All practice questions

13931 questions

Question 12721Question

As moist air masses ascend the windward slopes of a major mountain barrier, they cool adiabatically and deposit heavy precipitation. As the air descends on the opposite side, it warms adiabatically and absorbs moisture, resulting in arid or semi-arid conditions. Which climatic control and associated phenomenon are responsible for the dry climate on the leeward side?

Show answer & explanation

Answer: Relief acting as a climatic barrier to produce a rain-shadow zone

Answer

Relief acting as a climatic barrier to produce a rain-shadow zone
Relief serves as a major climatic control. When moist air encounters a mountain range, it is forced to ascend, cooling at the adiabatic lapse rate and releasing rain on the windward slope. Upon crossing the crest, the air descends the leeward side, warming adiabatically. This dry, warm descending air creates a dry belt known as a rain-shadow region.

Step-by-Step Solution

1
Analyze the physical process described in the stem
Air ascends windward slopes (orographic uplift), cools adiabatically, condenses, and precipitates, leaving dry air to descend the leeward slope.
Topography (relief) physically intercepts air masses.
2
Identify the climatic control and resultant feature
The climatic control is relief (orography) and the feature created on the sheltered leeward side is a rain-shadow zone.
Desiccated air warming adiabatically on the leeward side suppresses cloud formation and precipitation.

Key Concept

Relief and Orographic Rain-Shadow Effect
Question 12722Question

The table below presents crude birth rates (CBR) and crude death rates (CDR) per 1,0001,000 population for four administrative divisions in a West African country:

DivisionCrude Birth Rate (CBR)Crude Death Rate (CDR)
Division W45451818
Division X383888
Division Y282866
Division Z15151111

Based on the data provided, which division exhibits the highest annual Rate of Natural Increase (RNI)?

Show answer & explanation

Answer: Division X

Answer

Division X exhibits the highest annual Rate of Natural Increase (RNI) at 3.0%3.0\% (3030 per 1,0001,000).
Division X has the highest Rate of Natural Increase because subtracting its crude death rate of 8 per 1,000 from its crude birth rate of 38 per 1,000 yields a net natural increase of 30 per 1,000 (or 3.0% annually), which exceeds all other divisions.

Step-by-Step Solution

1
Recall the formula for Rate of Natural Increase (RNI)
RNI=Crude Birth Rate (CBR)Crude Death Rate (CDR)\text{RNI} = \text{Crude Birth Rate (CBR)} - \text{Crude Death Rate (CDR)}
Natural population growth excludes net migration and is determined solely by the difference between birth rates and death rates.
2
Calculate the RNI per 1,0001,000 for each division
Division W: 4518=2745 - 18 = 27 per 1,0001,000 (2.7%2.7\%)
Division X: 388=3038 - 8 = 30 per 1,0001,000 (3.0%3.0\%)
Division Y: 286=2228 - 6 = 22 per 1,0001,000 (2.2%2.2\%)
Division Z: 1511=415 - 11 = 4 per 1,0001,000 (0.4%0.4\%)
Evaluating each division systematically allows direct comparison.
3
Identify the division with the maximum RNI value
Division X has the maximum RNI of 3030 per 1,0001,000 (3.0%3.0\%).
Comparing 3030 per 1,0001,000 against 2727, 2222, and 44 confirms Division X is the highest.

Key Concept

Rate of Natural Increase (RNI)
Estimated Time:1m 15s
Question 12723Question

In major low-lying coastal urban zones of southern Nigeria, intense groundwater abstraction combined with frequent ocean storm surges frequently leads to severe subsurface degradation. Which environmental hazard is directly caused by this combination of human action and marine influence?

Show answer & explanation

Answer: Salinization of freshwater coastal aquifers

Answer

Salinization of freshwater coastal aquifers
In low-lying coastal settlements, over-extracting groundwater lowers the water table hydrostatic pressure. Combined with ocean storm surges, seawater infiltrates permeable coastal sediments, leading to the salinization of underground freshwater aquifers.

