All 27 questions, with what each one tests. Try any of them free in Gedara Sir to check your answer, with step-by-step working.
Man-days for a whole job from a fraction done
90 man-days
💡 What it's asking: A 'man-day' is one person working for one day. Count the man-days used for the part that is done, then scale up to the whole job.
- 6 people × 5 days = 30 man-days of work.
- Those 30 man-days finished only one third of the job.
- The whole job is 3 thirds, so it needs 30 × 3 = 90 man-days.
✅ One third of 90 is 30, which is exactly what 6 people did in 5 days.
සිංහලෙන් විසඳුම
'මිනිස් දිනය' යනු එක් අයෙක් එක් දිනක් කරන වැඩ ප්‍රමාණයයි. කළ කොටසට ගිය මිනිස් දින ගණන සොයා මුළු වැඩයටම විහිදන්න.
- පුද්ගලයන් 6 × දින 5 = මිනිස් දින 30 ක වැඩ.
- එම මිනිස් දින 30 න් අවසන් වූයේ වැඩයෙන් තුනෙන් එකක් පමණි.
- මුළු වැඩය තුනෙන් තුනක් නිසා අවශ්‍ය වන්නේ 30 × 3 = මිනිස් දින 90 කි.
Perimeter of a semicircular flower bed
36 m
💡 What it's asking: The whole edge of a semicircular bed has two parts: the curved half-circle and the straight diameter. Add them.
- Curved part = half of 2πr = πr = 22/7 × 7 = 22 m.
- Straight part = diameter = 2 × 7 = 14 m.
- Perimeter = 22 + 14 = 36 m.
✅ The curved edge (22 m) should be a bit longer than the straight one (14 m), about π/2 ≈ 1.6 times; 22 ÷ 14 ≈ 1.6. Good.
සිංහලෙන් විසඳුම
අර්ධ වෘත්තාකාර පාත්තියේ මුළු දාරයට කොටස් දෙකක් ඇත: වක්‍ර අර්ධ වෘත්තය සහ සරල විෂ්කම්භය. ඒවා එකතු කරන්න.
- වක්‍ර කොටස = 2πr න් අඩක් = πr = 22/7 × 7 = 22 m.
- සරල කොටස = විෂ්කම්භය = 2 × 7 = 14 m.
- පරිමිතිය = 22 + 14 = 36 m.
Order three fractions
Evaluate a product of binomials by substitution
Interior angle from an exterior angle of a triangle
Factors of Algebraic ExpressionsFactorise using a common binomial factor
First approximation of a square root
Whole amount from remainder after spending a fraction
Extra equal parts needed for two triangles to be congruent
Missing sector angle in a pie chart
Least Common Multiple of Algebraic ExpressionsLCM of three algebraic terms
Square root of a product
Angles of an equilateral triangle and an exterior angle
Area of a circle grazed by a tethered cow
Complete the square of a binomial
Simplify by subtracting algebraic expressions
Pythagoras Relationship · AreaArea of a square from its diagonal
Simplify a fraction expression with brackets
Square of 13 using a binomial expansion
How long food lasts with more students
Factors of Quadratic Expressions · Least Common Multiple of Algebraic Expressions · Factors of Algebraic ExpressionsDifference of squares, factorise, LCM, factorise a four-term expression
Perimeter · Area · Pythagoras RelationshipChord of a right-angled sector: length, segment perimeter and area
Square roots; pieces cut from a sheet; fraction of a fraction
Square with equal segments: prove pairs of triangles congruent
Squares of binomials: areas, completing a square, x² + 1/x²
Data Representation · FractionsIncome fractions as pie chart angles, ratio and amounts
Isosceles triangle proof; bisectors give perpendicular bisector
