All 42 questions, with what each one tests. Try any of them free in Gedara Sir to check your answer, with step-by-step working.
Days for more men to finish the same task
4 days
💡 What it's asking: The job is the same size, so more men finish it in fewer days. Find the total work in 'man-days' first.
- Total work = 8 men × 6 days = 48 man-days.
- A man-day is the work one man does in one day.
- Share it among 12 men: 48 ÷ 12 = 4 days.
✅ More men (12 > 8) should mean fewer days (4 < 6). ✓
සිංහලෙන් විසඳුම
කාර්යය එකම ප්‍රමාණයයි; එබැවින් මිනිසුන් වැඩි වූ විට දින අඩුවෙන් අවසන් වේ. පළමුව මුළු වැඩ ප්‍රමාණය 'මිනිස්-දින' වලින් සොයන්න.
- මුළු වැඩ = මිනිසුන් 8 × දින 6 = මිනිස්-දින 48.
- මිනිස්-දිනයක් යනු එක් අයෙක් දිනකට කරන වැඩයි.
- මිනිසුන් 12 අතර බෙදන්න: 48 ÷ 12 = දින 4.
Factorise using a common factor and difference of squares
2(x - 4)(x + 4)
💡 What it's asking: Always take out any common factor first. What is left here is a difference of two squares, which factorises into two brackets.
- Take out the common factor 2: 2(x² − 16).
- Notice x² − 16 = x² − 4², a difference of two squares.
- Use a² − b² = (a − b)(a + b): x² − 4² = (x − 4)(x + 4).
- Answer: 2(x − 4)(x + 4).
✅ Expand: 2(x² − 16) = 2x² − 32, which is the original expression. ✓
සිංහලෙන් විසඳුම
සැමවිටම පළමුව පොදු සාධකය පිටතට ගන්න. මෙහි ඉතිරි වන්නේ වර්ග දෙකක අන්තරයක් වන අතර එය වරහන් දෙකකට සාධක වේ.
- පොදු සාධකය 2 පිටතට ගන්න: 2(x² − 16).
- x² − 16 = x² − 4², වර්ග දෙකක අන්තරයක් බව බලන්න.
- a² − b² = (a − b)(a + b) භාවිත කරන්න: x² − 4² = (x − 4)(x + 4).
- පිළිතුර: 2(x − 4)(x + 4).
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