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.
Complete squares and give the first approximation of root 12
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.
- 3.5 × 3.5 = 12.25, so 3.5² = 12.25.
- 12 lies between 3.4² = 11.56 and 3.5² = 12.25.
- Gaps: 12 − 11.56 = 0.44 and 12.25 − 12 = 0.25.
- 0.25 is smaller, so √12 ≈ 3.5.
✅ 3.5² = 12.25 is only a quarter away from 12, so 3.5 is a close estimate.
සිංහලෙන් විසඳුම
මුලින් හිස් වර්ගය 3.5² පුරවන්න. පසුව 12 වර්ග දෙකෙන් කුමකට ළඟදැයි තීරණය කරන්න; එයින් √12 හි පළමු සන්නිකර්ෂණය ලැබේ.
- 3.5 × 3.5 = 12.25; එබැවින් 3.5² = 12.25.
- 12 පිහිටන්නේ 3.4² = 11.56 ත් 3.5² = 12.25 ත් අතරයි.
- පරතර: 12 − 11.56 = 0.44, 12.25 − 12 = 0.25.
- 0.25 කුඩා නිසා √12 ≈ 3.5.
Rewrite a base-2 logarithm in index form
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'.
- Rule: log_a N = n means aⁿ = N.
- Here the base a = 2, the log n = 3 and the number N = x.
- Index form: x = 2³.
- So x = 8.
✅ log₂ 8: 2 × 2 × 2 = 8 needs three 2s, so the log is 3.
සිංහලෙන් විසඳුම
ලඝුගණකයක් හා බලයක් එකම දේ ආකාර දෙකකින් කියයි. log₂ x = 3 යනු '2 හි 3 වන බලය x' යන්නයි.
- නීතිය: log_a N = n යනු aⁿ = N.
- මෙහි පාදය a = 2, ලඝුව n = 3, සංඛ්යාව N = x.
- දර්ශක ආකාරය: x = 2³.
- එබැවින් x = 8.
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Surface Area and Volume · Formulae · Logarithms IICylinder poured into a cuboid gives a formula; log table evaluation
Congruency · Angles Related to Straight Lines and Parallel Lines · Parallelograms IITrapezium with midpoint: congruent triangles and a parallelogram
Angles in a Circle · Angles Related to Straight Lines and Parallel LinesAngles in a circle with a parallel chord; locate the centre
Coin and coloured die: grid, independence, tree diagram
