Royal College, Colombo 07 Grade 11 Maths Term 2 Test 2022

Subtract two base-two numbers

Answer: 110 two (6)

💡 What it's asking: The easiest way is to change both base-two (binary) numbers to ordinary base ten, subtract, then change back.

1. 11001₂ = 8 + 0 + 0 + 1 = 9.
2. 211₂ = 2 + 1 = 3.
3. 39 − 3 = 6.
4. 46 = 4 + 2 = 110₂.

✅ Add back in base two: 110₂ + 11₂ = 1001₂ (6 + 3 = 9) ✓.

Solve an equation with unknown denominators

Answer: a = 10

💡 What it's asking: Both fractions have the same denominator a, so you can add the tops straight away, then solve.

1. 1Add the numerators: 3/a + 2/a = 5/a.
2. 2Set it equal: 5/a = 1/2.
3. 3Cross-multiply: a = 5 × 2 = 10.

✅ 3/10 + 2/10 = 5/10 = 1/2 ✓.

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