North Western Province Grade 10 Maths Term 2 Test 2023

Quarterly rates from an annual assessed value and a percentage

Answer: Rs 1,125

💡 What it's asking: Rates are a yearly percentage of the assessed value. Find the year's rates, then split it into four quarters.

1. 1Annual rates = 15% of Rs 30 000 = 15/100 × 30 000 = Rs 4500.
2. 2A year has 4 quarters.
3. 3One quarter = 4500 ÷ 4 = Rs 1125.

✅ 4 × 1125 = 4500, and 4500 is 15% of 30 000.

Factorise a difference of two squares

Answer: (x - 8)(x + 8)

💡 What it's asking: 64 is a perfect square (8²), so x² − 64 is a difference of two squares. Use a² − b² = (a − b)(a + b).

1. 1Write 64 as 8²: x² − 8².
2. 2Use a² − b² = (a − b)(a + b) with a = x, b = 8.
3. 3Answer: (x − 8)(x + 8).

✅ Expand: (x − 8)(x + 8) = x² + 8x − 8x − 64 = x² − 64.

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