North Western Province Grade 10 Maths Term 3 Test 2022

Complete squares and give the first approximation of root 12

Answer: 12.25; √12 ≈ 3.5

💡 What it's asking: First fill in the missing square, 3.5². Then decide which of the two squares 12 is nearer to; that gives the first approximation of √12.

1. 13.5 × 3.5 = 12.25, so 3.5² = 12.25.
2. 212 lies between 3.4² = 11.56 and 3.5² = 12.25.
3. 3Gaps: 12 − 11.56 = 0.44 and 12.25 − 12 = 0.25.
4. 40.25 is smaller, so √12 ≈ 3.5.

✅ 3.5² = 12.25 is only a quarter away from 12, so 3.5 is a close estimate.

Rewrite a base-2 logarithm in index form

Answer: x = 2³ (= 8)

💡 What it's asking: A logarithm and a power say the same thing in two ways. log₂ x = 3 means '2 to the power 3 gives x'.

1. 1Rule: log_a N = n means aⁿ = N.
2. 2Here the base a = 2, the log n = 3 and the number N = x.
3. 3Index form: x = 2³.
4. 4So x = 8.

✅ log₂ 8: 2 × 2 × 2 = 8 needs three 2s, so the log is 3.

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