All practice questions

Question 6321Question →

Match each coastal geomorphic process or mechanism on the left with its corresponding characteristic landform on the right.

Click a left item, then click its matching right item

Show answer & explanation

Answer

Continuous undercutting at a cliff base matches with Wave-cut platform; lateral sediment drift across an estuary matches with Spit; sediment bridging to an offshore island matches with Tombolo; and sea-level submergence of a river valley matches with Ria.

Each process correctly generates its characteristic landform: cliff base erosion produces a wave-cut platform, longshore drift creates a spit across sheltered water, wave energy dissipation behind an island forms a tombolo, and coastal submergence of river valleys results in a ria.

Step-by-Step Solution

1

Analyze cliff erosion processes.

Marine erosion at the cliff base forms a notch which collapses repeatedly, leaving a flat wave-cut platform exposed at low tide.

Hydraulic action and abrasion concentrate mechanical wave force at high-water level.

2

Analyze coastal sediment transport along estuaries.

Oblique swash and direct backwash move material along the coast until open water causes deposition, building a spit.

Reductions in current velocity where coastlines change direction force waves to drop carried sediment.

3

Evaluate wave interaction behind offshore islands.

Wave refraction creates a low-energy zone behind the island where deposition forms a connecting ridge called a tombolo.

Converging wave crests lose velocity in sheltered water behind coastal obstacles.

4

Examine the effect of relative sea-level rise on coastal river valleys.

Submergence of river valleys produces deep, branching estuaries called rias.

Post-glacial eustatic sea-level rise floods low-lying dendritic river drainage patterns.

Key Concept

Coastal erosional, depositional, and submergent processes and landforms

Question 6322Question →

Plantation agriculture in tropical West Africa is distinguished from traditional bush fallowing primarily by which of the following features?

Cultivation of single perennial cash crops on large, permanent estates using high capital input

Rotational cultivation of annual food crops across scattered plots with periodic field abandonment

Seasonal migration of farming families across agro-ecological belts following rainfall patterns

High reliance on small, fragmented peasant landholdings using simple traditional hand tools

Show answer & explanation

Answer: Cultivation of single perennial cash crops on large, permanent estates using high capital input

Answer

Cultivation of single perennial cash crops on large, permanent estates using high capital input

Plantation agriculture is a commercial farming system characterized by large permanent landholdings (estates), heavy capital investment in machinery and processing facilities, reliance on organized hired labor, and the specialized cultivation of a single perennial cash crop (monoculture) primarily for export.

Step-by-Step Solution

1

Analyze the structural characteristics of plantation agriculture.

Plantation agriculture is defined by large-scale commercial monoculture, high capital investment, hired labor, and permanent land tenure.

Commercial tree crops like rubber, oil palm, and cocoa require long-term land commitment and modern infrastructure.

2

Compare plantation agriculture with traditional bush fallowing.

Bush fallowing involves rotating plots of land for food crop production and leaving exhausted plots fallow, contrasting sharply with the permanent, large-scale estate structure of plantations.

Identifying key differences in land tenure, capital input, and crop choice resolves the distinguishing feature.

Key Concept

Structural differences between commercial plantation agriculture and traditional bush fallowing

Estimated Time:1m 0s

Question 6323Question →

A commercial agricultural enterprise plans to establish large-scale cocoa and oil palm plantations in Nigeria. Based on the spatial distribution of climatic conditions and vegetation belts across the country, which region provides the most ecologically suitable environment for these perennial cash crops?

The humid rainforest and derived savanna belts of southern Nigeria, characterized by annual rainfall exceeding

1500\text{ mm}

and a long wet season.

The dry Sudan savanna zone of northern Nigeria, where low relative humidity prevents fungal leaf blight and accelerates fruit harvesting.

The semi-arid Sahel savanna belt along the northern border, where sandy soils and intense solar radiation boost oil palm fruit yields.

The northern Guinea savanna belt, where prolonged seven-month dry spells with harmattan winds favor tree crop flowering.

Show answer & explanation

Answer: The humid rainforest and derived savanna belts of southern Nigeria, characterized by annual rainfall exceeding $1500\text{ mm}$ and a long wet season.

Answer

The humid rainforest and derived savanna belts of southern Nigeria provide the ecologically optimal conditions of high rainfall (

>1500\text{ mm}

) and short dry seasons required for perennial cash crops like cocoa and oil palm.

