Immediate Summary: Maths Lit Exam Division
In Mathematical Literacy, Paper 1 (Finance & Data Handling) tests Financial documents, Tax (PAYE/VAT), Tariffs, Cost Price vs Selling Price, Break-even analysis, and Statistical representations. Paper 2 (Measurement, Maps, Plans & Assembly) tests Perimeter/Area/Volume, Scale ratios, Travel itineraries, Layout plans, and Packaging efficiency. Both papers require reading contextual real-life South African documents accurately.
Worked Example 1: SARS Progressive Income Tax Calculation (Paper 1 · 7 Marks)
Financial Maths: Calculating Annual Tax Payable & Monthly PAYE
7 Marks (Paper 1)
Exam Scenario: Sipho is 42 years old and earns a gross monthly salary of R28,500. He contributes 7.5% of his basic salary toward a pension fund (which is tax-deductible). He has no medical aid.
Extract of SARS Tax Bracket Table:
• Bracket 1: R0 – R237,100 (18% of taxable income)
• Bracket 2: R237,101 – R370,500 (R42,678 + 26% of taxable income above R237,100)
• Bracket 3: R370,501 – R512,800 (R77,362 + 31% of taxable income above R370,500)
Tax Rebates: Primary Rebate (under 65): R17,235.
Question: Calculate Sipho's net monthly income after PAYE tax has been deducted.
Extract of SARS Tax Bracket Table:
• Bracket 1: R0 – R237,100 (18% of taxable income)
• Bracket 2: R237,101 – R370,500 (R42,678 + 26% of taxable income above R237,100)
• Bracket 3: R370,501 – R512,800 (R77,362 + 31% of taxable income above R370,500)
Tax Rebates: Primary Rebate (under 65): R17,235.
Question: Calculate Sipho's net monthly income after PAYE tax has been deducted.
Step 1: Calculate Annual Gross Income
Annual Gross = R28,500 × 12 = R342,000
Step 2: Calculate Allowable Pension Deduction
Annual Pension = 7.5% × R342,000 = 0.075 × 342,000 = R25,650
Step 3: Calculate Annual Taxable Income
Taxable Income = Gross Income - Allowable Deductions
Taxable Income = R342,000 - R25,650 = R316,350
Taxable Income = R342,000 - R25,650 = R316,350
Step 4: Identify Tax Bracket & Apply Bracket Formula
R316,350 falls into Bracket 2 (R237,101 – R370,500):
Amount above R237,100 = R316,350 - R237,100 = R79,250
Tax before Rebates = R42,678 + (26% × R79,250)
= R42,678 + R20,605 = R63,283
Tax before Rebates = R42,678 + (26% × R79,250)
= R42,678 + R20,605 = R63,283
Step 5: Deduct Primary Rebate to find Annual Tax Payable
Tax Payable = R63,283 - R17,235 (Primary Rebate) = R46,048
Step 6: Determine Monthly PAYE and Net Monthly Salary
Monthly PAYE = R46,048 / 12 = R3,837.33
Monthly Pension = R25,650 / 12 = R2,137.50
Net Monthly Income = R28,500 - (R3,837.33 + R2,137.50) = R22,525.17
Monthly Pension = R25,650 / 12 = R2,137.50
Net Monthly Income = R28,500 - (R3,837.33 + R2,137.50) = R22,525.17
Marking Memorandum Rubric:
• Annual gross multiplication × 12 (1 Mark)
• Pension deduction calculation (1 Mark)
• Taxable income subtraction (1 Mark)
• Correct bracket & difference above base (1 Mark)
• 26% calculation & base tax addition (1 Mark)
• Primary rebate subtraction (1 Mark)
• Final monthly PAYE / net salary (1 Mark)
• Annual gross multiplication × 12 (1 Mark)
• Pension deduction calculation (1 Mark)
• Taxable income subtraction (1 Mark)
• Correct bracket & difference above base (1 Mark)
• 26% calculation & base tax addition (1 Mark)
• Primary rebate subtraction (1 Mark)
• Final monthly PAYE / net salary (1 Mark)
Worked Example 2: Stepped Municipal Electricity Tariffs (Paper 1 · 5 Marks)
Measurement & Finance: Stepped Domestic Tariffs
5 Marks (Paper 1)
Exam Scenario: The City of Ekurhuleni charges domestic consumers on a stepped prepaid electricity tariff system (excluding 15% VAT):
• Block 1 (0 – 100 kWh): R1.65 per kWh
• Block 2 (101 – 400 kWh): R2.10 per kWh
• Block 3 (401 – 600 kWh): R2.75 per kWh
• Block 4 (> 600 kWh): R3.20 per kWh
Question: A household consumed 460 kWh during September. Calculate their total electricity bill, including 15% VAT.