Step-by-Step Solution

1
Analyze the geographical setting and drivers given in the stem.
The setting is low-lying coastal southern Nigeria experiencing high groundwater withdrawal and ocean storm surges.
Identifying the physical environment (coastal aquifer system) isolates hydrological hazards from inland geomorphic or atmospheric hazards.
2
Evaluate the hydraulic mechanisms resulting from excessive groundwater pumping near ocean boundaries.
Excessive abstraction reduces hydraulic head in freshwater aquifers, creating a pressure gradient that enables dense marine saltwater to encroach inland into underground water tables.
Storm surges exacerbate this by depositing saltwater on permeable surface soils, contaminating freshwater supplies.
3
Select the option that correctly identifies this environmental degradation process.
The correct hazard is saltwater intrusion/salinization of freshwater coastal aquifers.
Other listed options describe slope movements, surface soil erosion, or atmospheric phenomena.

Key Concept

Saltwater Intrusion and Coastal Aquifer Degradation
Question 12724Question

In parts of Nigeria with rugged topography, such as the Mandara Mountains and the edges of the Jos Plateau, local farmers construct stone terraces along hill slopes. What is the primary geographical reason for adopting this agricultural practice?

Show answer & explanation

Answer: To control soil erosion and retain soil moisture on steep slopes for intensive cultivation

Answer

To control soil erosion and retain soil moisture on steep slopes for intensive cultivation
Terrace farming is an effective soil conservation practice used on steep hillsides. By breaking long slopes into a series of flat steps, it slows down water runoff, prevents severe soil erosion, and traps essential moisture and nutrients required for crop production.

Step-by-Step Solution

1
Analyze the physical geography of highlands like the Mandara Mountains and Jos Plateau
These relief regions feature steep slopes that are highly vulnerable to soil erosion from surface runoff during heavy seasonal rains.
Steep gradients accelerate surface water velocity and wash away fertile topsoil.
2
Evaluate the agricultural response to rugged highland terrain
Farmers build step-like stone terraces across the slope to slow down water runoff, trap soil nutrients, and enable continuous crop cultivation.
Terracing is a classic soil conservation technique adapted to highland agricultural systems.

Key Concept

Terrace Farming and Soil Conservation in Nigerian Highland Agriculture
Question 12725Question

At a meteorological station in Jos, Nigeria, a weather observer records a maximum daily air temperature of 28.5C28.5^\circ\text{C} and a minimum daily air temperature of 17.5C17.5^\circ\text{C} using a Six's maximum and minimum thermometer. What is the mean daily temperature in C^\circ\text{C}?

Show answer & explanation

Answer: 23

Answer

The mean daily temperature is 23.0C23.0^\circ\text{C}.
The mean daily temperature is determined by taking the average of the daily maximum and minimum temperatures: 28.5C+17.5C2=23.0C\frac{28.5^\circ\text{C} + 17.5^\circ\text{C}}{2} = 23.0^\circ\text{C}.

Step-by-Step Solution

1
Sum the maximum daily temperature and minimum daily temperature recorded at the weather station.
28.5C+17.5C=46.0C28.5^\circ\text{C} + 17.5^\circ\text{C} = 46.0^\circ\text{C}
Finding the total combined temperature extreme values is the first step in calculating the arithmetic mean.
2
Divide the combined total temperature by 2.
46.0C2=23.0C\frac{46.0^\circ\text{C}}{2} = 23.0^\circ\text{C}
The mean daily temperature represents the average temperature over a 24-hour observation period.

Key Concept

Calculation of Mean Daily Temperature
Estimated Time:45s
Question 12726Question

If (x,y)(x, y) is a pair of positive integers satisfying the simultaneous equations x+2y=7x + 2y = 7 and x2+y2=13x^2 + y^2 = 13, what is the value of 2xy2x - y?

Show answer & explanation

Answer: 4

Answer

The value of 2xy2x - y is 4.
Substituting x=72yx = 7 - 2y into x2+y2=13x^2 + y^2 = 13 yields the quadratic 5y228y+36=05y^2 - 28y + 36 = 0, which factors as (5y18)(y2)=0(5y - 18)(y - 2) = 0. Since xx and yy must both be positive integers, the valid solution pair is (x,y)=(3,2)(x, y) = (3, 2). Evaluating 2xy2x - y gives 2(3)2=42(3) - 2 = 4.