The humid rainforest and derived savanna belts of southern Nigeria receive abundant rainfall (

>1500\text{ mm}

annually) with high atmospheric humidity and minimal dry-season moisture stress, matching the precise ecological envelope needed for cocoa and oil palm cultivation.

Step-by-Step Solution

1

Analyze crop ecological requirements

Cocoa (*Theobroma cacao*) and oil palm (*Elaeis guineensis*) are perennial tree crops requiring high humidity, temperatures between

24^\circ\text{C}

and

30^\circ\text{C}

, and high rainfall (

>1500\text{ mm}

) evenly distributed with a short dry period.

Tree cash crops cannot survive prolonged moisture deficits or low relative humidity.

2

Map requirements onto Nigerian ecological zones

Southern Nigeria (comprising states like Ondo, Cross River, Edo, Ogun, and Osun) falls within the Tropical Rainforest belt, receiving over

1500\text{--}3000\text{ mm}

of rainfall annually.

The latitudinal gradient of rainfall decreases from south to north across Nigeria.

3

Evaluate and eliminate unsuitable northern zones

Savanna belts (Guinea, Sudan, Sahel) in northern Nigeria experience dry seasons ranging from 5 to 9 months and rainfall under

1000\text{ mm}

, supporting grain crops (millet, sorghum) and groundnuts rather than tree crops.

Misattributing forest crops to northern savanna belts represents a common spatial geography misconception.

Key Concept

Ecological Zonation of Agricultural Crops in Nigeria

Estimated Time:1m 30s

Question 6324Question →

Match each African agricultural system or scheme listed on the left with its corresponding regional characteristic or main agricultural practice on the right.

Click a left item, then click its matching right item

Show answer & explanation

Answer

The Gezira Scheme matches large-scale gravity irrigation for cotton cultivation between the Blue and White Nile; Mediterranean Agriculture matches specialized commercial cultivation of citrus fruits and grapes in the Cape region; Plantation Farming matches monoculture of tree cash crops like oil palm, cocoa, and rubber on large estates; Pastoral Nomadism matches transhumant livestock rearing adapted to semi-arid conditions in the Sahelian zone.

Each agricultural system is accurately paired with its primary geographic zone, ecological adaptation, and dominant farming practices across Africa.

Step-by-Step Solution

1

Analyze the Gezira Scheme's geographical location and primary production system.

Gezira utilizes gravity-fed canal irrigation between the Nile rivers in Sudan to produce cotton on a commercial scale.

Irrigation infrastructure overcomes arid climate constraints in eastern Sudan.

2

Examine Mediterranean agricultural output in Southern and Northern Africa.

The Mediterranean climate zone (e.g., South Africa's Cape region) supports viticulture, olives, and citrus fruit farming.

Mild, wet winters and dry, warm summers favor specialized orchard and vine crops.

3

Identify the organizational features of plantation farming in tropical Africa.

Plantations operate as large estates growing single cash crops like rubber, oil palm, or cocoa for international trade.

High capital investment and labor force are centered on permanent tree crop monoculture.

4

Determine the survival strategy for livestock farmers in dry belt regions.

Pastoral nomads move herds across the Sahel to adapt to scarce rainfall and seasonal pasture growth.

Mobility (transhumance) prevents overgrazing and responds to erratic precipitation pattern distribution.

Key Concept

Spatial distribution and operational characteristics of major African agricultural systems

Question 6325Question →

A weather observer at a meteorological station needs to organize daily readings and equipment records. Match each weather element listed in Column I with its corresponding measuring instrument and standard unit of measurement in Column II. Which pairings correctly align every weather element with its designated instrument?

Click a left item, then click its matching right item

Show answer & explanation

Answer

Atmospheric Pressure matches with Aneroid Barometer (Millibars); Wind Speed matches with Cup Anemometer (Knots); Sunshine Duration matches with Campbell-Stokes Recorder (Hours); Relative Humidity matches with Hygrometer (Percentage).

Each weather element is correctly paired with its dedicated meteorological instrument and standard unit: Atmospheric Pressure is measured with an Aneroid Barometer (Millibars), Wind Speed with a Cup Anemometer (Knots), Sunshine Duration with a Campbell-Stokes Recorder (Hours), and Relative Humidity with a Hygrometer (Percentage).

Step-by-Step Solution

1

Identify the instrument and unit for Atmospheric Pressure

Atmospheric Pressure pairs with Aneroid Barometer (Millibars).

Air pressure is measured with barometers in millibars or hectopascals.

2

Identify the instrument and unit for Wind Speed

Wind Speed pairs with Cup Anemometer (Knots).

