All 45 questions, with what each one tests. Try any of them free in Gedara Sir to check your answer, with step-by-step working.
Quarterly rates from an annual assessed value and a percentage
Rs 1,125
💡 What it's asking: Rates are a yearly percentage of the assessed value. Find the year's rates, then split it into four quarters.
- Annual rates = 15% of Rs 30 000 = 15/100 × 30 000 = Rs 4500.
- A year has 4 quarters.
- One quarter = 4500 ÷ 4 = Rs 1125.
✅ 4 × 1125 = 4500, and 4500 is 15% of 30 000.
සිංහලෙන් විසඳුම
වරිපනම් යනු තක්සේරු වටිනාකමෙන් වාර්ෂික ප්රතිශතයකි. වසරේ වරිපනම සොයා, එය කාර්තු හතරකට බෙදන්න.
- වාර්ෂික වරිපනම = රු. 30 000 න් 15% = 15/100 × 30 000 = රු. 4500.
- වසරකට කාර්තු 4 ක් ඇත.
- එක් කාර්තුවක් = 4500 ÷ 4 = රු. 1125.
Factorise a difference of two squares
(x - 8)(x + 8)
💡 What it's asking: 64 is a perfect square (8²), so x² − 64 is a difference of two squares. Use a² − b² = (a − b)(a + b).
- Write 64 as 8²: x² − 8².
- Use a² − b² = (a − b)(a + b) with a = x, b = 8.
- Answer: (x − 8)(x + 8).
✅ Expand: (x − 8)(x + 8) = x² + 8x − 8x − 64 = x² − 64.
සිංහලෙන් විසඳුම
64 පූර්ණ වර්ගයකි (8²); එබැවින් x² − 64 වර්ග දෙකක අන්තරයකි. a² − b² = (a − b)(a + b) යොදන්න.
- 64, 8² ලෙස ලියන්න: x² − 8².
- a = x, b = 8 ලෙස a² − b² = (a − b)(a + b) යොදන්න.
- පිළිතුර: (x − 8)(x + 8).
Two unknown angles in a triangle split by a line from a vertex
Least Common Multiple of Algebraic ExpressionsLCM of three algebraic terms
Algebraic Fractions · Least Common Multiple of Algebraic ExpressionsSubtract two algebraic fractions with unlike denominators
Name a congruent triangle pair and the congruency case
Gradient of a line through two given points
Compare two pie-chart sectors as a multiple
Parallelograms I · Angles Related to Straight Lines and Parallel LinesSum of two angles in a parallelogram with a diagonal
Solve a quadratic equation given in factorised form
Write a shaded Venn region in set notation
Convert an index statement to logarithm form
Area · Area of Plane Figures between Parallel LinesParallelogram area from a triangle on the same base between parallels
Fill blanks to complete the square of a binomial
Angles Related to Straight Lines and Parallel LinesAngle from parallel lines crossed by two lines
Probability of choosing a student from one of two groups
Time to fill a tank at a given flow rate
Value of x + y from simultaneous equations without solving
Parallelograms I · Triangles · Angles Related to Straight Lines and Parallel LinesTrue or false on parallelogram, exterior angle and allied angle facts
Parallelograms I · Pythagoras RelationshipSide of a rhombus from its diagonals
Consecutive whole numbers between which a square root lies
Perimeter of a quarter-circle sector
Angle using opposite angles of two overlapping parallelograms
Data Representation and PredictionMedian of five marks
Locate a point using an angle bisector locus and a circle
Fractions of an amount spent and invested; find the original total
Card made of a rectangle and two sectors: arc, area, perimeter, ratio
Distance-time graph: stay time, speeds, complete the return journey
Pie chart with algebraic angles; counts and a corrected sector angle
Sample space and simple and complementary probabilities
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Man-days for a task, scaled work and total wages
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Graph of y = -ax^2 + b: table, turning point, positive range, find a
Banded income tax, then simple interest compared with the tax
Form and solve simultaneous equations for two prices
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Algebraic Fractions · Least Common Multiple of Algebraic Expressions · Factors of Algebraic ExpressionsSubtract algebraic fractions with a difference-of-squares denominator
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Equations · Factors of Quadratic ExpressionsQuadratic equation from a right triangle's area; find a side
Formulae · Binomial ExpressionsChange the subject of y = mx + c; use the binomial square identity
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Two-leg flight on bearings: sketch, scale drawing, back bearing
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Grouped data: modal class, median class, counts and a percentage
Arithmetic progression: next terms, general term, term number, membership test
Constructions · Loci and Constructions · Pythagoras RelationshipConstruct a right triangle, perpendicular bisector, circle; check with Pythagoras
Triangles · Parallelograms II · Angles Related to Straight Lines and Parallel LinesProve a triangle isosceles and a quadrilateral a parallelogram
Congruent triangles in a quadrilateral with equal diagonals; equal segments
Logarithms I · Logarithms IISolve a log equation; evaluate a product-quotient with log tables
Venn diagram of handedness and gender; shade a region; a probability
