Grade 9 : Social Science - 2. Shaping Earth (Set 2) | Concept of Maths

Question 1

1. High-precision GPS stations on the Indo-Australian Plate show it is moving northward at a velocity of $v = 2.5$ cm/year. Calculate the total distance $d$ in kilometers the plate will have traveled after $t = 10^5$ years.

A) 25 km

B) 2.5 km

C) 250 km

D) 0.25 km

Answer

Correct Answer: B

Solution: The distance $d$ is given by $d = v \\times t$. $$d = 2.5 \\text{ cm/year} \\times 100,000 \\text{ years} = 250,000 \\text{ cm}$$ Convert to kilometers: $$250,000 \\text{ cm} = 2,500 \\text{ m} = 2.5 \\text{ km}$$.

Question 2

2. A mountain stream flows from an elevation of $H_1 = 1450$ m down to a valley at $H_2 = 1250$ m. If the horizontal distance of the river's path is $L = 50$ km, what is the average river gradient $G$ in meters per kilometer (m/km)?

A) 4 m/km

B) 20 m/km

C) 0.25 m/km

D) 10 m/km

Answer

Correct Answer: A

Solution: Gradient $G = \\frac{\\Delta H}{L}$ where $\\Delta H = H_1 - H_2$. $$\\Delta H = 1450 \\text{ m} - 1250 \\text{ m} = 200 \\text{ m}$$ $$G = \\frac{200 \\text{ m}}{50 \\text{ km}} = 4 \\text{ m/km}$$.

Question 3

3. Geologists observe that a river carves a canyon at a vertical erosion rate of $r = 0.15$ mm/year. How many years will it take for the river to carve a gorge that is $H = 300$ meters deep?

A) 200,000 years

B) 45,000 years

C) 2,000,000 years

D) 20,000 years

Answer

Correct Answer: C

Solution: Convert depth to millimeters: $300 \\text{ m} = 300,000 \\text{ mm}$. Time $t = \\frac{H}{r}$: $$t = \\frac{300,000 \\text{ mm}}{0.15 \\text{ mm/year}} = 2,000,000 \\text{ years}$$.

Question 4

4. The Richter scale is logarithmic. Every increase of 1 unit in magnitude corresponds to a 10-fold increase in measured amplitude. How much larger is the ground motion amplitude of a Magnitude 6 earthquake compared to a Magnitude 4 earthquake?

A) 20 times

B) 100 times

C) 1,000 times

D) 2 times

Answer

Correct Answer: B

Solution: The difference in magnitude is $\\Delta M = 6 - 4 = 2$. The amplitude increase is $10^{\\Delta M}$. $$10^2 = 100 \\text{ times}$$.

Question 5

5. The Mid-Atlantic Ridge spreads apart at a rate of $2$ cm/year on each side of the ridge. Calculate the total width of the new ocean floor created between two points on opposite sides after $10^6$ years.

A) 20 km

B) 2 km

C) 40 km

D) 4 km

Answer

Correct Answer: C

Solution: Total spreading rate $v_{total} = 2 \\text{ sides} \\times 2 \\text{ cm/year} = 4 \\text{ cm/year}$. Total distance $d = v_{total} \\times t$: $$d = 4 \\text{ cm/year} \\times 1,000,000 \\text{ years} = 4,000,000 \\text{ cm}$$ Convert to kilometers: $4,000,000 \\text{ cm} = 40,000 \\text{ m} = 40 \\text{ km}$.

Question 6

6. A normal fault in a rock layer shows a vertical displacement (throw) of $120$ m and a horizontal displacement (heave) of $50$ m. Using the Pythagorean theorem, calculate the total net slip (the actual diagonal distance the rock moved).

A) 130 m

B) 170 m

C) 150 m

D) 110 m

Answer

Correct Answer: A

Solution: Total displacement $D = \\sqrt{x^2 + y^2}$. $$D = \\sqrt{120^2 + 50^2} = \\sqrt{14400 + 2500} = \\sqrt{16900} = 130 \\text{ m}$$.

Question 7

7. Physical weathering breaks a solid granite cube with a side length of $s = 10$ cm into smaller cubes with side lengths of $1$ cm each. By how much does the total surface area increase?

A) 600 sq cm

B) 6000 sq cm

C) 540 sq cm

D) 5400 sq cm

Answer

Correct Answer: D

Solution: Original Surface Area $A_1 = 6s^2 = 6(10)^2 = 600 \\text{ cm}^2$. Volume is $10^3 = 1000 \\text{ cm}^3$. Each $1$ cm cube has surface area $6(1)^2 = 6 \\text{ cm}^2$. Total area of $1000$ cubes $A_2 = 1000 \\times 6 = 6000 \\text{ cm}^2$. Increase $= A_2 - A_1 = 6000 - 600 = 5400 \\text{ cm}^2$.

Question 8

8. A glacier in the Himalayas is observed to flow at an average speed of $0.4$ meters per day. Calculate the total distance the ice at the surface moves during a leap year (366 days).

A) 146 m

B) 144 m

C) 146.4 m

D) 120.5 m

Answer

Correct Answer: C

Solution: Distance $d = \\text{speed} \\times \\text{time}$. $$d = 0.4 \\text{ m/day} \\times 366 \\text{ days} = 146.4 \\text{ m}$$.

Question 9

9. A river carries a sediment load of $2,000$ kg of silt per day. Assuming the rate remains constant, how many metric tonnes of silt are transported by the river over a period of 3 years (assume 365 days per year)? [1 tonne = 1000 kg]

A) 730 tonnes

B) 2190 tonnes

C) 219 tonnes

D) 6000 tonnes

Answer

Correct Answer: B

Solution: Total mass $M = 2000 \\text{ kg/day} \\times 365 \\text{ days/year} \\times 3 \\text{ years}$. $$M = 2,190,000 \\text{ kg}$$ Convert to tonnes: $M = \\frac{2,190,000}{1000} = 2190 \\text{ tonnes}$.

Question 10

10. Due to isostatic rebound after the last ice age, a landmass is rising at a rate of $8$ mm/year. What is the total vertical rise in meters over the last $12,000$ years?

A) 96 m

B) 9.6 m

C) 960 m

D) 0.96 m

Answer

Correct Answer: A

Solution: Total rise $H = 8 \\text{ mm/year} \\times 12,000 \\text{ years}$. $$H = 96,000 \\text{ mm}$$ Convert to meters: $96,000 \\text{ mm} = 96 \\text{ m}$.

Grade 9 : Social Science - 2. Shaping Earth (Set 2) | Concept of Maths