The rotation rate of anemometer cups measures wind velocity in knots or m/s.

3

Identify the instrument and unit for Sunshine Duration

Sunshine Duration pairs with Campbell-Stokes Recorder (Hours).

A glass sphere focuses rays onto a sensitized card to record sunshine duration in hours per day.

4

Identify the instrument and unit for Relative Humidity

Relative Humidity pairs with Hygrometer (Percentage).

Moisture relative to saturation level is measured using hygrometers or psychrometers as a percentage.

Key Concept

Weather Elements, Instruments, and Standard Units

Estimated Time:1m 30s

Question 6326Question →

Complete the literary analysis statement below by filling in the correct terms for the characterization technique and character type.

Fill in the blanks below

When a novelist reveals a persona's inner temperament through dialogue and physical actions rather than explicit narrator commentary, the writer employs characterization. Furthermore, a character who experiences significant psychological growth and moral transformation across the plot is described as a character.

Show answer & explanation

Answer

The first blank requires 'indirect' (or 'dramatic'/'implicit') characterization, and the second blank requires 'dynamic' (or 'round') character.

Indirect characterization is used when an author shows a character's personality through their speech, actions, and appearance without explicitly telling the reader. A dynamic character (often also a round character) undergoes essential internal changes, growth, or shift in perspective throughout the progression of the prose narrative.

Step-by-Step Solution

1

Identify the technique of revealing character traits through actions and dialogue without direct narrative statements.

Recognize that showing rather than telling constitutes indirect characterization.

Indirect characterization relies on implicit cues such as speech, behavior, thoughts, and interactions rather than explicit description by the narrator.

2

Identify the term for a character who undergoes significant internal change and development throughout a narrative.

Recognize that a character evolving over the course of the story is dynamic (or round).

Dynamic characters undergo fundamental changes in personality, outlook, or values, as opposed to static characters who remain unchanged.

Key Concept

Distinction between direct vs. indirect characterization techniques and static vs. dynamic character types in prose fiction.

Question 6327Question →

A weather observer at a meteorological station requires a continuous visual trace of fluctuations in atmospheric pressure over a 24-hour cycle. Which instrument is designed specifically to record these continuous pressure changes on a rotating drum chart?

Barograph

Hygrograph

Thermograph

Anemograph

Show answer & explanation

Answer: Barograph

Answer

Barograph

The barograph is a self-recording barometer. It contains a series of aneroid capsules that expand and contract with changes in atmospheric pressure. This movement is magnified through levers to a pen arm, which draws a continuous trace (barogram) on a paper chart wrapped around a clockwork-driven rotating cylinder.

Step-by-Step Solution

1

Identify the target atmospheric parameter and measurement format requested in the stem

The target parameter is atmospheric pressure, requiring a continuous graphical record (trace chart) rather than a single instantaneous reading.

Different meteorological instruments serve specific parameters and reading methods (instantaneous vs. self-recording).

2

Match the target parameter to the corresponding self-recording weather instrument

Atmospheric pressure recorded continuously on a rotating chart drum corresponds to a barograph.

The suffix '-graph' indicates a self-recording instrument, and the prefix 'baro-' relates to atmospheric pressure.

Key Concept

Continuous Recording Weather Instruments

Estimated Time:1m 0s

Question 6328Question →

The following figures were extracted from the books of Ade & Sons Manufacturing Enterprises for the financial year ended 31st December 2025:

- Direct materials used: ₦145,000
- Direct labor cost: ₦65,000
- Factory overhead expenses: ₦38,000
- Opening work-in-progress (1st Jan 2025): ₦22,000
- Closing work-in-progress (31st Dec 2025): ₦27,000

What is the total cost of production for the year?

Show answer & explanation

Answer: 243000

Answer

The total cost of production for the year is ₦243,000.

To calculate the total cost of production, add direct materials consumed (₦145,000) and direct labor (₦65,000) to find the prime cost of ₦210,000. Add factory overhead expenses (₦38,000) to obtain the gross cost of production of ₦248,000. Finally, add opening work-in-progress (₦22,000) and subtract closing work-in-progress (₦27,000) to arrive at the net cost of production of ₦243,000.

Step-by-Step Solution

1

Calculate Prime Cost

₦210,000

Prime cost is the sum of all direct manufacturing costs, including direct materials consumed and direct labor.

2

Add Factory Overheads

₦248,000

Factory overheads represent indirect factory costs incurred during the manufacturing process.

