, which simplifies to

-11x \le 19

. Dividing both sides by

-11

flips the inequality sign, yielding

x \ge -\frac{19}{11}

.

Step-by-Step Solution

1

Clear the denominators by multiplying both sides of the inequality by the lowest common multiple of 3 and 2, which is 6.

6 \cdot \left(\frac{1 - 4x}{3}\right) \le 6 \cdot \left(\frac{x + 7}{2}\right) \implies 2(1 - 4x) \le 3(x + 7)

Eliminating fractions simplifies the algebraic manipulation.

2

Expand both sides by distributing the factors.

2 - 8x \le 3x + 21

Removing parentheses allows grouping of like terms.

3

Rearrange terms by collecting terms containing

x

on the left and constants on the right.

-8x - 3x \le 21 - 2 \implies -11x \le 19

Isolating the variable term prepares for the final division step.

4

Divide both sides by

-11

and reverse the direction of the inequality sign.

x \ge -\frac{19}{11}

Dividing or multiplying an inequality by a negative real number requires flipping the inequality sign.

Key Concept

Solving linear inequalities involving fractions and reversing the inequality sign when dividing by a negative number.

Estimated Time:1m 30s

Question 7071Question →

The heights (in cm) of a seedling recorded over five consecutive weeks are $9$ , $13$ , $15$ , $17$ , and $21$ . What is the standard deviation of the heights?

Show answer & explanation

Answer: 4

Answer

The standard deviation of the seedling heights is 4 cm.

To find the standard deviation, first compute the mean: (9 + 13 + 15 + 17 + 21) / 5 = 15. Next, calculate the sum of squared deviations: (-6)^2 + (-2)^2 + 0^2 + 2^2 + 6^2 = 36 + 4 + 0 + 4 + 36 = 80. Divide by 5 to find the variance of 16. Finally, taking the square root of 16 gives the standard deviation of 4 cm.

Step-by-Step Solution

1

Calculate the mean of the data values

Mean = 15 cm

The mean is necessary to calculate the deviations of each data point.

2

Calculate the squared deviations from the mean

Squared deviations are 36, 4, 0, 4, and 36 (sum = 80)

Variance measures the average of squared deviations from the mean.

3

Calculate the population variance

Variance = 80 / 5 = 16

Dividing the sum of squared deviations by N gives the variance.

4

Calculate the standard deviation

Standard deviation = sqrt(16) = 4 cm

The standard deviation is the square root of the variance.

Key Concept

Standard Deviation of Ungrouped Data

Question 7072Question →

Arrange the following technical and biological stages involved in establishing an effective shelterbelt system to combat desertification in Northern Nigeria into their correct logical sequence, from initial planning to long-term maintenance:

Drag items to arrange them in the correct order

Show answer & explanation

Answer

The correct sequence for shelterbelt establishment is: (1) Baseline ecological mapping and species selection, (2) Site preparation, subsoiling, and perimeter fencing, (3) Staggered tree planting perpendicular to Harmattan winds, (4) Early-stage mulching and micro-irrigation, and (5) Long-term silvicultural maintenance and community management.

Establishing shelterbelts to halt sand dune encroachment and wind erosion in states like Sokoto, Jigawa, and Katsina follows a systematic ecological restoration workflow. It begins with scientific site assessment (mapping wind vectors and selecting drought-hardy species like Neem), followed by ground preparation and protective fencing. Tree planting must be oriented perpendicular to the dry Harmattan winds. Initial maintenance (mulching and temporary watering) ensures root anchorage into deeper soil strata, while long-term silvicultural management maintains optimum wind break porosity.

Step-by-Step Solution

1

Identify the preliminary planning step.

Baseline mapping of wind vectors and selecting drought-resistant species (Azadirachta indica/Acacia) must occur first before any field work.

Without site-specific wind orientation and species suitability analysis, afforestation projects in drylands fail.

2

Determine the site preparation phase.

Land clearing, subsoiling, and fence construction follow baseline planning.

Fencing must be established before planting to prevent immediate livestock destruction of seedlings.

3

Identify the primary planting operation.

Planting staggered rows perpendicular to the North-East Trade Winds.

Correct geometric layout ensures effective reduction of wind velocity across windward agricultural fields.

4

Determine the post-planting seedling establishment phase.

Applying mulch and micro-irrigation during initial dry seasons.

Young seedlings require moisture retention support for 1-2 years until deep taproots establish.

5

Identify the ongoing management phase.

Continuous monitoring, canopy thinning, and community pruning.

Shelterbelts require long-term density management to remain semi-permeable and prevent localized wind turbulence.

