Contextual Applications

Applying Mathematical Concepts to Real-World Scenarios in South Africa

CAPS Grade 10 Mathematical Literacy

This document explores the Contextual Applications section of the Grade 10 Mathematical Literacy CAPS curriculum, focusing on how mathematical concepts are applied to real-world scenarios in South Africa. The curriculum emphasizes practical problem-solving using mathematical tools across various domains.

1. Consumer Finances (Choosing the Best Option)

In the realm of consumer finances, students learn to compare different pricing structures to determine the most cost-effective option.

Cell Phone Contracts

Prepaid Rate: R2 per minute

Contract: R200 fixed fee + R1 per minute

Prepaid: C = 2x
Contract: C = 200 + 1x
2x = 200 + x → x = 200 minutes

At 200 minutes, both options cost the same. If you use more than 200 minutes, the contract is better.

Bank Charges

Bank A: R50 flat monthly fee

Bank B: R5 per transaction

Bank A: C = 50
Bank B: C = 5x
50 = 5x → x = 10 transactions

If you make more than 10 transactions, Bank B is cheaper.

Test Yourself: Consumer Finances

3 Questions
1 Prepaid: R3/min, Contract: R150 + R1/min. Break-even minutes?
50 minutes
75 minutes
100 minutes
150 minutes
2 Bank A: R40 flat fee, Bank B: R4 per transaction. Break-even transactions?
5 transactions
8 transactions
10 transactions
12 transactions
3 If you use 150 minutes, which is better: Prepaid R2/min or Contract R100 + R1/min?
Prepaid (R300)
Contract (R250)
Same cost
Can't compare
0/3

2. Transport and Travel

Transport and travel costs are calculated using fixed and variable rates. This section teaches students to predict travel expenses based on distance and fare structures.

Taxi / Uber Fares

Base Fare: R10

Rate per km: R5

C = 10 + 5d
For 15 km: 10 + 5(15) = R85

Delivery Fees

Delivery Fee: R20 base + R3 per km

C = 20 + 3d
For 10 km: 20 + 3(10) = R50

Transport Cost Calculator

Calculate the fare for different distances.

Taxi fare: R12 base + R8 per km. What is the cost for 8 km?
Hint: Total = Base + (Rate × km)

3. Household Utilities (Tariffs)

Understanding household utility costs is crucial for managing expenses. Students learn to interpret step tariffs for electricity and water.

Electricity Tariffs

Step 1: R1 per kWh for the first 100 kWh

Step 2: R1.50 per kWh for usage above 100 kWh

Usage (kWh) Calculation Cost (R)
50 kWh 50 × R1 R50
100 kWh 100 × R1 R100
150 kWh (100 × R1) + (50 × R1.50) R175
200 kWh (100 × R1) + (100 × R1.50) R250

Test Yourself: Utilities

3 Questions
1 Step 1: R2/kWh for first 50 kWh, Step 2: R3/kWh above 50 kWh. Cost for 80 kWh?
R160
R190
R210
R240
2 Water: First 10kl free, then R15/kl. Cost for 25kl?
R150
R225
R300
R375
3 If the slope of the graph increases after 100 kWh, this means:
Electricity gets cheaper
Electricity gets more expensive per unit
Electricity becomes free
Price stays the same
0/3

4. Environmental & Social Issues

This section focuses on understanding growth patterns and resource consumption.

Population Growth

P(t) = P₀ × 2^(t/10)
After 20 years: 1000 × 2² = 4000 people

Water Conservation

Days = 1000 ÷ (100 × n)
1 person: 10 days
5 people: 2 days

5. Small Business (Profit and Loss)

Market Day Example

Income: R20 per item sold

Expenses: R100 fixed rent + R5 per item

1

Income:
I = 20x

2

Expenses:
E = 100 + 5x

3

Break-even:
20x = 100 + 5x
15x = 100
x ≈ 6.67

Sell at least 7 items to break even.

Test Yourself: Small Business

2 Questions
1 Income: R15/item, Expenses: R80 fixed + R4/item. Break-even items?
6 items
7 items
8 items
9 items
2 If you sell 20 items at R25 each, with expenses R150 + R8/item, what is profit?
R190
R210
R340
R500
0/2

Exam Tip: In Paper 2, students must justify their answers with clear reasoning and evidence. For example, instead of simply stating that "Option A is better," they should articulate, "Option A is better because for any distance over 10 km, the total cost is lower than Option B, as shown on the graph."

Final Assessment: Contextual Applications

8 Questions

Test your ability to apply maths to real-world contexts.

1 Prepaid: R2.50/min, Contract: R150 + R1/min. Break-even minutes?
50
75
100
150
2 Taxi: R15 base + R6/km. Cost for 12 km?
R72
R87
R92
R102
3 Electricity: First 200 kWh @ R1.20, then R1.80. Cost for 300 kWh?
R360
R420
R480
R540
4 Bank A: R60 flat, Bank B: R6/transaction. Break-even transactions?
5
8
10
12
5 Population doubles every 8 years. If 500 now, how many in 16 years?
1000
1500
2000
4000
6 Business: Income R30/item, Expenses R200 + R10/item. Break-even items?
5
8
10
12
7 Water tank: 2000 litres, 4 people using 50L/day each. How many days?
5 days
10 days
15 days
20 days
8 If using more than 200 minutes, Contract A is cheaper. This means break-even was:
100 minutes
150 minutes
200 minutes
250 minutes
0/8

Conclusion

By mastering these concepts, students will be equipped to apply mathematical literacy to real-life situations, enhancing their decision-making skills in various contexts across consumer finances, transport, household utilities, environmental issues, and small business operations.