Step-by-Step Solution

1
Express xx in terms of yy using the linear equation x+2y=7x + 2y = 7.
x=72yx = 7 - 2y
Isolating xx allows substitution into the quadratic equation.
2
Substitute x=72yx = 7 - 2y into x2+y2=13x^2 + y^2 = 13 and expand.
(72y)2+y2=13    4928y+4y2+y2=13(7 - 2y)^2 + y^2 = 13 \implies 49 - 28y + 4y^2 + y^2 = 13
This reduces the system to a single quadratic equation in terms of yy.
3
Rearrange and solve the resulting quadratic equation 5y228y+36=05y^2 - 28y + 36 = 0.
(5y18)(y2)=0    y=2(5y - 18)(y - 2) = 0 \implies y = 2 or y=3.6y = 3.6
Factoring provides the possible values for yy.
4
Identify the integer solution pair and compute the target expression 2xy2x - y.
Since yy must be a positive integer, y=2y = 2 and x=3x = 3. Therefore, 2xy=2(3)2=42x - y = 2(3) - 2 = 4.
The non-integer solution is rejected based on the positive integer constraint.

Key Concept

Simultaneous Linear and Quadratic Equations
Estimated Time:1m 30s
Question 12727Question

Along a steep rocky headland, storm waves repeatedly force air under extreme pressure into narrow joints and bedding planes at the back of a sea cave. As waves surge into the cave, the rapid trapped air compression followed by explosive expansion causes vertical disintegration of the roof until an opening reaches the cliff top surface above. Which of the following coastal landforms is formed by this specific process?

Show answer & explanation

Answer: Blowhole

Answer

Blowhole
The correct answer describes a blowhole. Hydraulic action occurs when sea waves rush into a sea cave, compressing air trapped in fissures in the cave roof. The repeated sudden pressure changes shatter the rock above, creating a vertical shaft that penetrates the cliff surface.

Step-by-Step Solution

1
Analyze the geomorphic process described in the stem.
The mechanism involves wave energy forcing trapped air under pressure into cave roof joints, causing vertical erosion upward through the cliff.
Air compression wedging (hydraulic action) inside sea caves acts vertically on weakness lines in the roof.
2
Identify the resulting coastal erosional landform.
Vertical breaching of a sea cave roof to the cliff top forms a shaft known as a blowhole (or gloup).
Continued upward hydraulic erosion creates a vertical vent through which sea spray is forced during high tide or heavy seas.
3
Differentiate from alternative landforms.
Fluvial features (oxbow lakes, deltaic channels) and subaerial mass wasting features (scree slopes) do not originate from coastal cave hydraulic erosion.
Oxbow lakes and deltas belong to river system deposition, while scree slopes arise from freeze-thaw weathering and slope failure.

Key Concept

Coastal erosional processes and sea cave landform development
Estimated Time:1m 30s
Question 12728Question

Match each Köppen climate classification symbol on the left with its primary controlling atmospheric mechanism and seasonal characteristics on the right.

Click a left item, then click its matching right item

Items

Af (Equatorial Climate)
BWh (Hot Desert Climate)
Cs (Mediterranean Climate)
ET (Tundra Climate)

Matches

Show answer & explanation

Answer

Af matches with high year-round rainfall and ITCZ influence; BWh matches with extreme aridity under subtropical highs; Cs matches with dry summers and wet westerly winters; ET matches with severe cold and warmest month below 10°C.
Each Köppen symbol maps directly to its controlling atmospheric mechanism: Af is controlled by low pressure at the ITCZ, BWh by subtropical anticyclones, Cs by seasonal migration of high pressure and westerly wind belts, and ET by polar air mass dominance at high latitudes.

Step-by-Step Solution

1
Analyze Af climate characteristics
Af represents a tropical wet climate with continuous high temperatures and rainfall governed by the ITCZ.
The 'f' suffix in Köppen classification denotes fully humid conditions without a dry season.
2
Analyze BWh climate controls
BWh indicates a hot arid desert climate created by atmospheric subsidence in subtropical high-pressure zones.
Subtropical high-pressure belts cause sinking air that inhibits condensation and cloud formation.
3
Analyze Cs climate controls
Cs denotes a Mediterranean climate with dry summers and wet winters resulting from latitudinal wind belt shifts.
Poleward shift of subtropical highs brings summer dryness, while equatorward shift of westerlies brings winter rains.
4
Analyze ET climate characteristics
ET represents a tundra climate where high latitudinal location suppresses summer warming above 10°C.
High-latitude location leads to low solar incidence angles and long, harsh polar winters.

Key Concept

Köppen Climate Classification and World Climatic Controls
Question 12729Question

A candidate takes a two-stage driving examination consisting of a theoretical test followed by a practical test. The probability that the candidate passes the theoretical test is 0.750.75. If the candidate passes the theoretical test, the probability of passing the practical test is 0.800.80. However, if the candidate fails the theoretical test, the probability of passing the practical test is 0.200.20. What is the probability that the candidate passes exactly one of the two tests?

