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.
Annual rates at 5% of an assessed value
Rs. 1500
💡 What it's asking: Rates are a yearly tax: a percentage of the house's assessed annual value. Find 5% of 30 000.
- Write 5% as 5/100.
- Rates = 30 000 × 5/100.
- = 300 × 5 = Rs. 1500.
✅ 10% of 30 000 is 3000, and 5% is half of that, 1500 ✓.
සිංහලෙන් විසඳුම
වරිපනම යනු නිවසේ තක්සේරු වාර්ෂික වටිනාකමින් ප්රතිශතයක් ලෙස ගෙවන වාර්ෂික බද්දකි. 30 000 න් 5% සොයන්න.
- 5% භාගයක් ලෙස 5/100 ලියන්න.
- වරිපනම = 30 000 × 5/100.
- = 300 × 5 = රු. 1500.
Area of a square from its diagonal length
25 cm^2
💡 What it's asking: The diagonal splits the square into two right triangles. Pythagoras links the side a with the diagonal √50.
- Let each side be a. In right triangle ABC: a² + a² = AC².
- AC² = (√50)² = 50, so 2a² = 50.
- a² = 25, and the square's area is a² = 25 cm².
✅ Side 5 cm: diagonal = √(25 + 25) = √50 ✓.
සිංහලෙන් විසඳුම
විකර්ණය සමචතුරස්රය සෘජුකෝණී ත්රිකෝණ දෙකකට බෙදයි. පයිතගරස් මගින් a පාදය හා √50 විකර්ණය සම්බන්ධ වේ.
- එක් පාදයක් a ලෙස ගන්න. ABC සෘජුකෝණී ත්රිකෝණයේ: a² + a² = AC².
- AC² = (√50)² = 50; එබැවින් 2a² = 50.
- a² = 25; සමචතුරස්රයේ වර්ගඵලය a² = 25 cm².
Factorise a quadratic trinomial
Exterior angle of a right-angled triangle
Closest decimal approximation to a square root
Probability · Number PatternsProbability of drawing a triangular number from ten balls
Value of x + y from two equations without solving
Angle using an isosceles triangle and an exterior angle
Write a set in set-builder notation
Solve an index equation with a fractional power
Quadrilateral formed by perpendiculars to equal chords; perimeter
Draw two faces of a triangular prism with measurements
Solve a linear inequality; largest integer
Angles in a Circle · TrianglesAngle in a circle with a diameter and isosceles triangle
Gradient and intercept of a linear graph
Mark conditions and name the congruence case
Subtract algebraic fractions and pick the result
Time to fill a tank at a constant flow rate
Solve a quadratic of the form (x + a)^2 = k
Parallelograms I · Pythagoras RelationshipSecond diagonal of a rhombus
Simplify a log expression without tables
Fill in the terms of a binomial cube
Data Representation and PredictionRead a cut-off mark from a cumulative frequency curve
Angles of Polygons · TrianglesAngle in a triangle inside a regular hexagon
Locate a point using two loci in a rectangle
Fractions of land for vegetables, paddy, empty; whole area; ratio
Badge of a square, quarter circle and semicircle: arcs, perimeter, areas
Percentages · Inverse ProportionSimple interest on a loan and deposit; extra workers needed
Grid sample space for two dice; odd/even Venn diagram
Data Representation and PredictionComplete a histogram with unequal classes, frequency polygon, percentage
Share Market · PercentagesDividends, capital gain, buying shares versus compound interest
Graph of y = (x - 1)(x + 3): turning point, roots, shifted graph
Factors of Algebraic Expressions · EquationsDifference of squares; linear equation; simultaneous equations for toffees
Scale drawing with elevation and depression; saline drip time
Volume of Solids · Indices and Logarithms IINumber of nails from metal with wastage; log table calculation
Pythagoras' Theorem · EquationsPythagoras leads to a quadratic; solve with a given root
Arithmetic Progressions · Geometric ProgressionBulbs in frames: arithmetic sum versus geometric sum
Constructions · Loci and Constructions · Angles in a CircleConstruct a right triangle and rectangle, a circle; estimate a root
Mean daily cars by assumed mean; test a yearly claim
Venn diagram of men, women and diabetes with percentages
Midpoint Theorem · Parallelograms II · Area of Plane Figures between Parallel LinesMedians: parallelogram from midpoint theorem and area relation
Angles in a Circle · Equiangular TrianglesIsosceles triangle in a circle: angle doubling and ratio by similarity