3

Adjust for Opening and Closing Work-in-Progress

₦243,000

Opening WIP is added because it represents partially finished goods from the previous period completed in the current period. Closing WIP is deducted because it represents partially finished goods that are not yet complete at year-end.

Key Concept

Valuation and Adjustment for Work-in-Progress (WIP) in Manufacturing Accounts

Question 6329Question →

The financial summary of Anchor Recreation Club for the year ended 31st December 2025 shows the following figures:

Item / Transaction	Amount (₦)
Opening bank balance (1st Jan 2025)	45,000
Subscriptions received in cash	120,000
Life membership fees received	25,000
Purchase of new furniture	40,000
Payment of club rent	30,000
General office expenses paid	18,000
Depreciation on club house	8,000
Subscriptions accrued at year end	12,000

What is the closing cash and bank balance to be reported in the Receipts and Payments Account as at 31st December 2025?

₦ 102,000

₦ 114,000

₦ 94,000

�� 142,000

Show answer & explanation

Answer: ₦ 102,000

Answer

The closing cash and bank balance is ₦ 102,000.

The correct closing balance of ₦ 102,000 is derived by summarizing all cash inflows (Opening balance of ₦ 45,000 + Subscriptions received of ₦ 120,000 + Life membership fees of ₦ 25,000 = ₦ 190,000) and deducting all cash outflows (Furniture purchase of ₦ 40,000 + Club rent of ₦ 30,000 + Office expenses of ₦ 18,000 = ₦ 88,000). Non-cash items such as depreciation (₦ 8,000) and accrued subscriptions (₦ 12,000) are excluded.

Step-by-Step Solution

1

Identify all valid cash receipts (Debit side)

Total Receipts = Opening balance (₦ 45,000) + Subscriptions received (₦ 120,000) + Life membership fees (₦ 25,000) = ₦ 190,000

The Receipts and Payments Account includes all cash receipts (both capital and revenue).

2

Identify all valid cash payments (Credit side)

Total Payments = Purchase of furniture (₦ 40,000) + Club rent (₦ 30,000) + General office expenses (₦ 18,000) = ₦ 88,000

The Receipts and Payments Account records all cash payments regardless of expenditure type.

3

Identify and exclude non-cash or non-transaction items

Depreciation (₦ 8,000) and Subscriptions accrued (₦ 12,000) are excluded.

The Receipts and Payments Account operates strictly on a cash basis; non-cash items and accruals are omitted.

4

Calculate the closing balance

Closing Balance = Total Receipts (₦ 190,000) - Total Payments (₦ 88,000) = ₦ 102,000

Subtracting total cash payments from total cash receipts yields the ending cash/bank balance.

Key Concept

Scope and preparation of the Receipts and Payments Account

Question 6330Question →

Cold ocean currents flowing along the western margins of continents in tropical latitudes significantly alter coastal weather. Which mechanism explains how the Benguela Current causes hyper-arid climatic conditions in the Namib Desert?

It chills the low-level air mass, producing a temperature inversion that suppresses vertical convection and condensation.

It rapidly evaporates surface seawater, causing humid rain-bearing winds to drop precipitation entirely over the ocean before reaching land.

It generates intense low-pressure atmospheric cells that force cloud cover to diverge away from the coastline.

It permanently diverts the Intertropical Convergence Zone to the Northern Hemisphere throughout the entire year.

Show answer & explanation

Answer: It chills the low-level air mass, producing a temperature inversion that suppresses vertical convection and condensation.

Answer

The cold Benguela Current chills the lower atmospheric layer, creating a temperature inversion that stabilizes the air mass and suppresses convective precipitation.

The correct option states that the current chills the low-level air mass, producing a temperature inversion that suppresses vertical convection. As the cold Benguela Current flows northward along the Namibian coast, it cools the lower layers of the atmosphere. This dense, chilled air sits beneath warmer air aloft, creating a stable temperature inversion. Because warm air above prevents the cool surface air from rising, convective clouds cannot form, leading to extreme desert conditions along the coast.

Step-by-Step Solution

1

Identify the primary climatic control acting on the coastal desert region.

The Benguela Current is a cold ocean current flowing northward along the southwestern coast of Africa.

Ocean currents regulate air temperature and moisture capacity of overlying air masses.

2

Analyze how cold ocean currents influence atmospheric stability.

Air directly in contact with cold ocean surface waters is cooled from below, while upper atmospheric air remains warmer.

Cool air is denser than warm air, creating a stable thermal inversion layer where air cannot rise easily.