Key Concept

Shelterbelt Design and Afforestation Protocols for Desertification Management in Northern Nigeria

Estimated Time:2m 0s

Question 7073Question →

During an economic geography assessment of commercial transport corridors in West Africa, an analyst evaluates why landlocked nations often experience severe trade deficits despite preferential tariff agreements under regional integration bodies like ECOWAS. Which of the following factors represents the primary structural obstacle hindering intra-regional commercial efficiency for these nations?

Extensive transit delays, non-tariff barriers, and high overland freight costs between maritime ports and hinterland markets

Restrictive trade quota policies imposed by their overlapping mandatory membership in the Southern African Development Community (SADC)

The operational requirement forcing all raw material processing facilities to be located in urban consumption centers rather than near resource extraction sites

A structural trade imbalance resulting from an inverted dependency ratio where the working-age population far outnumbers non-working dependents

Show answer & explanation

Answer: Extensive transit delays, non-tariff barriers, and high overland freight costs between maritime ports and hinterland markets

Answer

Extensive transit delays, non-tariff barriers, and high overland freight costs between maritime ports and hinterland markets

Landlocked developing nations face severe logistical and economic handicaps in international trade. Transport friction—caused by poor road/rail links, long customs delays at transit borders, and heavy freight charges across coastal host countries—acts as a major non-tariff barrier that inflates import costs and suppresses export competitiveness, even within preferential trade zones like ECOWAS.

Step-by-Step Solution

1

Analyze the geographical and structural constraints of landlocked nations in commercial geography

Landlocked countries depend entirely on transit corridors through coastal neighbors to reach international maritime trade routes.

Maritime transport handles over 80% of global trade volume, making port access critical for cost-effective export and import flows.

2

Evaluate the impact of non-tariff and infrastructural barriers on trade integration

Inadequate road/rail networks, frequent border customs bottlenecks, and transit fees significantly inflate the final cost of traded commodities.

Even when tariffs are removed via trade agreements (such as ECOWAS trade schemes), physical and administrative non-tariff barriers restrict trade volume.

3

Select the option that correctly identifies these physical and logistical trade barriers

The option highlighting transit delays, non-tariff barriers, and high overland freight costs correctly identifies the key obstacle.

High transport friction is the recognized major impediment to commercial development in landlocked developing regions.

Key Concept

Factors influencing commercial trade networks and transport geography in landlocked developing nations

Estimated Time:2m 0s

Question 7074Question →

Southeastern Nigeria experiences severe environmental degradation due to catastrophic gully erosion triggered by human activities and physical vulnerability. Arrange the following geomorphic stages in the correct chronological sequence of gully morphogenesis from initial disturbance to advanced structural enlargement.

Drag items to arrange them in the correct order

Show answer & explanation

Answer

The correct chronological sequence begins with vegetation clearance causing raindrop splash erosion, followed by surface runoff concentration into rills, then channel deepening through headward scouring into gullies, and culminates in groundwater sapping and sidewall mass slumping.

Gully erosion develops systematically from surface destabilization to deep structural collapse. The process begins with the removal of plant cover, exposing soil to splash erosion. Next, unabsorbed runoff concentrates into rills. As flow energy increases, rills deepen into gullies via headward erosion. Finally, when the gully floor reaches groundwater levels, seepage (basal sapping) and bank undercutting induce slope instability and mass slumping.

Step-by-Step Solution

1

Identify the initiating trigger of soil degradation.

Deforestation or land clearing exposes bare soil to splash erosion, breaking down soil aggregates.

Vegetation removal is the primary anthropogenic antecedent condition.

2

Trace the initial hydrological response of surface runoff.

Infiltrative capacity is exceeded, leading to sheet wash and small micro-channel (rill) incision.

Runoff gathers momentum and concentrates into discrete paths.

3

Determine the phase where rills transition into active gullies.

Concentrated flow scours deep into weak, un-consolidated subsoil strata, expanding rills through headward erosion.

Hydraulic force increases bed scouring depth beyond normal tillage or agricultural recovery.

4

Identify the mature stage dominated by subsurface hydrology and mass wasting.

Groundwater seepage (basal sapping) undermines sidewalls, causing structural mass slumping and rapid gully expansion.

Deep gullies intersect the local water table, introducing geotechnical failure mechanisms.

Key Concept

Morphogenesis of Gully Erosion and Mass Wasting Feedback Loops

Question 7075Question →

In a Geographic Information System (GIS), descriptive non-spatial information such as the name, population density, and land-use category of an administrative district is classified as which type of data?

Attribute data

Spatial data

Vector data

Raster data

Show answer & explanation

Answer: Attribute data

Answer

Attribute data

Attribute data represents tabular, non-spatial characteristics such as names, counts, or categories that describe geographic features mapped within a GIS.

Step-by-Step Solution

1

Analyze the characteristic of data described in the prompt.

The parameters listed (district names, population statistics, land-use categories) are non-spatial descriptions.

