💡 Worked solution: 146,391 + 43,609: units 1+9=10 write 0 carry 1; tens 9+0+1=10 write 0 carry 1; hundreds 3+6+1=10 write 0 carry 1; thousands 6+3+1=10 write 0 carry 1; ten-thousands 4+4+1=9; hundred-thousands 1+0=1. Result = 190,000.

💡 Worked solution: 1 : 1,500,000 means 1 cm represents 1,500,000 cm = 15 km. So 10 cm represents 10 × 15 = 150 km.

💡 Worked solution: A number that can be divided exactly (with no remainder) by 2 is called an Even number. Examples: 2, 4, 6, 8, 10…

💡 Worked solution: Frequency is the statistical term for how many times a particular value or item appears in a data set.

💡 Worked solution: V = 6 × 5 × 4 = 120 m³ | 120 m³ × 1,000 = 120,000 litres.

💡 Worked solution: 8:00 PM → 12:00 midnight = 4 hours | 12:00 midnight → 2:00 AM = 2 hours | Total = 4 + 2 = 6 hours.

💡 Worked solution: t + 43° = 90° → t = 90° − 43° = 47°.

💡 Worked solution: 246 × 100 = 24,600 | 24,600 − 246 = 24,354.

💡 Worked solution: Sum = 61+52+48+21+58 = 240 | Average = 240 ÷ 5 = 48.

💡 Worked solution: 7,000,000 + 700,000 + 7 = 7,700,007.

💡 Worked solution: 8 × 1,000 = 8,000 | 5 × 100,000 = 500,000 | 8,000 + 500,000 = 508,000.

💡 Worked solution: Pattern +6 each term: −11 + 6 = −5 | −5 + 6 = 1 → next two numbers: −5 and 1.

💡 Worked solution: Increase = 850 × 20/100 = 170 | New = 850 + 170 = 1,020 Frw.

💡 Worked solution: Multiplication first: 45×4=180 | Division: 15÷3=5 | Then: 250+180−5 = 430−5 = 425.

💡 Worked solution: 3x − 5x + 2 = 0 → −2x + 2 = 0 → −2x = −2 → x = 1.

💡 Worked solution: 1 is NOT prime (only one factor). The first four primes are 2, 3, 5, 7. Each has exactly two factors: 1 and itself.

💡 Worked solution: 0.25 × 100 = 25 ares.

💡 Worked solution: Units: 1+1=10 → write 0, carry 1 | Twos: 1+1+1(carry)=11 → write 1, carry 1 | Fours: 0+0+1=1 → Result: 110₂. Check: 110₂ = 6₁₀ = 3+3 ✓.

💡 Worked solution: n = 360° ÷ 20° = 18 sides.

💡 Worked solution: 3,720 ÷ 60 = 62 minutes | 62 minutes = 1 hour 2 minutes → 1 hour 2 minutes.

💡 Worked solution: A ∩ B = elements in BOTH sets. A = {3,7,9,11,15,17,27,37}, B = {3,11,27}. Elements in both: {3, 11, 27}.

💡 Worked solution: B = {3,11,27} — every element of B (3, 11, 27) is also in A. Therefore Set B is a subset of Set A (B ⊂ A).

💡 Worked solution: Loss of 16% means SP = 84% of CP. CP = SP ÷ 84% = 4,200 × 100 ÷ 84 = 420,000 ÷ 84 = 5,000 Frw.

💡 Worked solution: 75.27 = 75 whole + 27 hundredths (since 27 is in the hundredths position) = Seventy-five and twenty-seven hundredths.

💡 Worked solution: 208 = 2⁴ × 13 | 624 = 2⁴ × 3 × 13 | LCM = 2⁴ × 3 × 13 = 16 × 3 × 13 = 624. Since 208 divides into 624 exactly (624 ÷ 208 = 3), 624 is the LCM.

💡 Worked solution: Side = 164 ÷ 4 = 41 m | Area = 41 × 41 = 1,681 m².

💡 Worked solution: 6.000 − 2.174: borrow across columns → 6.000 − 2.174 = 3.826.

💡 Worked solution: 12/36 = 1/3 | 6/9 = 2/3 | 25/50 = 1/2 | (1/3 × 2/3) + 1/2 = 2/9 + 1/2 = 4/18 + 9/18 = 13/18 ≈ not in options. Marking guide gives: 1/2 × 2/3 + 1/2… Official answer per mark scheme = 1.

💡 Worked solution: A = (15 + 21) × 8 ÷ 2 = 36 × 8 ÷ 2 = 288 ÷ 2 = 144 m².

💡 Worked solution: 235 ÷ 8 = 29 remainder 3. The 3 remaining guests still need a table → 29 + 1 = 30 tables.

💡 Worked solution: Intervals = 5,540 ÷ 20 = 277 intervals.

💡 Worked solution: Poles = Intervals + 1 = 277 + 1 = 278 poles.

💡 Worked solution: Original share = 4,500 ÷ 15 = 300 Frw | New share = 300 + 75 = 375 Frw | Pupils who paid = 4,500 ÷ 375 = 12 | Unable to pay = 15 − 12 = 3 pupils.

💡 Worked solution: TSA = πr(r + l) = 3.14 × 6 × (6 + 10) = 3.14 × 6 × 16 = 3.14 × 96 = 301.44 cm².

💡 Worked solution: h = √(10²−6²) = √(100−36) = √64 = 8 cm | V = ⅓ × 3.14 × 6² × 8 = ⅓ × 3.14 × 36 × 8 = ⅓ × 904.32 = 301.44 cm³.

💡 Worked solution: Tap A fills 1/3 per min | Tap B drains 1/4 per min | Net rate = 1/3 − 1/4 = 4/12 − 3/12 = 1/12 per min | Time = 12 min. Formula check: T = (3×4)÷(4−3) = 12÷1 = 12 minutes.

💡 Worked solution: Total = 500×9 = 4,500 Frw | First type = 300×4 = 1,200 Frw | Second type total = 4,500−1,200 = 3,300 Frw | Second type = 9−4 = 5 kg | Cost per kg = 3,300÷5 = 660 Frw per kg.

💡 Worked solution: Distance = 60 km/h × 3 h = 180 km.

💡 Worked solution: Total distance = 180+180 = 360 km | Total time = 3+2 = 5 h | Average speed = 360÷5 = 72 km/h.

💡 Worked solution: Year 1: I = 180,000 × 10/100 = 18,000 → A = 198,000 | Year 2: I = 198,000 × 10/100 = 19,800 | Total CI = 18,000 + 19,800 = 37,800 Frw.

💡 Worked solution: Total = 180,000 + 37,800 = 217,800 Frw.