All 41 questions, with what each one tests. Try any of them free in Gedara Sir to check your answer, with step-by-step working.
Men needed to finish a job faster, via man-days
10 men
💡 What it's asking: Measure the job in man-days (one man working one day). Find the whole job from the half that took 4 men 5 days, then share it over 4 days.
- Half the job = 4 men × 5 days = 20 man-days.
- The whole job = 2 × 20 = 40 man-days.
- To finish the whole job in 4 days: 40 ÷ 4 = 10 men.
✅ 10 men × 4 days = 40 man-days, exactly the whole job.
සිංහලෙන් විසඳුම
කාර්යය මිනිස්-දින වලින් (එක් අයෙකු එක් දිනක් වැඩ කිරීම) මනින්න. මිනිසුන් 4 දෙනෙකු දින 5 කින් කළ අඩෙන් මුළු කාර්යය සොයා, දින 4 ට බෙදන්න.
- කාර්යයෙන් අඩක් = මිනිසුන් 4 × දින 5 = මිනිස්-දින 20.
- මුළු කාර්යය = 2 × 20 = මිනිස්-දින 40.
- මුළු කාර්යය දින 4 කින් නිම කිරීමට: 40 ÷ 4 = මිනිසුන් 10.
Factorise a difference of two squares
(5x - 3)(5x + 3)
💡 What it's asking: Both terms are perfect squares with a minus between them, so use the difference of two squares: A² − B² = (A − B)(A + B). (The Sinhala paper uses a instead of x.)
- 25x² is the square of 5x, because 5x × 5x = 25x².
- 9 is the square of 3.
- So 25x² − 9 = (5x)² − 3² = (5x − 3)(5x + 3).
✅ Multiply out: (5x − 3)(5x + 3) = 25x² + 15x − 15x − 9 = 25x² − 9.
සිංහලෙන් විසඳුම
පද දෙකම පූර්ණ වර්ග වන අතර ඒවා අතර ඍණ ලකුණක් ඇත; එබැවින් වර්ග දෙකක අන්තරය භාවිත කරන්න: A² − B² = (A − B)(A + B). (සිංහල පත්‍රයේ x වෙනුවට a ඇත.)
- 25x² යනු 5x හි වර්ගයයි, මන්ද 5x × 5x = 25x².
- 9 යනු 3 හි වර්ගයයි.
- එබැවින් 25x² − 9 = (5x)² − 3² = (5x − 3)(5x + 3).
Unknown angle from a triangle's angle sum
Round off and Scientific NotationOrder numbers given in scientific notation
Add two algebraic fractions with numeric denominators
Angles of a Triangle · Inverse ProportionTriangle angles from a ratio; classify the triangle
First approximation of a square root
Radius of a 60-degree sector from its arc length
Angles Related to Straight Lines and Parallel Lines · TrianglesAngle between parallel lines using co-interior and exterior angles
Solve a linear equation with a fractional term
Change the subject of a formula with fractions
Complete the exterior angle theorem statement
Sides of a regular polygon from interior-exterior difference
Congruency · Angles of a TriangleSide length from two congruent triangles sharing a side
Profit percentage on a sale
Data Representation and PredictionMissing value from a given mean
Least Common Multiple of Algebraic ExpressionsLCM of three numbers
Congruence case for halves of an isosceles triangle
Write a shaded Venn region in set notation
Back bearing from a given bearing
Angles Related to Straight Lines and Parallel Lines · Angles of a TriangleTwo angles from parallel lines and crossing transversals
Solve a linear inequality and show it on a number line
Angle in a triangle with an isosceles part
Simplify a power of a negative power
Locus sketch: perpendicular bisector and parallel lines at a distance
Paint used in fractions of a container; find capacity
Inverse Proportion · PercentagesPartnership: investment ratio, profit shares by time, profit percentage
Probability · ProbabilityRandom experiment features; sample space and simple probabilities
Pie chart of a salary: total, sector angle, amounts, ratio
Percentages · PercentagesBroker commission, marked price after discount, cost price from a loss
Algebraic Expressions · AreaAlgebraic areas of a rectangle, triangle and trapezium
Graph y = 3x - 2, line through two points, intersection
Factors of Quadratic Expressions · EquationsFactorise a trinomial, evaluate by factors, simultaneous equations for prices
Surface Area and Volume · Liquid Measurements · RateTank capacity, water height, square base side; filling time
Frequency Distributions · Data Representation and PredictionRange, mode, median and mean of electricity use; monthly estimate
Number pattern from a general term: terms, term number, non-term
Constructions · Pythagoras RelationshipConstruct a right triangle, Pythagoras relation, perpendicular bisector, circle
Isosceles triangle theorem; angles and right triangles in a figure
Map scale; bearings sketch and scale drawing for a distance
Read sets from a Venn diagram; subsets, complement, union
Congruent triangles from equal parallel sides; angle expression by exterior angles
