St. Patrick's School 4E5N Elementary Mathematics Papers 2023-2025 (GA1, Mastery Review, Prelims)

Table of Contents GA1 1 2025 GA 1 2 2024 GA 1 3 2023 GA 1 Mastery Review 4 2025 MR 5 2024 MR 6 2023 MR Preliminary Examinations 7 2025 Prelims Paper 1 8 2025 Prelims Paper 2 9 2024 Prelims Paper 1 10 2024 Prelims Paper 2 11 2023 Prelims Paper 1 12 2023 Prelims Paper 2 Page 10 Page 22 Page 32 Page 42 Page 65 Page 89 Page 117 Page 139 Page 163 Page 186 Page 212 Page 234

Mathematics (Syllabus 4052) SUBJECT CONTENT Conten Learnt In Check List PROBLEMS IN REAL WORLD CONTEXT (Paper 1 & 2) Convert money according to the exchange rate given Sec 2 ☐ Calculation of simple interest Sec 2 ☐ Calculation of compound interest Sec 3 ☐ Concept of hire purchase Sec 2 ☐ Calculation of GST and service charge Sec 2 ☐ Interpreting table and calculation of income tax Sec 2 ☐ Interpreting table and calculation of utilities bills Sec 2 ☐ Page 1

Topic/Sub- topic Content Learnt in Check list NUMBER AND ALGEBRA N1 Numbers & their operations Primes and prime factorisation Sec 1 ☐ Finding highest common factor (HCF) and lowest common multiple (LCM), squares, cubes, square roots and cube roots by prime factorisation Sec 1 ☐ Negative numbers, integers, rational numbers, real numbers, and their four operations Sec 1 ☐ Calculations with calculator Sec 1 ☐ Representation and ordering of numbers on the number line Sec 1 ☐ use of the symbols <, >,  , Sec 1 ☐ approximation and estimation (including rounding off numbers to a required number of decimal places or significant figures and estimating the results of computation) Sec 1 ☐ Use of standard form 10nA , where n is an integer, and 1 10A  Sec 3 ☐ Positive, negative, zero and fractional indices Sec 3 ☐ Laws of indices Sec 3 ☐ N2 Ratio and Proportion Ratios involving rational numbers Sec 1 ☐ Writing a ratio in its simplest form Sec 1 ☐ Map scales (distance and area) Sec 2 ☐ Direct and inverse proportion Sec 2 ☐ N3 Percentage Expressing one quantity as a percentage of another Sec 1 ☐ Comparing two quantities by percentage Sec 1 ☐ Percentages greater than 100% Sec 1 ☐ Increasing/decreasing a quantity by a given percentage Sec 1 ☐ Reverse percentages Sec 1 ☐ N4 Rate and speed Rates and average rates (including the concepts of speed and average speed) Sec 1 ☐ Conversion of units (e.g. km/h to m/s) Sec 1 ☐ Page 2

Topic/Sub- topic Content Learnt in Check list NUMBER AND ALGEBRA N5 Algebraic expressions and formulae Using letters to represent numbers Sec 1 ☐ Intepreting notations: Sec 1 ☐ Evaluation of algebraic expressions and formulae Sec 1 ☐ Translation of simple real-world situations into algebraic expressions Sec 1 ☐ Recognizing and representing patterns/relationships by finding an algebraic expression for the nth term Sec 1 ☐ Addition and subtraction of linear expressions Sec 2 ☐ Simplification of linear expressions such as: Sec 2 ☐ Use brackets and extract common factors Sec 2 ☐ Factorisation of linear expressions of the form ax + bx + kay + kby Sec 2 ☐ Expansion of the product of algebraic expressions Sec 2 ☐ Changing the subject of a formula Sec 2 ☐ Finding the value of an unknown quantity in a given formula Sec 1 ☐ Use of special algebraic identities:  (a + b)2 = a2 + 2ab + b2  (a - b)2 = a2 - 2ab + b2  a 2 – b2 = (a + b)(a – b) Sec 2 ☐ Factorisation of quadratic expressions ax2 + bx + c Sec 2 ☐ Multiplication and division of simple algebraic fractions such as : Sec 2 ☐ Page 3