Show answer & explanation

Answer: 0.2

Answer

The probability that the candidate passes exactly one of the two tests is 0.2.
To pass exactly one test, the candidate must either pass theory and fail practical (0.75×0.20=0.150.75 \times 0.20 = 0.15) or fail theory and pass practical (0.25×0.20=0.050.25 \times 0.20 = 0.05). Since these two outcomes cannot happen at the same time, their probabilities are added: 0.15+0.05=0.200.15 + 0.05 = 0.20.

Step-by-Step Solution

1
Calculate the probability of passing the theoretical test and failing the practical test.
P(TheoryPractical)=0.75×(10.80)=0.15P(\text{Theory} \cap \text{Practical}') = 0.75 \times (1 - 0.80) = 0.15
The probability of failing practical given passing theory is 10.80=0.201 - 0.80 = 0.20.
2
Calculate the probability of failing the theoretical test and passing the practical test.
P(TheoryPractical)=(10.75)×0.20=0.05P(\text{Theory}' \cap \text{Practical}) = (1 - 0.75) \times 0.20 = 0.05
The probability of failing theory is 10.75=0.251 - 0.75 = 0.25.
3
Sum the probabilities of the two mutually exclusive outcomes.
0.15+0.05=0.200.15 + 0.05 = 0.20
Passing exactly one test is the union of two disjoint compound events.

Key Concept

Compound probability laws and conditional independence structure in sequential events
Estimated Time:1m 30s
Question 12730Question

A constant-volume gas thermometer registers a pressure of 60kPa60\,\text{kPa} at the ice point (0C0^\circ\text{C}) and 84kPa84\,\text{kPa} at the steam point (100C100^\circ\text{C}). What is the temperature in degrees Celsius when the pressure registered by the thermometer is 72kPa72\,\text{kPa}?

Show answer & explanation

Answer: 50

Answer

The temperature corresponding to a pressure reading of 72kPa72\,\text{kPa} is 50C50^\circ\text{C}.
Using the linear relation for a constant-volume gas thermometer: T=PTP0P100P0×100CT = \frac{P_T - P_0}{P_{100} - P_0} \times 100^\circ\text{C}. Substituting PT=72kPaP_T = 72\,\text{kPa}, P0=60kPaP_0 = 60\,\text{kPa}, and P100=84kPaP_{100} = 84\,\text{kPa} yields T=72608460×100=1224×100=50CT = \frac{72 - 60}{84 - 60} \times 100 = \frac{12}{24} \times 100 = 50^\circ\text{C}.

Step-by-Step Solution

1
Identify the thermometric property values at the fixed points and target state.
P0=60kPaP_0 = 60\,\text{kPa}, P100=84kPaP_{100} = 84\,\text{kPa}, and PT=72kPaP_T = 72\,\text{kPa}.
These represent the pressure values corresponding to 0C0^\circ\text{C}, 100C100^\circ\text{C}, and the unknown temperature TT respectively.
2
Set up the linear scale conversion equation.
T=PTP0P100P0×100CT = \frac{P_T - P_0}{P_{100} - P_0} \times 100^\circ\text{C}
Temperature changes linearly with the thermometric property (gas pressure at constant volume).
3
Calculate the numerical value.
T=1224×100=50CT = \frac{12}{24} \times 100 = 50^\circ\text{C}
Simplifying the fraction 1224=0.5\frac{12}{24} = 0.5 and multiplying by 100100 gives 5050.

Key Concept

Temperature measurement using constant-volume gas pressure as a thermometric property
Question 12731Question

In a humid tropical environment, acidic groundwater reacts with orthoclase feldspar present in granite bedrock. Through a reaction where hydroxyl (OHOH^-) and hydrogen (H+H^+) ions replace potassium cations, the hard rock is decomposed in-situ into soft kaolin clay. Which chemical weathering process does this transformation describe?

Show answer & explanation

Answer: Hydrolysis

Answer

Hydrolysis
Hydrolysis is the chemical weathering process wherein water molecules dissociate into hydrogen (H+H^+) and hydroxyl (OHOH^-) ions that replace mineral cations (such as potassium in orthoclase feldspar), breaking down granite in-situ into kaolin clay.

