All 44 questions, with what each one tests. Try any of them free in Gedara Sir to check your answer, with step-by-step working.
First approximation of a square root using given squares
3.5
💡 What it's asking: A first approximation of a square root means the closest value with one decimal place. Use the squares given and see which one 12 is nearer to.
- Look at the two squares on either side of 12: 3.4² = 11.56 and 3.5² = 12.25.
- Find how far 12 is from each: 12 − 11.56 = 0.44 and 12.25 − 12 = 0.25.
- 0.25 is smaller, so 12 is closer to 3.5².
- So the first approximation of √12 is 3.5.
✅ 3.5 × 3.5 = 12.25, which is very close to 12, so 3.5 makes sense.
සිංහලෙන් විසඳුම
වර්ගමූලයක පළමු සන්නිකර්ෂණය යනු දශමස්ථාන එකක් සහිත ආසන්නතම අගයයි. දී ඇති වර්ග අතරින් 12 වඩා ළඟ කුමකටදැයි බලන්න.
- 12 ට දෙපසින් ඇති වර්ග දෙක බලන්න: 3.4² = 11.56, 3.5² = 12.25.
- 12 සිට එක් එක් වර්ගයට දුර සොයන්න: 12 − 11.56 = 0.44, 12.25 − 12 = 0.25.
- 0.25 කුඩා නිසා 12 වඩා ළඟ 3.5² ටයි.
- එබැවින් √12 හි පළමු සන්නිකර්ෂණය 3.5 වේ.
Expand the product of two binomials
x² − 3x − 10
💡 What it's asking: To expand two brackets, every term in the first bracket must multiply every term in the second. Then add the like terms together.
- Multiply the first terms: x × x = x².
- Multiply the outer and inner pairs: x × 2 = 2x and −5 × x = −5x.
- Multiply the last terms: −5 × 2 = −10.
- Add the x terms: 2x − 5x = −3x, giving x² − 3x − 10.
✅ Put x = 1: (1 − 5)(1 + 2) = −12, and 1 − 3 − 10 = −12. They match.
සිංහලෙන් විසඳුම
වරහන් දෙකක් ප්‍රසාරණය කිරීමේදී පළමු වරහනේ සෑම පදයක්ම දෙවන වරහනේ සෑම පදයකින්ම ගුණ කළ යුතුය. ඉන්පසු සමජාතීය පද එකතු කරන්න.
- මුල් පද ගුණ කරන්න: x × x = x².
- පිට හා ඇතුළු පද යුගල ගුණ කරන්න: x × 2 = 2x, −5 × x = −5x.
- අවසාන පද ගුණ කරන්න: −5 × 2 = −10.
- x පද එකතු කරන්න: 2x − 5x = −3x. එවිට x² − 3x − 10 ලැබේ.
List the complement of a set from a Venn diagram
Angles Related to Straight Lines and Parallel LinesAngles formed by parallel lines and a transversal
Missing value from a given mode
Profit percentage from cost and selling price
Angles Related to Straight Lines and Parallel LinesAngles on a straight line with a right angle
Radius of a quarter circle from its arc length
Simplify a quotient of powers with positive indices
Factors of Quadratic ExpressionsFactorise a trinomial quadratic expression
Side of a parallelogram by equating two area calculations
Least Common Multiple of Algebraic ExpressionsLCM of three algebraic terms
Base angle of an isosceles triangle
Height of a triangle from its area, inside a trapezium
Interior angle using the exterior angle theorem
Subtract algebraic fractions with a common denominator
State the congruence condition for two triangles
Days needed when the number of workers changes
Area of a trapezium from sum of parallel sides and height
Angle using corresponding parts of congruent triangles
Solve a linear equation with brackets
Locate a point on a perpendicular bisector at a fixed distance
Probability of one category from a two-way table
Angles Related to Straight Lines and Parallel LinesAngles in a trapezium using parallel lines
Gradient and intercept of a linear function
Successive fractions of a bottle of water; find capacity
Arc length, Pythagoras diagonal and perimeter of a logo
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Area of a shaded composite region with a sector
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Pie chart: sector angles, totals, and a redrawn chart angle
Inverse proportion with water supply and changing number of students
Venn diagram entry, shading, set notation and subsets
Percentages · PercentagesLoan interest, marked price discounts and profit comparison
Table and graph of a linear function; intersection with y = x
Binomial Expressions · EquationsArea expression with a squared binomial; solve for x
Solve a pair of simultaneous equations
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Factors of Quadratic ExpressionsFactorise a trinomial and a difference of two squares
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Mode, range and mean from a frequency table; projection
Scale diagram from bearings and distances; read bearing and distance
Number patterns from general terms; term values and differences
Cuboid tank volumes, water level and displaced volume
Construct a perpendicular bisector, a triangle, angle bisector and circle
Parallelograms I · CongruencyParallelogram perpendiculars: congruent triangles and equal lengths
Isosceles triangle proofs: exterior angle, isosceles, equilateral
Sets from card numbers and simple probabilities