N6 Functions and Graphs Cartesian coordinates in two dimensions I.e. Plotting and reading of coordinates (x, y) Sec 2 ☐ Linear functions (y = ax + b) and quadratic functions (y = ax2 + bx + c) i.e. able to identify equation of linear and quadratic graphs Sec 2 ☐ Graphs of linear functions Sec 1 ☐ The gradient of a linear graph as the ratio of the vertical change to the horizontal change (positive and negative gradients) Sec 1 ☐ Graphs of quadratic functions and their properties:  positive or negative coefficient of x2  maximum and minimum points  symmetry Sec 2 ☐ Sketching the graphs of quadratic functions given in the form:  2( )y x p q    2( )y x p q    ( )( )y x a x b    ( )( )y x a x b   Sec 3 ☐ Graphs of power functions of the form ny ax , where n = 2, 1,0,1,2,3  and simple sums of not more than three of these Sec 3 ☐ Graphs of exponential functions xy ka , where a is a positive integer Sec 3 ☐ Estimation of the gradient of a curve by drawing a tangent Sec 3 ☐ N7 Equations and Inequalities Solving linear equations in one variable Sec 1 ☐ Solving simple fractional equations that can be reduced to linear equations such as: Sec 2 ☐ Solving simultaneous linear equations in two variable by  Substitution and elimination methods  Graphical method Sec 2 ☐ Topic/Sub- topic Content Learnt in Check list Addition and subtraction of algebraic fractions with linear or quadratic denominator such as: Sec 2 ☐ Page 4

Solving quadratic equations in one unknown by  Factorisation  Use of formula i.e. 2 4 2 b b acx a     Completing the square for 2y x px q    Graphical method Sec 2 Sec 3 ☐ Solving fractional equations that can be reduced to quadratic equations such as: Sec 3 ☐ Formulating equations to solve problems Sec 3 ☐ Solving linear inequalities in one variable, and representing the solution on the number line Sec 2 Sec 3 ☐ N8 Set Language and notation Use of set language and the following notation: Sec 4 ☐ Union and intersection of two sets ☐ Venn diagrams ☐ N9 Matrices Display of information in the form of a matrix of any order Sec 4 ☐ Interpreting the data in a given matrix ☐ Product of a scalar quantity and a matrix ☐ Problems involving the calculation of the sum and product (where appropriate) of two matrices ☐ Page 5

Topic/Sub- topic Content Learnt in Check list GEOMETRY AND MEASUREMENT (Paper 1) G1 Angles, Triangles and Quadrilaterals Identifying right, acute, obtuse and reflex angles Sec 1 ☐ Identifying vertically opposite angles, angles on a straight line and angles at a point Sec 1 ☐ Angles formed by two parallel lines and a transversal:  Corresponding angles  Interior angles  Alternate angles Sec 1 ☐ Knowing the properties of  Triangles, special quadrilaterals and regular polygons (pentagon, hexagon, octagon and decagon etc), including symmetry properties Sec 1 ☐ Classifying special quadrilaterals on the basis of their properties Sec 1 ☐ Angle sum of interior and exterior angles of any convex polygon Sec 1 ☐ Construction of (using compasses, ruler, set squares and protractors):  simple geometrical figures from given data Sec 1 ☐ G2 Congruence and similarity Congruent figures and similar figures Sec 2 ☐ Properties of congruent figures  corresponding sides and angles are equal Sec 2 ☐ Properties of similar figures  corresponding angles are equal  corresponding sides are proportional Sec 2 ☐ Enlargement and reduction of a plane figure Sec 2 ☐ Scale drawings Sec 3 ☐ Construction of (using compasses, ruler, set squares and protractors):  perpendicular bisectors  angle bisectors Sec 3 ☐ Determining whether two triangles are congruent or similar based on their respective tests Sec 3 ☐ Ratio of areas of similar plane figures Sec 3 ☐ Ratio of volumes of similar solids Sec 3 ☐ Solving simple problems involving similarity and congruence Sec 3 ☐ Page 6

Topic/Sub- topic Content Learnt in Check list G3 Properties of circles Symmetry properties of circles:  equal chords are equidistant from the centre  the perpendicular bisector of a chord passes through the centre  tangents from an external point are equal in length  the line joining an external point to the centre of the circle bisects the angle between the tangents Sec 3 ☐ Angle properties of circles:  angle in a semicircle is a