Singapore O-Level Mathematics
4052 Mathematics and 4049 Additional Mathematics
160 of 161 skills covered
✓ covered · ◐ partial · ○ not yet · — excluded
4052 · N1. Numbers and their operations
| skill | lessons | ||
|---|---|---|---|
| 1.1 | primes and prime factorisation | The Sieve of Eratosthenes, Prime Factorization | ✓ covered |
| 1.2 | finding highest common factor (HCF) and lowest common multiple (LCM), squares, cubes, square roots and cube roots by prime factorisation | The Highest Common Factor, The Lowest Common Multiple, Squares and Square Roots, Cubes and Cube Roots, Roots by Prime Factorization | ✓ covered |
| 1.3 | negative numbers, integers, rational numbers, real numbers and their four operations | Below Zero, Adding and Subtracting Across Zero, Subtracting Negative Numbers, Multiplying and Dividing Negative Numbers, Rational and Irrational Numbers | ✓ covered |
| 1.4 | calculations with calculatorthe app is deliberately calculator-free — a mental-math product cannot honestly teach calculator technique; recorded, not closable by a lesson | — excluded | |
| 1.5 | representation and ordering of numbers on the number line | Below Zero, Ordering Negative Numbers | ✓ covered |
| 1.6 | use of <, >, ≤, ≥ | Inequalities, Two-Step Inequalities | ✓ covered |
| 1.7 | approximation and estimation (including rounding off numbers to a required number of decimal places or significant figures, and estimating the results of computation) | Rounding Decimals to One and Two Decimal Places, Significant Figures, Estimating with One Significant Figure, Rounding to Estimate | ✓ covered |
4052 · N2. Ratio and proportion
| skill | lessons | ||
|---|---|---|---|
| 2.1 | ratios involving rational numbers | Ratio, Three-Part Ratios | ✓ covered |
| 2.2 | writing a ratio in its simplest form | Tidying a Ratio | ✓ covered |
| 2.3 | problems involving ratio | The Unitary Method, Bar Models for Ratio, Combining Two Ratios, Rewriting a Ratio to Match a Share | ✓ covered |
4052 · N3. Percentage
| skill | lessons | ||
|---|---|---|---|
| 3.1 | expressing one quantity as a percentage of another | Percentage, Comparing with Percent | ✓ covered |
| 3.2 | comparing two quantities by percentage | Comparing with Percent | ✓ covered |
| 3.3 | percentages greater than 100% | Percentage Increase | ✓ covered |
| 3.4 | increasing/decreasing a quantity by a given percentage (including concept of percentage point) | Percentage Increase, Taking a Percent Off, Percentage Change | ✓ covered |
| 3.5 | reverse percentages | Reverse Percentages | ✓ covered |
| 3.6 | problems involving percentages | Sales Tax, Simple Interest, Finding a Percent | ✓ covered |
4052 · N4. Rate and Speed
| skill | lessons | ||
|---|---|---|---|
| 4.1 | concepts of average rate, speed, constant speed and average speed | Rates, Speed, Average Speed | ✓ covered |
| 4.2 | conversion of units (e.g. km/h to m/s) | Converting Compound Units | ✓ covered |
| 4.3 | problems involving rate and speed | Rate, Total, Units, Speed, Average Speed | ✓ covered |
4052 · N5. Algebraic expressions and formulae
| skill | lessons | ||
|---|---|---|---|
| 5.1 | using letters to represent numbers | Algebraic Notation | ✓ covered |
| 5.2 | interpreting notations: ab as a × b; a/b as a ÷ b; a², a³, a²b; 3y as y + y + y; 3(x + y); (3 + y)/5 | Algebraic Notation | ✓ covered |
| 5.3 | evaluation of algebraic expressions and formulae | Substitution | ✓ covered |
| 5.4 | translation of simple real-world situations into algebraic expressions | Writing Formulas from Words, Forming Equations | ✓ covered |
| 5.5 | recognising and representing patterns/relationships by finding an algebraic expression for the nth term | Term-to-Term Rules, The nth Term | ✓ covered |
| 5.6 | addition and subtraction of linear expressions | Like Terms | ✓ covered |
| 5.7 | simplification of linear expressions such as −2(3x − 5) + 4x; 2x/3 − 3(x − 5)/2 | Like Terms, Expanding Brackets | ✓ covered |
| 5.8 | use brackets and extract common factors | Expanding Brackets, Factoring by Common Factor | ✓ covered |
4052 · N6. Functions and graphs
| skill | lessons | ||
|---|---|---|---|
| 6.1 | Cartesian coordinates in two dimensions | The Coordinate Plane | ✓ covered |
| 6.2 | graph of a set of ordered pairs as a representation of a relationship between two variables | The Coordinate Plane, Coordinate Geometry | ✓ covered |
| 6.3 | linear functions y = ax + b | y = mx + c | ✓ covered |
| 6.4 | graphs of linear functions | y = mx + c, Coordinate Geometry | ✓ covered |
| 6.5 | the gradient of a linear graph as the ratio of the vertical change to the horizontal change (positive and negative gradients) | Gradient from Two Points | ✓ covered |