3

Relate atmospheric stability to precipitation outcomes.

Without vertical convection, moist air cannot rise, expand, cool adiabatically, and condense into rain clouds, producing fog and extreme aridity.

Vertical convective uplift is essential for thunderstorm and cloud formation.

Key Concept

Climatic Controls - Ocean Currents and Aridity

Question 6331Question →

The National Environmental Standards and Regulations Enforcement Agency (NESREA) holds statutory responsibility for enforcing environmental regulations and standards across Nigeria's oil and gas sector.

True

False

Show answer & explanation

Answer: False

Answer

The statement is False. NESREA's statutory enforcement authority specifically excludes Nigeria's oil and gas sector, which is monitored by NOSDRA.

The statement is false because while NESREA is Nigeria's primary environmental enforcement agency for non-oil sectors, the NESREA Act of 2007 explicitly restricts it from enforcing environmental standards within the oil and gas industry. Environmental protection and spill response in that sector are legally delegated to NOSDRA.

Step-by-Step Solution

1

Identify the primary agency and legal framework mentioned in the statement.

The statement references NESREA (established under the NESREA Act of 2007) and its mandate in the oil and gas sector.

Determining jurisdictional scope requires evaluating agency enabling laws.

2

Analyze the statutory limitations of NESREA's mandate.

Section 7 of the NESREA Act explicitly exempts the oil and gas industry from NESREA's enforcement jurisdiction.

Environmental enforcement in Nigeria's petroleum sector is specialized under NOSDRA (National Oil Spill Detection and Response Agency).

3

Evaluate the validity of the statement based on legal mandate distribution.

Because NESREA does not regulate the oil and gas sector, the statement is false.

Confusing NESREA's broad general mandate with NOSDRA's specialized petroleum sector mandate is a common misconception.

Key Concept

Division of statutory mandates among Nigerian environmental protection agencies

Question 6332Question →

Match each major vegetation biome on the left with its corresponding plant structural adaptation and characteristic soil type on the right.

Click a left item, then click its matching right item

Show answer & explanation

Answer

Tropical Rainforest matches with multilayered canopy, drip-tip leaves, and leached oxisols. Mediterranean Woodland matches with sclerophyllous waxy leaves and terra rossa soils. Coniferous Boreal Forest matches with needle-like leaves, snow-shedding branches, and podzols. Tropical Savanna matches with drought-resistant umbrella crowns and fire-resistant bark.

Each biome exhibits structural morphology suited to its moisture and thermal regime: rainforest plants feature drip-tips and buttress roots on oxisols; Mediterranean plants feature sclerophyllous waxy leaves on terra rossa soils; boreal conifers feature needle-like leaves on podzols; savanna vegetation features fire-resistant bark and umbrella crowns adapted to wet-dry cycles.

Step-by-Step Solution

1

Analyze Tropical Rainforest adaptations and soils.

Identified high rainfall leading to intense leaching (oxisols/latosols) and plant features like buttress roots and drip tips.

Extreme moisture and rapid organic decomposition create nutrient-poor, highly leached soils.

2

Analyze Mediterranean Woodland adaptations and soils.

Identified summer drought conditions requiring sclerophyllous (small, waxy) foliage on terra rossa soils.

High evaporation during dry summers necessitates structures that prevent transpiration loss.

3

Analyze Coniferous Boreal Forest adaptations and soils.

Identified cold subarctic climate requiring needle leaves and conical tree form on acidic podzol soils.

Slow decomposition of resinous pine needles acidifies the soil profile.

4

Analyze Tropical Savanna adaptations and soils.

Identified seasonal moisture shifts requiring umbrella crowns and thick bark.

Trees must survive prolonged dry seasons and seasonal bushfires.

Key Concept

Ecological adaptations of vegetation biomes to climatic controls and soil profiles

Estimated Time:1m 30s

Question 6333Question →

A cannonball is fired from ground level with an initial speed of $50\text{ m/s}$ at an angle $\theta$ above the horizontal such that $\tan \theta = \frac{4}{3}$ . Assuming acceleration due to gravity $g = 10\text{ m/s}^2$ and neglecting air resistance, what is the magnitude of the velocity of the cannonball at the highest point of its trajectory?