GIS data is broadly divided into location geometry (spatial) and non-locational characteristics (attribute).

2

Identify the standard GIS data classification for descriptive records.

Tabular records containing names, values, or categories connected to geometric features form attribute data.

Attribute data provides answers to 'what', 'who', or 'how much' regarding spatial features.

Key Concept

GIS Fundamentals: Spatial versus Attribute Data

Question 7076Question →

Match each contour line pattern listed on the left with the corresponding relief landform it represents on the right.

Click a left item, then click its matching right item

Show answer & explanation

Answer

The correct matches are: Concentric closed contours decreasing inward match with Depression or Basin; V-shaped contours pointing uphill match with River Valley or Stream Bed; Contours closely spaced above and widely spaced below match with Concave Slope; Two high closed contour sets separated by a narrow dip match with Saddle or Col.

Each contour pattern corresponds directly to a distinct landform: inward-decreasing closed contours represent a depression; uphill-pointing V-contours mark a river valley; steep-then-gentle contour density indicates a concave slope; and a low ridge between two peaks forms a saddle or col.

Step-by-Step Solution

1

Analyze contour spacing and elevation trends for closed ring patterns.

Decreasing values toward the center signify a depression rather than a hill summit.

Topographic elevation decreases toward the middle in depressions.

2

Examine V-shaped contour orientation relative to elevation values.

The apex pointing toward higher terrain indicates water flow direction down the valley line.

Valleys cut into terrain such that contour V-shapes point up-valley toward higher ground.

3

Evaluate contour density variations from higher to lower elevations.

Steep slope near the top transition to gentle slope at the bottom defines a concave profile.

Contour spacing directly correlates with slope steepness (close = steep, wide = gentle).

4

Identify relief between two high hilltops.

The low region connecting two summits represents a saddle or col.

A saddle is formed by the low area between two surrounding high points.

Key Concept

Relief Representation and Contour Patterns

Question 7077Question →

In Newton's law of universal gravitation, the gravitational force $F$ between two point masses $m_1$ and $m_2$ separated by a distance $r$ is expressed as $F = G \frac{m_1 m_2}{r^2}$ , where $G$ is the universal gravitational constant. What is the dimensional formula of $G$ in terms of mass ( $\text{M}$ ), length ( $\text{L}$ ), and time ( $\text{T}$ )?

\text{M}^{-1}\text{L}^3\text{T}^{-2}

\text{M}^{1}\text{L}^3\text{T}^{-2}

\text{M}^{-1}\text{L}^2\text{T}^{-2}

\text{M}^{-1}\text{L}^3\text{T}^{-1}

Show answer & explanation

Answer: $\text{M}^{-1}\text{L}^3\text{T}^{-2}$

Answer

\text{M}^{-1}\text{L}^3\text{T}^{-2}

The dimensional formula of the universal gravitational constant

G

is derived by expressing

G = \frac{F r^2}{m_1 m_2}

. Substituting the basic dimensions of force (

\text{M}\text{L}\text{T}^{-2}

), radius squared (

\text{L}^2

), and mass squared (

\text{M}^2

) gives

\frac{(\text{M}\text{L}\text{T}^{-2})(\text{L}^2)}{\text{M}^2} = \text{M}^{-1}\text{L}^3\text{T}^{-2}

.

Step-by-Step Solution

1

Make

G

the subject of the formula

G = \frac{F \cdot r^2}{m_1 \cdot m_2}

To analyze the dimensions of

G

, isolate it on one side of the equation.

2

Substitute the fundamental dimensions for force, distance, and mass

[F] = \text{M}\text{L}\text{T}^{-2}, [r^2] = \text{L}^2, [m_1 m_2] = \text{M}^2

Force is mass times acceleration, giving dimensions

\text{M}\text{L}\text{T}^{-2}

, while distance squared gives

\text{L}^2

and the product of two masses gives

\text{M}^2

.

3

Simplify the dimensional expression

[G] = \frac{(\text{M}\text{L}\text{T}^{-2}) \cdot \text{L}^2}{\text{M}^2} = \text{M}^{1-2} \text{L}^{1+2} \text{T}^{-2} = \text{M}^{-1}\text{L}^3\text{T}^{-2}

Apply laws of indices for fundamental dimensions

\text{M}

,

\text{L}

, and

\text{T}

.

Key Concept

Dimensional Analysis of Physical Constants

Estimated Time:1m 15s

Question 7078Question →

Based on physical environment, historical influences, and economic activities, different geographical sub-regions of Nigeria exhibit varying population concentrations. Order the following sub-regions from LOWEST population density to HIGHEST population density.

