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.
Choose the first approximation of a square root
3.3
💡 What it's asking: A first approximation of a square root is the root rounded to one decimal place. Find which two perfect squares 11 lies between, then test the options.
- 11 lies between 9 = 3² and 16 = 4², so √11 is 3 point something.
- 11 is 2 steps along a gap of 7 (from 9 to 16), so √11 ≈ 3 + 2/7 ≈ 3.3.
- Test by squaring: 3.3² = 10.89, which is closer to 11 than 3.2² = 10.24. So the answer is 3.3.
✅ 3.3 × 3.3 = 10.89, only just under 11, so 3.3 is the best one-decimal estimate.
සිංහලෙන් විසඳුම
වර්ගමූලයක පළමු සන්නිකර්ෂණය යනු එක් දශමස්ථානයකට වටයන ලද මූලයයි. 11 කුමන පූර්ණ වර්ග දෙක අතරදැයි සොයා විකල්ප පරීක්ෂා කරන්න.
- 11, 9 = 3² ත් 16 = 4² ත් අතර නිසා √11 යනු 3 දශම යමක්.
- 9 සිට 16 දක්වා පරතරය 7 කින් 11 ඇත්තේ පියවර 2 ක් ඉදිරියෙන් නිසා √11 ≈ 3 + 2/7 ≈ 3.3.
- වර්ග කර පරීක්ෂා කරන්න: 3.3² = 10.89; එය 3.2² = 10.24 ට වඩා 11 ට ආසන්නයි. පිළිතුර 3.3.
Simplify a quotient with a negative index
x³/2
💡 What it's asking: A negative power on the bottom of a fraction can move to the top as a positive power. Then simplify the numbers.
- 1/x⁻² = x², so dividing by x⁻² is the same as multiplying by x².
- 2x/(4x⁻²) = 2x × x² / 4 = 2x³/4.
- Cancel 2 from top and bottom: x³/2.
✅ Try x = 2: 2 × 2 ÷ (4 × 1/4) = 4 ÷ 1 = 4, and 2³/2 = 4. They match.
සිංහලෙන් විසඳුම
භාගයක හරයේ ඇති ඍණ දර්ශකයක් ධන දර්ශකයක් ලෙස ලවයට ගෙන යා හැක. ඉන්පසු සංඛ්‍යා සරල කරන්න.
- 1/x⁻² = x², එබැවින් x⁻² න් බෙදීම x² න් ගුණ කිරීමට සමානයි.
- එවිට 2x/(4x⁻²) = 2x × x² / 4 = 2x³/4 ලැබේ.
- ලවයෙන් හා හරයෙන් 2 කපා හරින්න: x³/2.
Perimeter of a quarter-circle sector in terms of r and π
Convert a base-10 logarithm to index form and evaluate
Exterior angle of an isosceles triangle with a 110° apex
Actual length from a scale ratio
Equations · Algebraic FractionsSolve an equation with algebraic fractions
Positive integer solutions of a linear inequality
Triangles · Angles Related to Straight Lines and Parallel LinesAngle using an isosceles triangle and a parallel line
Simple interest at a monthly rate
Match angles to make two triangles congruent by AAS
Change the subject of a formula with a fraction
Term that completes a perfect square
Number of elements of a set from its complement
Annual rates percentage from quarterly rates
Line through the origin parallel to a given line
Angles Related to Straight Lines and Parallel Lines · TrianglesAngle using parallel lines and a triangle angle sum
Rate · Liquid MeasurementsHours to fill a cube tank at a given pump rate
Factors of Algebraic ExpressionsFactorise using a common factor and difference of squares
Parallelogram side from perimeter; height from area
Area of a parallelogram on the same base as another
Insert subset and membership symbols
Least Common Multiple of Algebraic ExpressionsLCM of three algebraic expressions
Choose quadrilaterals whose markings guarantee a parallelogram
Rectangle perimeter using Pythagoras on a diagonal
Fractions of a salary spent; find an amount
Rectangle with a quarter-circle bed: arc, perimeter, area, cost
Simple interest loan: monthly rate, total, instalments
Data Representation · ProbabilityPie chart of activities: angles, counts, probability, ratio
Nested Venn diagram of exam passes
Percentages · PercentagesImport duty and marked price; income tax from slabs
Graph of a quadratic: axis of symmetry, range, vertical shift
Simultaneous equations for pens and erasers; linear and quadratic equations
Factors of Algebraic Expressions · Factors of Quadratic Expressions · Algebraic FractionsFactorise; evaluate using difference of squares; combine algebraic fractions
Logarithms I · Logarithms IILaws of logarithms; product and quotient with log tables
Man-hours for parts of a building as workers change
General term of a sequence; test a term; terms from a formula
Constructions · Loci and ConstructionsConstruct a triangle, a perpendicular, an angle bisector and a circle
Data Representation and PredictionMode, fraction and mean from a discrete frequency table
Congruent triangles from equal altitudes; isosceles triangles; an angle
Parallelograms II · Congruency · Angles of PolygonsParallelogram properties; regular hexagon diagonals form a rectangle
Distance-time graph of a bus trip; speeds and arrival time