30\text{ m/s}

0\text{ m/s}

40\text{ m/s}

50\text{ m/s}

Show answer & explanation

Answer: $30\text{ m/s}$

Answer

30\text{ m/s}

At the maximum height of a projectile's flight, the vertical velocity component drops to zero due to gravity, while the horizontal component remains unchanged because horizontal acceleration is zero. For a launch speed of

50\text{ m/s}

at an angle with

\tan \theta = \frac{4}{3}

,

\cos \theta = \frac{3}{5}

. The magnitude of the velocity at apex is therefore equal to

u_x = 50 \times \frac{3}{5} = 30\text{ m/s}

.

Step-by-Step Solution

1

Resolve the initial velocity vector into orthogonal horizontal and vertical components.

Given

\tan \theta = \frac{4}{3}

, the trigonometric ratios are

\cos \theta = \frac{3}{5}

and

\sin \theta = \frac{4}{5}

. Thus,

u_x = 50 \times \frac{3}{5} = 30\text{ m/s}

and

u_y = 50 \times \frac{4}{5} = 40\text{ m/s}

.

Resolving 2D projectile motion into independent orthogonal components simplifies kinematic analysis.

2

Determine the velocity components at the apex (highest point) of the trajectory.

At maximum height, the vertical velocity component

v_y = 0\text{ m/s}

. Since there is no horizontal acceleration, the horizontal velocity component remains

v_x = u_x = 30\text{ m/s}

.

Gravity acts purely vertically, reducing vertical velocity to zero at the apex while leaving horizontal velocity unchanged.

3

Calculate the magnitude of total velocity at maximum height.

v = \sqrt{v_x^2 + v_y^2} = \sqrt{30^2 + 0^2} = 30\text{ m/s}

.

The magnitude of a 2D velocity vector is determined by combining its orthogonal components using the Pythagorean formula.

Key Concept

Velocity components at maximum height in projectile motion

Question 6334Question →

Match each statistical mapping technique on the left with the cartographic representation principle and data type it utilizes on the right.

Click a left item, then click its matching right item

Show answer & explanation

Answer

Dot Map pairs with uniform point symbols representing discrete distributions; Choropleth Map pairs with shading intensities within administrative boundaries for average densities; Flow Map pairs with varying line thickness depicting volume of movement; Isopleth Map pairs with lines connecting points of equal value for continuous phenomena.

Each mapping technique matches its primary cartographic design function: dot maps represent absolute discrete quantities using uniform point symbols; choropleth maps represent spatial densities using shading aggregated inside administrative units; flow maps convey directional movement and volume via proportional line widths; and isopleth maps depict continuous environmental variables by linking points of equal magnitude with isolines.

Step-by-Step Solution

1

Identify the data symbol type for Dot Maps.

Dot maps use point symbols of fixed value to represent discrete counts across a region.

This establishes the relationship between Dot Map and uniform point symbols.

2

Identify the spatial boundary and shading rule for Choropleth Maps.

Choropleth maps rely on predetermined administrative boundaries filled with graded shading to show average ratios or densities.

This pairs Choropleth Map with administrative unit shading.

3

Analyze how dynamic movement data is represented cartographically.

Flow maps use proportional line widths along travel channels to quantify movements like trade or migration.

This pairs Flow Map with varying line thickness along movement paths.

4

Examine continuous spatial surface mapping using contour-like lines.

Isopleth maps interpolate continuous distributions (e.g., isotherms, isobars) by connecting equal numerical values.

This matches Isopleth Map with lines of equal value across surfaces.

Key Concept

Cartographic principles of statistical maps and quantitative spatial data representation

Question 6335Question →

During a prismatic compass survey of a farmland, a student records the forward bearing of line PQ as $125^\circ$ . Assuming both stations are completely free from local attraction, what is the back bearing of line QP?

305^\circ

055^\circ

215^\circ

125^\circ

Show answer & explanation

Answer: $305^\circ$

Answer

The back bearing of line QP is

305^\circ

.

In prismatic compass surveying, the forward bearing and back bearing of any line differ by exactly

180^\circ

. When the forward bearing is less than

180^\circ

, adding

180^\circ

gives the back bearing (

125^\circ + 180^\circ = 305^\circ

).

Step-by-Step Solution

1

Identify the forward bearing and check if it is greater or less than

180^\circ

.

The forward bearing is

125^\circ

, which is less than

180^\circ

.

The rule for converting forward bearing (FB) to back bearing (BB) depends on whether FB is greater than or less than

180^\circ

.

2

Apply the bearing conversion formula:

\text{BB} = \text{FB} + 180^\circ

when

\text{FB} < 180^\circ

.

\text{BB} = 125^\circ + 180^\circ = 305^\circ

.