Step-by-Step Solution

1
Analyze the process described in the scenario
The scenario describes an in-situ chemical reaction where ions from groundwater (H+H^+ and OHOH^-) react with feldspar in granite, altering it into kaolin clay.
Chemical weathering involves chemical reactions that alter the mineral composition of rocks at or near the surface.
2
Identify the specific chemical weathering mechanism
Hydrolysis specifically describes the reaction between water ions and silicate minerals like feldspar to form clay minerals.
Mass wasting processes involve downslope displacement under gravity, while metamorphism occurs deep underground under extreme heat/pressure.

Key Concept

Chemical weathering of silicate minerals via Hydrolysis
Estimated Time:1m 0s
Question 12732Question

An environmental management team in Nigeria is configuring a Geographic Information System (GIS) to analyze continuous geographical phenomena across a river basin, such as elevation gradients and soil moisture distribution. Which of the following GIS data models is most suitable for accurately representing these continuous spatial phenomena?

Show answer & explanation

Answer: The raster data model, because it represents continuous surface features through an array of grid cells, each storing a specific value.

Answer

The raster data model is most suitable because it represents continuous surface features through an array of grid cells, each storing a specific attribute value.
The raster data model divides geographical space into a continuous grid of cells (pixels), where every cell stores a measurement representing phenomena that vary continuously across a surface, such as land elevation, temperature, or moisture levels.

Step-by-Step Solution

1
Identify the nature of the spatial phenomena being modeled
Elevation gradients and soil moisture distribution vary smoothly across space without defined boundaries, making them continuous spatial phenomena.
Geographical data is categorized into discrete features (with clear boundaries) and continuous surfaces (changing seamlessly across space).
2
Select the GIS data structure optimized for continuous surface representation
The raster data structure represents space as a regular tessellation of grid cells or pixels, assigning a scalar value to every cell location.
Raster grids are mathematically and structurally ideal for continuous elevation models (DEMs), satellite imagery, and environmental gradients.

Key Concept

Raster vs. Vector GIS Data Models for Continuous and Discrete Phenomena
Estimated Time:1m 0s
Question 12733Question

Match each weather measuring instrument on the left with its specific operational mechanism or structural feature on the right.

Click a left item, then click its matching right item

Items

Fortin Barometer
Campbell-Stokes Sunshine Recorder
Six's Maximum and Minimum Thermometer
Hair Hygrometer

Matches

Show answer & explanation

Answer

Fortin Barometer matches with the flexible leather cistern and ivory pointer mechanism; Campbell-Stokes Sunshine Recorder matches with the solid glass sphere focusing solar rays; Six's Maximum and Minimum Thermometer matches with the U-shaped tube containing mercury, alcohol, and steel indices; Hair Hygrometer matches with tracking changes in the physical length of organic fibers.
Each instrument correctly corresponds to its distinct mechanical component: the Fortin barometer relies on an adjustable leather cistern with an ivory zero pointer; the Campbell-Stokes sunshine recorder relies on a glass sphere lens; Six's thermometer uses a U-tube with alcohol, mercury, and steel indices; and the hair hygrometer utilizes tension variations in organic hair strands.

Step-by-Step Solution

1
Analyze the operational mechanism for atmospheric pressure measurement
Identify the Fortin Barometer as the instrument utilizing a leather cistern adjusted via a screw until mercury touches an ivory point zero datum.
Precision barometric readings require establishing a fixed reservoir reference level.
2
Analyze the operating principle of sunshine recorders
Identify the Campbell-Stokes recorder as using a glass sphere lens to scorch a line on card strip.
Concentrating direct solar radiation burns paper selectively during sunny intervals.
3
Analyze dual-extreme temperature recording instruments
Identify Six's Thermometer as using a U-tube filled with alcohol and mercury driving steel indices.
Differential thermal expansion of liquid columns pushes steel markers to extreme limits.
4
Analyze humidity measuring principles based on organic material expansion
Identify the hair hygrometer as utilizing human/animal hair elasticity changes caused by humidity.
Hygroscopic organic fibers naturally elongate as moisture absorption increases.

Key Concept

Operating Principles and Structural Features of Weather Station Instruments
Question 12734Question

Below is a list of specific rock specimens alongside various geological formation mechanisms and economic applications. Match each rock specimen to its corresponding origin process and primary practical utilization.

