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.
Rates percentage from annual value and rates paid
8%
💡 What it's asking: Rates are a percentage of the annual value. We know both amounts, so we work backwards to find that percentage.
- Rate % = rates paid ÷ annual value × 100.
- Put in the numbers: 4800 ÷ 60 000 × 100.
- 4800 ÷ 60 000 = 0.08, and 0.08 × 100 = 8%.
✅ 8% of 60 000 = 600 × 8 = 4800, the rates paid.
සිංහලෙන් විසඳුම
වරිපනම වාර්ෂික වටිනාකමේ ප්‍රතිශතයකි. මුදල් දෙකම දන්නා නිසා ප්‍රතිශතය සොයන්න.
- වරිපනම් ප්‍රතිශතය = ගෙවූ වරිපනම ÷ වාර්ෂික වටිනාකම × 100.
- අගයන් ආදේශ කරන්න: 4800 ÷ 60 000 × 100.
- ගණනය කරන්න: 4800 ÷ 60 000 = 0.08; 0.08 × 100 = 8%.
Angle in a figure of two isosceles triangles
a = 40°
💡 What it's asking: The tick marks show equal lengths, so we have two isosceles triangles. Use equal base angles and the exterior angle rule to walk across the figure.
- Left triangle: two equal sides, so its two base angles are equal: both 35°.
- The exterior angle at the foot of the inner line = sum of the two opposite angles = 35 + 35 = 70°.
- Right triangle: the inner line equals the right side, so the angles opposite them are equal: both 70°.
- Angles in a triangle add to 180°: a = 180 − 70 − 70 = 40°.
✅ Right triangle: 70 + 70 + 40 = 180°. It works.
සිංහලෙන් විසඳුම
ලකුණු කළ ඉරි සමාන දිග පෙන්වයි; එබැවින් සමද්විපාද ත්‍රිකෝණ දෙකක් ඇත. සමාන පාද කෝණ සහ බාහිර කෝණ නීතිය යොදන්න.
- වම් ත්‍රිකෝණය: සමාන පාද දෙකක් නිසා පාද කෝණ දෙක සමානයි: දෙකම 35°.
- ඇතුළත රේඛාවේ පාමුල බාහිර කෝණය = අභ්‍යන්තර සම්මුඛ කෝණ දෙකේ එකතුව = 35 + 35 = 70°.
- දකුණු ත්‍රිකෝණය: ඇතුළත රේඛාව දකුණු පාදයට සමාන නිසා ඒවාට සම්මුඛ කෝණ සමානයි: දෙකම 70°.
- ත්‍රිකෝණයේ කෝණ එකතුව 180°: a = 180 − 70 − 70 = 40°.
LCM of three algebraic terms
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Write an index statement in logarithm form
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Radius of a reflex sector from its area
Line equation from intercept and a point
Angles in a Circle · TrianglesAngles in semicircle with isosceles triangles from radii
Data Representation and PredictionInterquartile range of nine data values
Parallel to a side divides sides proportionally
Curved surface area of a cylinder from circumference
Factors of Algebraic ExpressionsFactorise a quadratic trinomial
Tenth term of a geometric progression as a power of 2
Rough sketch for an angle of depression from a building
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Angles in the same segment with a diameter
Solve a linear equation with a fraction
Total surface area of a cone in terms of a
Shade union of a set with complement of another
Midpoint theorem: identify the quadrilateral formed
Algebraic Fractions · EquationsEquation with algebraic fractions leading to a quadratic
Locus sketch: equidistant from two sides and two corners
Fractions · Fractions · PercentagesFractions of money deposited and spent; marked price after discount
Quarter-circle plot with an inner sector: perimeter and areas
Share Market · PercentagesShare capital gain and dividend; simple interest loan amount
Data Representation · Data Representation and PredictionPie chart sector angles; histogram with unequal class width
Grid of outcomes for two marked dice; tree diagram for two students
Percentages · PercentagesCompare compound and simple interest deposits split in a ratio
Graph of y=(x-1)(x+3): roots, negative interval, vertex form, translation
Area of sheet minus isosceles triangle gives quadratic; choose valid root
Simultaneous equations for foundation labour costs; check a budget
Statue height from two angles of elevation by scale drawing
Frequency Distributions · ProbabilityGrouped data of packet masses: probability, mean, maximum loss
Arithmetic progression of questions per paper
Constructions · Loci and ConstructionsConstruct a 10-8-6 triangle, equal angle point, perpendicular bisector, circle
Chords of a Circle · Angles in a Circle · Angles Related to Straight Lines and Parallel LinesChord perpendicular to radius and parallel lines give an equilateral triangle
Volume of Solids · Formulae · Indices and Logarithms IIWater around a sphere poured into a square cuboid; log-table evaluation
Midpoint theorem and converse in an isosceles triangle with produced side
Venn diagram of girls and report writers in a class