Back bearing represents the opposite direction (

180^\circ

difference) along the same line.

Key Concept

Forward and Back Bearing Conversion in Prismatic Compass Surveying

Estimated Time:1m 0s

Question 6336Question →

City A is located at longitude $25^\circ\text{W}$ and City B is located at longitude $65^\circ\text{E}$ . Calculate the difference in local solar time between the two cities in hours.

Show answer & explanation

Answer: 6

Answer

The time difference between City A and City B is 6 hours.

Because City A (

25^\circ\text{W}

) and City B (

65^\circ\text{E}

) lie in opposite hemispheres relative to the Greenwich Meridian (

0^\circ

), the total longitudinal difference between them is the sum of their absolute longitudes (

25^\circ + 65^\circ = 90^\circ

). Given that Earth rotates

15^\circ

of longitude every hour (

360^\circ / 24\text{ hours}

), dividing

90^\circ

by

15^\circ\text{/hour}

gives a total time difference of 6 hours.

Step-by-Step Solution

1

Calculate the total angular distance between the two longitudes.

25^\circ\text{W} + 65^\circ\text{E} = 90^\circ

Because the two locations are in different hemispheres (West and East), their longitudinal values must be added to find the total separation across the Prime Meridian.

2

Convert longitudinal degrees into time difference.

90^\circ / 15^\circ\text{ per hour} = 6\text{ hours}

Earth completes one full rotation of

360^\circ

in 24 hours, which corresponds to an angular velocity of

15^\circ

per hour.

Key Concept

Calculating time difference from longitudinal distance across hemispheres.

Question 6337Question →

A ship captain at sea observes local solar noon ( $12:00\text{ PM}$ ) on Monday. At that precise moment, a radio time signal from Greenwich ( $0^\circ$ ) indicates that Greenwich Mean Time (GMT) is $05:20\text{ PM}$ on Monday. What is the longitude of the ship in degrees West of the Prime Meridian?

Show answer & explanation

Answer: 80

Answer

The longitude of the ship is

80^\circ\text{W}

(80 degrees West).

The time difference between local solar noon (

12:00\text{ PM}

) and GMT (

05:20\text{ PM}

) is 5 hours and 20 minutes, or

5\frac{1}{3}

hours. Multiplying

5.333\text{ hours}

by

15^\circ

per hour yields

80^\circ

. Since local solar time is behind GMT, the ship is situated

80^\circ

West of the Prime Meridian.

Step-by-Step Solution

1

Calculate the time difference between local solar time and Greenwich Mean Time (GMT)

05:20\text{ PM} - 12:00\text{ PM} = 5\text{ hours and } 20\text{ minutes} = 5.333\text{ hours}

The distance in longitude is directly proportional to the difference between local time and GMT.

2

Convert the time difference into angular distance in degrees of longitude

5\frac{1}{3}\text{ hours} \times 15^\circ/\text{hour} = 80^\circ

Earth rotates

360^\circ

in 24 hours, which corresponds to

15^\circ

of longitude for every 1 hour of time difference.

3

Determine hemisphere direction based on whether local time is ahead or behind GMT

Western Hemisphere (

80^\circ\text{W}

)

Local time (

12:00\text{ PM}

) is earlier than GMT (

05:20\text{ PM}

), placing the ship west of the Prime Meridian.

Key Concept

Calculating longitude using local time and Greenwich Mean Time (GMT)

Question 6338Question →

An open storage container is designed in the shape of a frustum of a right circular cone. The top radius of the container is $4\text{ m}$ , the bottom radius is $1\text{ m}$ , and its vertical height is $7\text{ m}$ . Taking $\pi = \frac{22}{7}$ , what is the volume of the container in cubic metres ( $\text{m}^3$ )?

Show answer & explanation

Answer: 154

Answer

The volume of the container is

154\text{ m}^3

.

Using the volume formula for a frustum of a cone

V = \frac{1}{3}\pi h (R^2 + Rr + r^2)

with

R = 4\text{ m}

,

r = 1\text{ m}

,

h = 7\text{ m}

, and

\pi = \frac{22}{7}

yields

V = \frac{1}{3} \times \frac{22}{7} \times 7 \times (16 + 4 + 1) = 22 \times 7 = 154\text{ m}^3

.

Step-by-Step Solution

1

Identify the given dimensions of the frustum of the cone.

Top radius

R = 4\text{ m}

, bottom radius

r = 1\text{ m}

, height

h = 7\text{ m}

, and

\pi = \frac{22}{7}

.

