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.
Customs duty at a percentage of an item's value
Rs. 6,000
💡 What it's asking: Customs duty is a tax on imported goods, worked out as a percentage of their value. We need 12% of Rs 50,000.
- Write 12% as 12/100.
- Find 1% of 50,000: 50,000 ÷ 100 = 500.
- 12% is 12 × 500 = 6,000, so the duty is Rs 6,000.
✅ 10% of 50,000 is 5,000, and 12% should be a little more: 6,000 fits.
සිංහලෙන් විසඳුම
තීරු බද්ද යනු ආනයනික භාණ්ඩවල වටිනාකමෙන් ප්රතිශතයක් ලෙස අය කරන බද්දකි. අපට අවශ්ය රු. 50,000 න් 12% යි.
- 12% යනු 12/100 ලෙස ලියන්න.
- 50,000 න් 1% සොයන්න: 50,000 ÷ 100 = 500.
- 12% යනු 12 × 500 = 6,000; එබැවින් තීරු බද්ද රු. 6,000.
Arc length of a 45° sector
33 cm
💡 What it's asking: The arc is the curved edge of a 45° slice of a circle. 45° is one eighth of a full turn, so the arc is one eighth of the whole circumference.
- Fraction of the circle: 45/360 = 1/8.
- Whole circumference = 2πr = 2 × 22/7 × 42 = 264 cm.
- Arc = 1/8 × 264 = 33 cm.
✅ The radius is 42 cm; a 45° arc is a short curve, a bit shorter than the radius, so 33 cm is reasonable.
සිංහලෙන් විසඳුම
චාපය යනු 45° කේන්ද්රික ඛණ්ඩයක වක්ර දාරයයි. 45° යනු සම්පූර්ණ භ්රමණයෙන් අටෙන් එකක් නිසා චාපය මුළු පරිධියෙන් අටෙන් එකකි.
- වෘත්තයෙන් කොටස: 45/360 = 1/8.
- මුළු පරිධිය = 2πr = 2 × 22/7 × 42 = 264 cm.
- චාපය = 1/8 × 264 = 33 cm.
LCM of two algebraic terms
Solve a simple linear equation
Name the included angles needed for SAS congruence
Write a shaded Venn region in set notation
Write a logarithm statement in index form
Whole circle area from a quarter sector's area
First approximation of a square root using given squares
Solve for x from angles of a triangle in ratio
Factors of Quadratic ExpressionsFactorise a trinomial quadratic expression
Number in a category from a pie chart sector angle
Algebraic Fractions · Least Common Multiple of Algebraic ExpressionsAdd algebraic fractions with unlike denominators
Exterior angle of a triangle on a straight line
Equation of a line from gradient and intercept
Parallelograms I · Angles of a TriangleOpposite angle of a parallelogram using a right-angled triangle
Solve a quadratic equation in factorised form
Hours for more machines doing the same task
Number in Q from union and intersection counts
Solve a pair of simultaneous equations for one unknown
Parallelogram area from a triangle on half its base
Base angle of an isosceles triangle from an exterior angle
Average speed in metres per second
Logarithm from an index statement
Decide congruence of two right triangles and state the case
List a set of primes; Venn diagram from given counts
Fractions of tank water used; capacity and filling time
Pie chart of persons in divisions: counts, angles, ratio
Square card with two quarter circles removed: areas, ribbon length, cost
Man-hours for harvesting by hand versus by machine; compare costs
Income tax in bands as a percentage of income
Trapezium flower beds around a pond; form and solve a quadratic
Graph of y = 4 - x²: turning point, maximum, roots, increasing range
Logarithms II · Least Common Multiple of Algebraic Expressions · Algebraic FractionsDivision by log tables; LCM and difference of algebraic fractions
Factors of Algebraic Expressions · EquationsFactorise by grouping; simultaneous equations for vans and buses
Perimeter · Area · EquationsWindow frame from wire: find r from perimeter, then area
Triangles · Parallelograms IIAngle bisectors and equal sides: prove equal angles and a rhombus
Congruency · Triangles · AreaRHS congruence gives an isosceles triangle; ratio of triangle areas
Pie chart of donations: missing angle, totals, table, new angle
Angles in a right triangle with a point on the hypotenuse; isosceles proof
Venn diagram of girls and assignment submitters; redraw after change
Parallelograms II · Area · Angles Related to Straight Lines and Parallel LinesEqual areas give equal sides; prove a parallelogram; find an angle
