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.
Men needed to finish the same work in fewer days
9 men
💡 What it's asking: The amount of work stays the same. Fewer days means you need more men, so count the work in 'man-days' first.
- Work out the total work: 6 men × 3 days = 18 man-days.
- The same 18 man-days must now fit into 2 days.
- Men needed = 18 ÷ 2 = 9 men.
✅ 9 men × 2 days = 18 man-days, the same work as before.
සිංහලෙන් විසඳුම
කාර්යය එකමයි. දින ගණන අඩු වන විට මිනිසුන් වැඩි දෙනෙක් අවශ්‍යයි. ඒ නිසා මුලින්ම කාර්යය 'මිනිස් දින' වලින් ගණන් කරන්න.
- මුළු කාර්යය: මිනිසුන් 6 × දින 3 = මිනිස් දින 18.
- එම මිනිස් දින 18 දැන් දින 2 ක් තුළ නිම කළ යුතුයි.
- අවශ්‍ය මිනිසුන් = 18 ÷ 2 = 9 දෙනෙක්.
Solve an equation with algebraic fractions
x = 6
💡 What it's asking: This is an equation with x in the denominators. Join the two fractions on the left into one, then cross-multiply.
- Find a common denominator for 2x and 4x: it is 4x.
- Change 1/(2x) to 2/(4x) by multiplying top and bottom by 2.
- Add: 2/(4x) + 1/(4x) = 3/(4x), so 3/(4x) = 1/8.
- Cross-multiply: 4x × 1 = 3 × 8, so 4x = 24.
- Divide by 4: x = 6.
✅ Put x = 6 back: 1/12 + 1/24 = 2/24 + 1/24 = 3/24 = 1/8. It works.
සිංහලෙන් විසඳුම
හරයේ x ඇති සමීකරණයකි. වම් පැත්තේ භාග දෙක එක භාගයක් කර, හරස් ගුණ කරන්න.
- 2x සහ 4x සඳහා පොදු හරය සොයන්න: එය 4x යි.
- 1/(2x) හි ලවය හා හරය 2 න් ගුණ කර 2/(4x) ලෙස ලියන්න.
- එකතු කරන්න: 2/(4x) + 1/(4x) = 3/(4x); එබැවින් 3/(4x) = 1/8.
- හරස් ගුණ කරන්න: 4x × 1 = 3 × 8, එනම් 4x = 24.
- 4 න් බෙදන්න: x = 6.
Angle in an isosceles triangle from equal sides
Write an index statement in logarithm form
Arc length of the remaining three-quarter sector
Angle at apex split by altitude of isosceles triangle
Time to fill half a tank at a given rate
Gradient and intercept of a line in non-standard form
Subtract algebraic fractions
Area of Plane Figures between Parallel LinesParallelogram area from diagonal and perpendicular
Factors of Algebraic ExpressionsFactorise using common factor and difference of squares
Total repayment of a simple interest loan
Perimeter of triangle cut off by midpoint parallel line
Data Representation and PredictionFirst quartile of seven values
Fourth term of a geometric progression
Angles in a Circle · TrianglesAngle using angle in semicircle and isosceles triangle
Least Common Multiple of Algebraic ExpressionsLCM of three algebraic terms
Angles in a Circle · TrianglesAngle using centre angle and isosceles triangles of radii
Volume of a triangular prism
Union count from a Venn diagram
Chords of a Circle · TrianglesAngle in triangle of radii using perpendicular bisector
Smallest integer satisfying a linear inequality
Probability a boy is chosen as leader
Sketch angle of depression from a window
Locate point by intersecting two loci
Fractions of a pumpkin harvest; wholesaler profit percentage
Wall hanging: semicircle perimeter, total area, equal rectangle
Percentages · Share MarketRates and rent, then shares: dividend and return percentage
Probability · ProbabilityGrid for two rounds; tree diagram for two teams
Data Representation and PredictionComplete grouped table; ogive; interquartile range
Share Market · PercentagesShares income reinvested in a two-year compound interest deposit
Graph of y = x² - 4x - 1: negative range, turning point, roots
Trapezium area gives a quadratic; solve by completing the square
Scale drawing with elevation and depression angles
Simultaneous equations for ticket prices
Grouped sugar sales: mean, company total, compare extremes
Soap rows decreasing by 3: terms, sum, extension check
Constructions · Chords of a Circle · CongruencyConstruct triangle, bisector, circle through chord; prove congruence
Midpoint Theorem · Equiangular TrianglesMidpoint theorem: parallel sides, half perimeter, equiangular triangles
Volume of Solids · Indices and Logarithms IICone with hemisphere removed; radius by logarithms
Chains of congruent triangles to prove an angle bisector
Venn diagram of exam passes; subset case
