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.
Selling price after a percentage profit
Rs 2365
💡 What it's asking: A 10% profit means the selling price is the cost plus 10% of the cost.
- Profit = 10/100 × 2150 = Rs 215.
- Selling price = cost + profit = 2150 + 215 = Rs 2365.
- Shortcut: cost + 10% is 110% of the cost, and 110/100 × 2150 = 2365.
✅ 10% of 2150 is easy: move the decimal point one place to get 215, so the answer is about Rs 2365.
සිංහලෙන් විසඳුම
10% ලාභයක් යනු විකුණුම් මිල = ගැනුම් මිල + ගැනුම් මිලෙන් 10% යන්නයි.
- ලාභය = 10/100 × 2150 = රු. 215.
- විකුණුම් මිල = ගැනුම් මිල + ලාභය = 2150 + 215 = රු. 2365.
- කෙටි ක්රමය: ගැනුම් මිල + 10% යනු ගැනුම් මිලෙන් 110% කි; 110/100 × 2150 = 2365.
Factorise a difference of two squares
(a - 3b)(a + 3b)
💡 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).
- a² is the square of a.
- 9b² is the square of 3b, because 3b × 3b = 9b².
- So a² − 9b² = a² − (3b)² = (a − 3b)(a + 3b).
✅ Multiply out: (a − 3b)(a + 3b) = a² + 3ab − 3ab − 9b² = a² − 9b².
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).
- a² යනු a හි වර්ගයයි.
- 9b² යනු 3b හි වර්ගයයි, මන්ද 3b × 3b = 9b².
- එබැවින් a² − 9b² = a² − (3b)² = (a − 3b)(a + 3b).
Add two decimals
Solve a simple linear equation with a fraction
Subtract algebraic fractions with related denominators
Union of two listed sets
Perimeter of a semicircular stage
Angles Related to Straight Lines and Parallel Lines · Angles of a TriangleTwo angles using parallel lines and a triangle
Approximate a square root to one decimal place
Parallelograms I · Angles Related to Straight Lines and Parallel LinesAngle bisectors in a parallelogram meet at a right angle
Area of a leaf shape formed by two quarter circles
Angles of a Triangle · Angles Related to Straight Lines and Parallel LinesAngle where a line crosses a triangle, using exterior angles
Days for a job given man-hours for a quarter of it
Tank capacity from a fraction full and litres needed
Change the subject of a formula with r in the denominator
Angles Related to Straight Lines and Parallel LinesAngle between two parallel lines in terms of x
Marked price from a discounted selling price
Angles Related to Straight Lines and Parallel Lines · Angles of a TriangleAngles with parallel lines and a bisected angle
Angles in a Circle · TrianglesAngle at the centre from an isosceles triangle of radii
Data Representation and PredictionMode and median of algebraic data values
Exterior angle and sides of a regular polygon
Gradient and intercept from a rearranged linear equation
Least Common Multiple of Algebraic ExpressionsLCM of three algebraic terms
Angle in a triangle split by an equal-length line
Constructions · Parallelograms ILocate rhombus vertices from its diagonals by construction
Fractions · Direct ProportionFractions of gases in a cylinder: volumes, ratio, percentage
Garden plan with sectors: arc, perimeter, areas, cost
Man-days for husking coconuts and the wage cost
List sets, find intersections, unions, complements, a probability
Interpret a pie chart of preferred subjects
Chain of profits from tailor to customer; tailor's profit percent
Graph y = 2x - 1 and y = 2x; gradient and parallel lines
Grouped frequency table: modal and median class, mean, percentage
Binomial Expressions · Factors of Algebraic ExpressionsFactor difference of squares; use identities for m + n, m - n
Simultaneous equations for book and pen prices; linear equation
Surface Area and Volume · Liquid MeasurementsCapacities of cuboid containers and water height
Arithmetic progression of ribbon pieces: terms and position
Constructions · Chords of a CircleRight triangle construction, perpendicular bisector, circle through vertices
Prove the exterior angle theorem; angle chase with a bisector
Ship bearings: scale diagram, distance and return bearing
List sets, draw a Venn diagram, count regions
Congruency · Angles Related to Straight Lines and Parallel LinesCongruent triangles in a trapezium; bisectors between parallels meet at 90°