• Block 1 (0 – 100 kWh): R1.65 per kWh
• Block 2 (101 – 400 kWh): R2.10 per kWh
• Block 3 (401 – 600 kWh): R2.75 per kWh
• Block 4 (> 600 kWh): R3.20 per kWh
Question: A household consumed 460 kWh during September. Calculate their total electricity bill, including 15% VAT.
Step 1: Break down 460 kWh into blocks
• Block 1 (First 100 kWh): 100 kWh
• Block 2 (Next 300 kWh, up to 400): 300 kWh
• Block 3 (Remaining to reach 460): 460 - 400 = 60 kWh
• Block 2 (Next 300 kWh, up to 400): 300 kWh
• Block 3 (Remaining to reach 460): 460 - 400 = 60 kWh
Step 2: Calculate cost per block
Block 1 Cost = 100 × R1.65 = R165.00
Block 2 Cost = 300 × R2.10 = R630.00
Block 3 Cost = 60 × R2.75 = R165.00
Total Excl. VAT = R165.00 + R630.00 + R165.00 = R960.00
Block 2 Cost = 300 × R2.10 = R630.00
Block 3 Cost = 60 × R2.75 = R165.00
Total Excl. VAT = R165.00 + R630.00 + R165.00 = R960.00
Step 3: Add 15% South African VAT
VAT Amount = 0.15 × R960.00 = R144.00
Total Electricity Bill (Incl. VAT) = R960.00 + R144.00 = R1,104.00
Total Electricity Bill (Incl. VAT) = R960.00 + R144.00 = R1,104.00
Examiner Trap: Many learners mistakenly multiply the entire 460 kWh by the Block 3 rate (460 × R2.75). This scores zero marks because stepped tariffs apply rate changes only to the units within that specific block.
Worked Example 3: Topographical Map Scale Conversion (Paper 2 · 4 Marks)
Maps & Plans: Ratio Scale to Real-World Distance
4 Marks (Paper 2)
Question: On a South African 1:50,000 topographical map, the straight-line distance between two cell towers measures 7.4 cm with a ruler. Calculate the actual real-world distance between the two towers in kilometres (km).
Step 1: Apply the ratio scale definition
Scale = 1 : 50,000 (1 cm on paper represents 50,000 cm in reality)
Real Distance = 7.4 cm × 50,000 = 370,000 cm
Real Distance = 7.4 cm × 50,000 = 370,000 cm
Step 2: Convert centimetres to metres, then kilometres
Recall conversion factors: \( 1\text{ m} = 100\text{ cm} \), and \( 1\text{ km} = 1,000\text{ m} \).
Distance in metres = 370,000 cm / 100 = 3,700 m
Distance in kilometres = 3,700 m / 1,000 = 3.7 km
Distance in kilometres = 3,700 m / 1,000 = 3.7 km
Short-cut Metric Rule: In a 1:50,000 scale map, every 2 cm on paper equals exactly 1 km on the ground (since \( 50,000 \text{ cm} = 0.5 \text{ km} \)). Hence: \( 7.4 \times 0.5 = 3.7 \text{ km} \).