North Western Province, Grade 11 Mathematics, term 3, 2025. 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 in English and Sinhala.
Annual rates from assessed value and rate percentage
Rs 6 720
💡 What it's asking: Rates are a yearly tax worked out as a percentage of the house's assessed annual value. So find 8% of Rs. 84 000.
- Write 8% as a fraction: 8/100.
- Multiply by the assessed value: 84 000 × 8/100.
- Cancel the zeros first: 840 × 8 = 6720.
- So the annual rates are Rs. 6720.
✅ 10% of 84 000 is 8400, so 8% should be a bit less than that. Rs. 6720 fits.
සිංහලෙන් විසඳුම
වරිපනම් බද්ද යනු නිවසේ වාර්ෂික තක්සේරු වටිනාකමින් ප්‍රතිශතයක් ලෙස වසරකට ගෙවන බද්දකි. එබැවින් රු. 84 000 න් 8% සොයන්න.
- 8% භාගයක් ලෙස ලියන්න: 8/100.
- තක්සේරු වටිනාකමෙන් ගුණ කරන්න: 84 000 × 8/100.
- මුලින්ම බිංදු කපා හරින්න: 840 × 8 = 6720.
- එබැවින් වාර්ෂික වරිපනම රු. 6720.
Find x + y from a pair of simultaneous equations without solving
x + y = 5
💡 What it's asking: You don't need x and y separately. Look for a quick trick: adding the two equations gives equal amounts of x and y.
- Add the left sides: (3x − y) + (x + 5y) = 4x + 4y.
- Add the right sides: 7 + 13 = 20.
- So 4x + 4y = 20.
- Divide everything by 4: x + y = 5.
✅ Solving fully gives x = 2.4 and y = 2.6, and 2.4 + 2.6 = 5. Same answer.
සිංහලෙන් විසඳුම
x සහ y වෙන වෙනම අවශ්‍ය නැත. කෙටි ක්‍රමයක් සොයන්න: සමීකරණ දෙක එකතු කළ විට x සහ y සමාන ප්‍රමාණවලින් ලැබේ.
- වම් පස එකතු කරන්න: (3x − y) + (x + 5y) = 4x + 4y.
- දකුණු පස එකතු කරන්න: 7 + 13 = 20.
- එවිට 4x + 4y = 20.
- සියල්ල 4 න් බෙදන්න: x + y = 5.
Base angle of an isosceles triangle with a 110 degree apex
Best first approximation of a square root from given squares
Solve a simple equation with x in the denominator
Find x from a base-2 logarithm equation
Angle and side in two overlapping parallelograms
Least Common Multiple of Algebraic ExpressionsLCM of two algebraic terms
Probability a random student does not study art
Data Representation and PredictionComplete a frequency table and histogram with unequal class widths
Sixth term of a geometric progression as a power of 2
Chords of a Circle · Pythagoras RelationshipDistance from centre to a chord using triangle perimeter
Solve a linear inequality and show it on a number line
Angle at circumference is half the angle at centre
Divide algebraic terms and simplify
Height of a cylinder label from circumference and curved area
Gradient of a line from two marked points
Sketch two different faces of a triangular prism with measurements
Length of a line through midpoints using the midpoint theorem
Name a set in a Venn diagram and describe a shaded region
Time to fill the rest of a tank at a given flow rate
Radius of a semicircle with given perimeter
Angle using the angle in a semicircle and same segment
Opposite and exterior angles of a cyclic quadrilateral
Locate a point on a path using a locus
Fractions of new officers sent to departments; find totals
Window frame: semicircle and rectangle areas, wood area, paint needed
Data Representation · FractionsPie chart of vehicles: totals, sector angles, value of a group
Probability · ProbabilityTwo coloured dice: grid of outcomes and tree diagram
Percentages · Share MarketSimple interest deposit and shares: dividend and selling price
Annual interest rate for an instalment plan on reducing balance
Graph of a quadratic: maximum, positive range, root estimates sqrt 2
Equations · Algebraic FractionsSimultaneous equations for gifts; subtract algebraic fractions
Form and solve a quadratic from an area; side length
Grouped data: modal class, mean by assumed mean, cost estimate
Angles of elevation and depression with a tree and a pole
Arithmetic Progressions · EquationsWire cut into lengths in arithmetic progression; sums and checking a claim
Constructions · ConstructionsConstruct triangle, perpendicular, circle through three points and a tangent
Volume of Solids · Indices and Logarithms IIWater from a hemisphere into cylinders; radius via logarithms
Congruent triangles and isosceles triangle results with a parallel line
Tangents · Cyclic Quadrilaterals · Parallelograms IITangent-chord angle and cyclic quadrilateral to prove a parallelogram
Venn diagram of class preferences, then a third set added