Drag items to arrange them in the correct order

Show answer & explanation

Answer

The correct sequence from lowest to highest population density is: Borgu sector of the Niger Valley, followed by the Jos Plateau rural agricultural zone, then the Cocoa Belt of South-Western Nigeria, and finally the Anambra-Imo heartland of South-Eastern Nigeria.

The correct sequence orders the sub-regions by increasing population density: Borgu sector of the Niger Valley (<50 persons/km²), Jos Plateau (100–200 persons/km²), South-Western Cocoa Belt (300–500 persons/km²), and Anambra-Imo heartland (>800 persons/km²). This reflects the combined influence of environmental quality, historical defense/slave-trade impacts, and economic production belts in Nigeria.

Step-by-Step Solution

1

Identify the sparsely populated Middle Belt trough location.

The Borgu sector of the Niger Valley represents the lowest population density (<50 persons/km²) among the given sub-regions owing to physical constraints and historical depopulation.

Establishing the baseline item for the lowest density position.

2

Identify the moderate-density upland refuge zone.

The Jos Plateau rural agricultural zone occupies the next position with a moderate density (100–200 persons/km²), favored by cool climate and mining history compared to the surrounding river valleys.

Placing the moderate-density highland area above the low-density river basin.

3

Compare the high-density southern agricultural belts.

The Cocoa Belt of South-Western Nigeria has high density (300–500 persons/km²), but the Anambra-Imo heartland of South-Eastern Nigeria exhibits an extremely high rural density (>800 persons/km²).

Ranking the two densely populated southern regions in ascending order.

Key Concept

Regional variation of population distribution and density across Nigeria

Question 7079Question →

If $50.0\text{ cm}^3$ of a saturated solution of potassium chloride ( $\text{KCl}$ ) contains $14.9\text{ g}$ of the salt at $298\text{ K}$ , what is the solubility of potassium chloride at this temperature in $\text{mol dm}^{-3}$ ? (Molar mass of $\text{KCl} = 74.5\text{ g mol}^{-1}$ )

Show answer & explanation

Answer: 4

Answer

The solubility of potassium chloride at

298\text{ K}

is

4.0\text{ mol dm}^{-3}

.

First, the mass concentration is determined by scaling the

14.9\text{ g}

in

50.0\text{ cm}^3

to

1000\text{ cm}^3

, giving

298.0\text{ g dm}^{-3}

. Dividing

298.0\text{ g dm}^{-3}

by the molar mass of

\text{KCl}

(

74.5\text{ g mol}^{-1}

) yields

4.0\text{ mol dm}^{-3}

.

Step-by-Step Solution

1

Calculate the mass of solute present per cubic decimetre (1000 cm³) of saturated solution.

Mass concentration = 298.0 g dm⁻³

Solubility is expressed relative to 1 dm³ of solution volume.

2

Divide the mass concentration in g dm⁻³ by the molar mass of KCl.

Solubility = 4.0 mol dm⁻³

Molar solubility equals mass concentration divided by molar mass (M).

Key Concept

Solubility Determination in Moles per Decimetre Cubed

Estimated Time:1m 30s

Question 7080Question →

If a light ray undergoes successive reflections from two plane mirrors inclined at an angle $\theta$ to each other in a single plane, the total angle of deviation produced in the ray is independent of the initial angle of incidence at the first mirror.

True

False

Show answer & explanation

Answer: True

Answer

The statement is TRUE. The total angle of deviation experienced by a ray after two successive reflections at inclined plane mirrors is

\delta = 360^\circ - 2\theta

, which depends only on the angle of inclination

\theta

and is independent of the initial angle of incidence.

The net angular deviation for a ray undergoing two successive reflections at plane mirrors inclined at angle

\theta

is

\delta = 360^\circ - 2\theta

. Since the initial angle of incidence

i_1

cancels out during geometric summation, the total deviation is completely independent of the angle of incidence.

Step-by-Step Solution

1

Determine the deviation at the first mirror

\delta_1 = 180^\circ - 2i_1

For a single reflection at a plane mirror with angle of incidence

i_1

, the angle of deviation is

\delta_1 = 180^\circ - 2i_1

.

2

Express the angle of incidence at the second mirror in terms of inclination angle

\theta

i_2 = \theta - i_1

From the geometric construction of the ray path inside the triangle formed by the two mirror surfaces, the interior angle relationship gives

i_1 + i_2 = \theta

.

3

Calculate the total deviation after both reflections

\delta = \delta_1 + \delta_2 = (180^\circ - 2i_1) + (180^\circ - 2i_2) = 360^\circ - 2(i_1 + i_2) = 360^\circ - 2\theta

Summing the individual deviations eliminates the variable

i_1

, demonstrating that the total deviation depends only on the inclination angle

\theta

.

Key Concept

Total Angle of Deviation for Inclined Plane Mirrors

Answer

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