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.
Workers needed to finish a job in fewer days
6 men
📝 The English paper says four men can complete the task in four days (the Sinhala paper says twelve men).
💡 What it's asking: Measure the whole job in man-days (men × days). The job stays the same size, so fewer days needs more men.
- The job = 4 men × 4 days = 16 man-days.
- To finish in 3 days: 16 ÷ 3 = 5⅓ men.
- You cannot have part of a man, so 6 men are needed.
සිංහලෙන් විසඳුම
මුළු කාර්යය මිනිස් දිනවලින් (මිනිසුන් × දින) මනින්න. කාර්යය එක හා සමාන නිසා දින අඩු වන විට මිනිසුන් වැඩිපුර අවශ්‍යයි.
- සිංහල පත්‍රය: මිනිසුන් 12 දින 4, එබැවින් කාර්යය = 12 × 4 = මිනිස් දින 48.
- දින 3 කින් නිම කිරීමට: අවශ්‍ය මිනිසුන් = 48 ÷ 3 = 16.
- ඉංග්‍රීසි පත්‍රයේ මිනිසුන් 4 ලෙස ඇත: 4 × 4 = මිනිස් දින 16, 16 ÷ 3 = 5⅓; එවිට මිනිසුන් 6 ක් අවශ්‍යයි. ඉහත පිළිතුර සිංහල අගයන් අනුගමනය කරයි.
Angle in a triangle from straight-line and exterior angles
x = 50 degrees
💡 What it's asking: Use the straight line at B to find one angle of triangle BEC, then use the exterior angle at E.
- ABCD is a straight line, so angle EBC = 180° − 120° = 60°.
- The 110° at E is an exterior angle of triangle BEC, so it equals the two opposite interior angles: 110° = 60° + x.
- x = 110° − 60° = 50°.
✅ Triangle BEC: 60° + 50° + 70° (= 180° − 110°) = 180° ✓.
සිංහලෙන් විසඳුම
B හි සරල රේඛාවෙන් BEC ත්‍රිකෝණයේ කෝණයක් සොයා, E හි බාහිර කෝණය යොදන්න.
- ABCD සරල රේඛාවක් නිසා EBC කෝණය = 180° − 120° = 60°.
- E හි 110° යනු BEC ත්‍රිකෝණයේ බාහිර කෝණයක් නිසා සම්මුඛ අභ්‍යන්තර කෝණ දෙකේ එකතුවට සමානයි: 110° = 60° + x.
- එබැවින් x = 110° − 60° = 50°.
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Equations · Pythagoras' TheoremSimultaneous equations from perimeter and side difference; prove right angle
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Constructions · Constructions · TangentsConstruct triangle, circumcircle, tangent at a vertex; find an angle
Triangles · Congruency · Angles Related to Straight Lines and Parallel LinesProve isosceles base-angle theorem; congruence and a parallel line
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