සා/පෙළ ගණිතය 2023 ප්‍රශ්න පත්‍රය

Annual rates as a percentage of annual assessed value

පිළිතුර: Rs 2,880

💡 ප්‍රශ්නයේ අදහස: වරිපනම යනු දේපළේ තක්සේරු වටිනාකමේ ප්‍රතිශතයක් ලෙස ගණනය කරන වාර්ෂික බද්දකි.

1. 124 000 න් 1% = 240.
2. 2එවිට: 12% = 12 × 240 = 2880.
3. 3වාර්ෂික වරිපනම = රු. 2880.

✅ 10% = 2400 නිසා 12% ටිකක් වැඩි විය යුතුයි: 2880 ගැළපේ.

Exterior angle of a triangle equals the two interior opposite angles

පිළිතුර: x = 40

💡 ප්‍රශ්නයේ අදහස: B හි බාහිර කෝණය දුර ඇති අභ්‍යන්තර කෝණ දෙකේ එකතුවට සමානයි.

1. 1දුර ඇති කෝණ: C හි x සහ A හි 2x.
2. 2x + 2x = 120°, එනම් 3x = 120°.
3. 3එවිට: x = 40.

✅ 40°, 80°, 60° (= 180° − 120°) එකතුව 180°.

Least common multiple of three algebraic terms

Triangles with equal area on the same base between parallels

Converting a logarithm to index form

Dividing algebraic fractions

Exterior angle of a cyclic quadrilateral with parallel chord

Monthly income tax on the part of income above a threshold

Perimeter of a square joined to a circular sector

Equation of a straight line through two points

Angles in a circle with a diameter and cyclic quadrilateral

Completing a histogram with an unequal class interval

Angles in same segment and alternate angles in a circle

Water height after pouring from a prism into a cylinder

Factorising a quadratic expression given one factor

Common ratio of a geometric progression from two terms

Angle of elevation from a right triangle with a known angle

Expected number from a probability

Chord midpoint perpendicular and angle in a semicircle

Equation with algebraic fractions

Cylinder height when curved area is four times the base

List elements of a complement union a set from a Venn diagram

Pythagoras in an isosceles triangle with surd height

Solving a simple quadratic equation

Locus of a point equidistant from three points

Man-days and fractions of work done in stages

Arc length, sector area, triangle area and rectangle dimensions

Share purchase, dividend, sale, and VAT on tiles

Sample space grid and tree diagram for two boxes

Reading a cumulative frequency curve and building a pie chart

Compound interest, equivalent simple interest rate, then simple interest

Reading and translating the graph of a quadratic function

Forming and solving a quadratic for a path width

Simultaneous equations from a sharing situation

Bearings and trigonometric ratios in a right-angled triangle

Modal class and mean from a grouped frequency table

Terms and sums of two arithmetic progressions

Constructing a tangent circle, angle bisector and perpendicular

Proving cyclic quadrilateral, alternate segment angles and equal tangents

Volume equation for melted solids and log table calculation

Three-set Venn diagram with disjoint sets

Converse of midpoint theorem, congruency, parallelogram and area ratio