Click a left item, then click its matching right item

Items

Rhyolite
Chert
Amphibolite
Dolomite

Matches

Show answer & explanation

Answer

Rhyolite matches the extrusive felsic volcanic rock utilized as decorative stone; Chert matches the microcrystalline siliceous sedimentary rock used for abrasives; Amphibolite matches the regional metamorphic rock derived from mafic precursors; Dolomite matches the magnesium-replaced carbonate sedimentary rock used as a metallurgical flux.
Each rock specimen is accurately paired based on its primary genetic category (igneous, sedimentary, metamorphic), mineral composition, and commercial utilization in industrial and construction settings.

Step-by-Step Solution

1
Identify the genetic classification and composition of Rhyolite
Rhyolite is the extrusive equivalent of granite, characterized by rapid lava cooling and high silica content.
Extrusive volcanic cooling produces fine-grained textures distinguishing rhyolite from intrusive granite.
2
Determine the formation environment of Chert
Chert consists of microcrystalline quartz deposited from siliceous skeletal remains or inorganic silica precipitates.
Siliceous chemical sedimentary rocks differ fundamentally from clastic mudstones and organic limestones.
3
Analyze the protolith and metamorphic grade of Amphibolite
Amphibolite forms via regional metamorphic alteration of mafic igneous rocks under elevated temperatures and pressures.
Hornblende mineral dominance reflects high-grade alteration of basaltic parent material.
4
Evaluate the diagenetic alteration involved in forming Dolomite
Dolomite forms when magnesium ions replace calcium ions in existing limestone, creating a magnesium-rich carbonate.
Magnesium substitution alters chemical properties, making dolomite suitable for high-temperature refractory applications.

Key Concept

Rock Types, Formation Processes, and Economic Importance
Question 12735Question

During an field investigation of coastal landforms along a rocky cliff line, geographers observed narrow, steep-sided sea inlets created where marine wave action enlarged weak structural joints and faults, eventually causing the collapse of sea cave roofs. Which coastal landform is produced by this process?

Show answer & explanation

Answer: Geo

Answer

Geo
A geo is a deep, narrow, steep-sided inlet formed along a rocky coast when hydraulic action and abrasion enlarge joints and sea caves, eventually causing the cave roof to collapse inward.

Step-by-Step Solution

1
Identify the primary erosional process and coastal structural feature described in the stem.
High-energy wave action (hydraulic action and abrasion) targets vertical joint planes along a cliff face.
Marine erosion concentrates along structural weaknesses in coastal rocks to form sea caves.
2
Analyze the sequential development leading to cliff-line retreat.
Continued wave excavation and air compression enlarge the cave until its roof weakens and collapses.
The complete collapse of a sea cave roof leaves a deep, narrow, steep-sided trench extending inland.
3
Match the defined geomorphic feature with standard geography nomenclature.
The steep-sided coastal inlet formed by sea cave roof collapse is termed a geo.
Distinguishes marine erosion inlets from fluvial landforms, weathering features, and coral reefs.

Key Concept

Formation of Geos via Coastal Wave Erosion and Cave Roof Collapse
Estimated Time:1m 0s
Question 12736Question

In ABC\triangle ABC, side b=10 cmb = 10\text{ cm}, side c=6 cmc = 6\text{ cm}, and A=120\angle A = 120^\circ. What is the length of side aa in centimeters?

Show answer & explanation

Answer: 14

Answer

The length of side aa is 14 cm14\text{ cm}.
Applying the Cosine Rule a2=b2+c22bccosAa^2 = b^2 + c^2 - 2bc \cos A with b=10 cmb = 10\text{ cm}, c=6 cmc = 6\text{ cm}, and A=120\angle A = 120^\circ gives a2=102+622(10)(6)(0.5)=100+36+60=196a^2 = 10^2 + 6^2 - 2(10)(6)(-0.5) = 100 + 36 + 60 = 196. Taking the square root yields a=14 cma = 14\text{ cm}.

Step-by-Step Solution

1
Identify the given parameters and select the relevant trigonometric rule
Given sides b=10 cmb = 10\text{ cm}, c=6 cmc = 6\text{ cm}, and included angle A=120\angle A = 120^\circ. Use the Cosine Rule: a2=b2+c22bccosAa^2 = b^2 + c^2 - 2bc \cos A.
The Cosine Rule is required because two sides and the included angle (SAS) are given to find the third side.
2
Substitute the known values into the Cosine Rule equation
a2=102+622(10)(6)cos(120)a^2 = 10^2 + 6^2 - 2(10)(6) \cos(120^\circ)
This sets up a single equation with the unknown side length aa.
3
Evaluate the cosine term and simplify the arithmetic expression
a2=100+36120(0.5)=136+60=196a^2 = 100 + 36 - 120(-0.5) = 136 + 60 = 196
Since 120120^\circ is an obtuse angle in the second quadrant, cos(120)=0.5\cos(120^\circ) = -0.5, changing the minus sign in the formula to a plus sign.
4
Calculate the principal square root to find aa
a=196=14 cma = \sqrt{196} = 14\text{ cm}
Side length must be a positive scalar quantity.