Establishing known parameter values for the frustum volume formula.

2

Apply the standard formula for the volume of a frustum of a circular cone.

V = \frac{1}{3}\pi h (R^2 + Rr + r^2)

This formula accounts for the non-uniform cross-sectional area of a truncated cone.

3

Calculate the sum of the squares and the product of the radii.

R^2 + Rr + r^2 = 4^2 + (4)(1) + 1^2 = 16 + 4 + 1 = 21

Evaluating the quadratic radius factor in the frustum equation.

4

Substitute all numeric values and simplify.

V = \frac{1}{3} \times \frac{22}{7} \times 7 \times 21 = 22 \times 7 = 154\text{ m}^3

Simplifying by cancelling

7

in the numerator and denominator, then dividing

21

by

3

yields

22 \times 7 = 154

.

Key Concept

Volume of a Frustum of a Cone

Question 6339Question →

In the agro-allied manufacturing sector of southern Nigeria (such as in Ondo, Imo, and Cross River states), oil palm fruits undergo a specific sequence of industrial processing stages to yield refined vegetable oil and industrial palm kernel products. Arrange the following processing stages in the correct chronological sequence from raw harvest treatment to final industrial refining.

Drag items to arrange them in the correct order

Show answer & explanation

Answer

The correct sequence begins with sterilization and steam digestion, followed by mechanical pressing, clarification and drying of crude oil, and concludes with industrial fractionation and secondary refining.

The industrial processing of palm oil in Nigeria follows a logical progression from raw material stabilization to final product refining. Harvested fruit bunches are first sterilized and digested with steam to stop enzymatic degradation and break down pulp fibers. Next, mechanical presses squeeze out crude palm oil and separate palm nuts. The crude oil is then clarified and dried to remove water and suspended sludge. Finally, purified crude palm oil undergoes industrial fractionation and secondary refining to produce liquid cooking oil (olein), solid fats (stearin), and soaps.

Step-by-Step Solution

1

Identify the primary raw-material preparation stage.

Sterilization and steam digestion stop acidification and soften fruit tissue.

Raw agricultural inputs require enzymatic stabilization before physical oil extraction can begin.

2

Determine the primary extraction stage.

Mechanical pressing extracts crude palm oil and yields palm nuts.

Softened pericarp must be mechanically compressed to yield liquid crude oil.

3

Determine the primary purification stage.

Clarification and centrifugation separate water, cell debris, and fibrous sludge from the oil.

Crude oil extracted from presses contains moisture and particulates that cause rapid spoilage if not removed.

4

Identify the value-addition secondary manufacturing stage.

Industrial fractionation produces refined edible olein, solid stearin, and specialty fats.

Pure crude palm oil undergoes thermal separation and refining in downstream processing plants to create marketable consumer and industrial goods.

Key Concept

Agro-allied Industrial Processing Stages in Southern Nigeria

Question 6340Question →

Given the matrices $A = \begin{pmatrix} 4 & x \\ -1 & 3 \end{pmatrix}$ and $B = \begin{pmatrix} 2 & 1 \\ 3 & 4 \end{pmatrix}$ , if the determinant of the product matrix $AB$ is $95$ , what is the value of $x$ ?

Show answer & explanation

Answer: 7

Answer

The value of

x

is

7

.

Using the property

\det(AB) = \det(A)\det(B)

, we find

\det(B) = (2)(4) - (1)(3) = 5

and

\det(A) = (4)(3) - (x)(-1) = 12 + x

. Setting

5(12 + x) = 95

yields

60 + 5x = 95

, which solves to

x = 7

.

Step-by-Step Solution

1

Calculate the determinant of matrix

B

\det(B) = (2)(4) - (1)(3) = 5

The determinant of a

2 \times 2

matrix

\begin{pmatrix} a & b \\ c & d \end{pmatrix}

is

ad - bc

.

2

Express the determinant of matrix

A

in terms of

x

\det(A) = (4)(3) - (x)(-1) = 12 + x

Applying the determinant formula to matrix

A

gives

12 - (-x) = 12 + x

.

3

Apply the determinant product property

\det(AB) = \det(A) \cdot \det(B)

5(12 + x) = 95

The determinant of the product of two square matrices is equal to the product of their individual determinants.

4

Solve the linear equation for

x

60 + 5x = 95 \implies 5x = 35 \implies x = 7

Subtract

60

from both sides and divide by

5

to isolate

x

.

Key Concept

Determinant of Matrix Product Property

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