Key Concept

Cosine Rule for Side Length in Oblique Triangles
Question 12737Question

A binary operation \ast is defined on the set of real numbers R\mathbb{R} by ab=a+b4a \ast b = a + b - 4. If x1x^{-1} represents the inverse of an element xx under the operation \ast, what is the value of xx such that x3=101x \ast 3 = 10^{-1}?

Show answer & explanation

Answer: 1-1

Answer

The value of xx is 1-1.
First, the identity element ee is determined using ae=aa \ast e = a, which gives a+e4=a    e=4a + e - 4 = a \implies e = 4. Next, the inverse 10110^{-1} is calculated from 10101=410 \ast 10^{-1} = 4, yielding 10+1014=4    101=210 + 10^{-1} - 4 = 4 \implies 10^{-1} = -2. Finally, setting x3=2x \ast 3 = -2 gives x+34=2    x1=2    x=1x + 3 - 4 = -2 \implies x - 1 = -2 \implies x = -1.

Step-by-Step Solution

1
Find the identity element ee under the operation \ast.
e=4e = 4
By definition of an identity element, ae=a    a+e4=a    e=4a \ast e = a \implies a + e - 4 = a \implies e = 4.
2
Determine the inverse of 1010, denoted 10110^{-1}, under \ast.
101=210^{-1} = -2
By definition of an inverse element, 10101=e    10+1014=4    6+101=4    101=210 \ast 10^{-1} = e \implies 10 + 10^{-1} - 4 = 4 \implies 6 + 10^{-1} = 4 \implies 10^{-1} = -2.
3
Substitute 101=210^{-1} = -2 into the given equation x3=101x \ast 3 = 10^{-1} and solve for xx.
x=1x = -1
Using the definition of the operation, x3=x+34=x1x \ast 3 = x + 3 - 4 = x - 1. Setting x1=2x - 1 = -2 yields x=1x = -1.

Key Concept

Identity and Inverse Elements in Binary Operations
Question 12738Question

A hydrologist analyzing satellite imagery of Nigeria observes a drainage network where short tributary streams flow down parallel ridges and join the main stream almost at right angles, controlled by alternating bands of hard and soft folded sedimentary rocks. In which of the following physical regions of Nigeria is this trellis drainage pattern most prominently developed?

Show answer & explanation

Answer: The folded sedimentary belt of the Benue Trough

Answer

The folded sedimentary belt of the Benue Trough
The correct option is the folded sedimentary belt of the Benue Trough. Trellis drainage patterns form in regions with folded sedimentary topography where softer strata weather into parallel valleys while resistant strata form ridges. Tributaries cut through weak rock belts and join the master stream at right angles along fault lines and fold axes, which is characteristic of the Benue valley sedimentary structure.

Step-by-Step Solution

1
Identify the key structural and landform characteristics described in the stem.
The network displays tributaries joining main rivers at right angles along parallel ridges of folded sedimentary rock (trellis pattern).
Trellis drainage develops specifically in areas where geology exhibits folded or faulted parallel rock strata of varying resistance.
2
Evaluate the relief and geological structure of Nigeria's physical regions.
The Benue Trough is a major Cretaceous rift basin with folded sedimentary structures, creating lineaments and parallel ridges conducive to trellis drainage.
Crystalline plateaus develop radial drainage, deltaic lowlands develop distributary networks, and uniform flat plains develop dendritic patterns.
3
Match the specific drainage pattern to the corresponding physical region.
The folded sedimentary belt of the Benue Trough is the correct physical region.
Structural control from fold axes in the Benue valley directly produces the right-angled tributary alignments characteristic of trellis drainage.

Key Concept

Structural control of drainage patterns in Nigerian physical regions
Question 12739Question

Match each African transport and trade corridor listed on the left with the landlocked state dependency and coastal port gateway it serves on the right.

Click a left item, then click its matching right item

Items

Dakar–Bamako Transport Corridor
Northern Logistics Corridor
Nacala Transit Corridor
Maputo Development Corridor

Matches

Show answer & explanation

Answer

Dakar–Bamako Transport Corridor connects landlocked Mali to Dakar (Senegal); Northern Logistics Corridor connects landlocked Uganda and Rwanda to Mombasa (Kenya); Nacala Transit Corridor connects landlocked Malawi to Nacala (Mozambique); Maputo Development Corridor connects landlocked Eswatini and Gauteng to Maputo (Mozambique).
Each transport corridor in Africa serves distinct landlocked hinterlands: the Dakar–Bamako route links Mali to Senegal; the Northern Corridor links Uganda and Rwanda to Kenya's Mombasa port; the Nacala Corridor provides Malawi with access to Mozambique's deep-water port; and the Maputo Corridor connects Eswatini and South Africa to Maputo.

Step-by-Step Solution

1
Identify the West African transport link for landlocked Mali
Mali relies heavily on Senegal's port of Dakar via the Dakar–Bamako rail and road corridor.
Mali is landlocked and Dakar provides its primary maritime trade outlet to the Atlantic Ocean.
2
Identify East Africa's main northern trade arterial corridor
The Northern Corridor connects Kenya's port of Mombasa to Uganda, Rwanda, Burundi, and South Sudan.
Mombasa acts as the strategic Indian Ocean gateway for landlocked East African nations.
3
Analyze Southern African transport networks for Malawi and Eswatini
Malawi is linked to Nacala in northern Mozambique, while Eswatini and Gauteng link to Maputo in southern Mozambique.
Nacala possesses a natural deep-water harbour servicing Malawi, whereas Maputo handles trade from Eswatini and eastern South Africa.

Key Concept

African Transport Corridors, Port Hinterlands, and Landlocked State Dependencies
Estimated Time:2m 0s
Question 12740Question

Agricultural production systems in Nigeria exhibit a strong spatial distribution governed by the south-to-north latitudinal rainfall gradient. Arrange the following crop and agricultural production belts in order from the far South (highest annual rainfall) to the far North (lowest annual rainfall):

Drag items to arrange them in the correct order

Show answer & explanation

Answer

The correct sequence from South to North is: Oil palm and rubber commercial tree crop belt, followed by Cocoa and root tuber production belt, then Grain maize, grain legumes, and cotton production belt, and finally Millet, sorghum, and pastoral cattle rearing belt.
Agricultural systems in Nigeria are primarily controlled by annual rainfall duration and amount, which decline along a latitudinal gradient from south to north. The southernmost humid forest zone receives the highest rainfall (>2,000 mm), favoring moisture-demanding tree crops like oil palm and rubber. Moving north into the forest-savanna transition, cocoa and root crops dominate. Further north in the sub-humid Guinea Savanna, lower rainfall supports cereal crops like maize and industrial crops like cotton. In the northernmost Sudan and Sahel Savanna, low rainfall (<700 mm) restricts crop farming to drought-resistant grains like millet and sorghum, alongside pastoral cattle herding.

Step-by-Step Solution

1
Analyze the climatic and moisture requirements of each agricultural system in Nigeria.
Tree cash crops like oil palm and rubber require heavy precipitation (>2000 mm), root tubers and cocoa require moderate-to-high rainfall, cereal grains and cotton require moderate seasonal rainfall, while millet and pastoral cattle rearing thrive in low-rainfall semi-arid environments.
Mean annual precipitation in Nigeria decreases progressively from over 3,000 mm along the southern coast to less than 600 mm near the northern border.
2
Map each agricultural belt to its corresponding ecological zone along the latitudinal gradient.
Southern Rainforest Belt -> Derived Savanna / Forest Transition Zone -> Guinea Savanna -> Sudan/Sahel Savanna.
Ecological zones in Nigeria run in east-west bands parallel to lines of latitude.
3
Sequence the items from the southernmost coastal zone to the northernmost border zone.
The correct sequence starts with oil palm and rubber, proceeds to cocoa and yam, continues to cotton and maize, and finishes with millet, sorghum, and pastoralism.
This order accurately reflects the decreasing rainfall gradient from South to North.

Key Concept

Latitudinal Zonation of Agricultural Systems in Nigeria
PreviousPage 637 / 697Next
All practice questions — JAMB UTME | Examkin