4052 · N7. Equations and inequalities
| skill | lessons | ||
|---|---|---|---|
| 7.1 | concept of equation | Solving Linear Equations, Forming Equations | ✓ covered |
| 7.2 | solving linear equations in one variable | Solving Linear Equations, Equations with Brackets, Equations with the Unknown on Both Sides | ✓ covered |
| 7.3 | solving simple fractional equations that can be reduced to linear equations, e.g. (x − 2)/3 + x/4 = 3; 6/(x − 2) = 3 | Equations with Fractions | ✓ covered |
| 7.4 | formulating a linear equation in one variable to solve problems | Forming Equations | ✓ covered |
4052 · G1. Angles, triangles and polygons
| skill | lessons | ||
|---|---|---|---|
| 1.1 | right, acute, obtuse and reflex angles | Angles | ✓ covered |
| 1.2 | vertically opposite angles, angles on a straight line, angles at a point | Vertically Opposite Angles, Angles on a Line, Angles at a Point | ✓ covered |
| 1.3 | angles formed by two parallel lines and a transversal: corresponding angles, alternate angles, interior angles | Angles in Parallel Lines | ✓ covered |
| 1.4 | properties of triangles, special quadrilaterals and regular polygons (pentagon, hexagon, octagon and decagon), including symmetry properties | Angles in a Triangle, Special Quadrilaterals, Rhombus and Kite, The Interior Angle of a Regular Polygon, Symmetry | ✓ covered |
| 1.5 | classifying special quadrilaterals on the basis of their properties | Special Quadrilaterals | ✓ covered |
| 1.6 | angle sum of interior and exterior angles of any convex polygon | Angles in a Polygon, The Interior Angle of a Regular Polygon | ✓ covered |
| 1.7 | construction of simple geometrical figures from given data using compasses, ruler, set squares and protractors, where appropriate | Constructing a Perpendicular Bisector, Constructing an Angle Bisector, Constructing a Perpendicular from a Point, Measuring and Drawing Angles, Constructing a Triangle | ✓ covered |
4052 · G5. Mensuration
| skill | lessons | ||
|---|---|---|---|
| 5.1 | area of parallelogram and trapezium | Area of a Parallelogram, Area of a Trapezium | ✓ covered |
| 5.2 | problems involving perimeter and area of composite plane figures | Area of Composite Shapes | ✓ covered |
| 5.3 | volume and surface area of prism and cylinder | Prisms and Cylinders, Surface Area of a Cuboid, Surface Area of a Cylinder | ✓ covered |
| 5.4 | conversion between cm² and m², and between cm³ and m³ | Converting Units of Area | ✓ covered |
| 5.5 | problems involving volume and surface area of composite solids | Prisms and Cylinders, Scaling Area and Volume | ✓ covered |
4052 · S1. Data handling and analysis
| skill | lessons | ||
|---|---|---|---|
| 1.1 | simple concepts in collecting, classifying and tabulating data | Categorical and Numerical Data, Tally and Frequency Tables | ✓ covered |
| 1.2 | analysis and interpretation of: tables, bar graphs, pictograms, line graphs, pie charts | Reading Tables, Bar Charts, Reading Bar Charts, Reading Pictograms, Line Graphs, Pie Charts | ✓ covered |
| 1.3 | purposes and uses, advantages and disadvantages of the different forms of statistical representations | Choosing a Chart, Categorical and Numerical Data, Misleading Graphs | ✓ covered |
| 1.4 | explaining why a given statistical diagram leads to misinterpretation of data | Misleading Graphs | ✓ covered |
4052 · Secondary Two
| skill | lessons | ||
|---|---|---|---|
| N2 2.4 | map scales (distance and area) | Map Scales, Scaling Area | ✓ covered |
| N2 2.5 | direct and inverse proportion | Direct Proportion, Inverse Proportion, The Constant of Proportionality, Proportion by Unit Value | ✓ covered |
| N5 5.9 | expansion of the product of algebraic expressions | Expanding Two Brackets | ✓ covered |
| N5 5.10 | changing the subject of a formula | Changing the Subject of a Formula, Making a Twice-Appearing Letter the Subject | ✓ covered |
| N5 5.11 | finding the value of an unknown quantity in a given formula | Substitution | ✓ covered |
| N5 5.12 | use of (a + b)² = a² + 2ab + b²; (a − b)² = a² − 2ab + b²; a² − b² = (a + b)(a − b) | Algebraic Identities | ✓ covered |
| N5 5.13 | factorisation of linear expressions of the form ax + bx + kay + kby | Factoring by Grouping | ✓ covered |
| N5 5.14 | factorisation of quadratic expressions ax² + bx + c | Factoring Quadratics, Factoring Quadratics with a Leading Coefficient | ✓ covered |
| N5 5.15 | multiplication and division of simple algebraic fractions, e.g. (3a/4b²)(5ab/3); 3a/4 ÷ 9a²/10 | Algebraic Fractions, Adding and Multiplying Algebraic Fractions | ✓ covered |
| N5 5.16 | addition and subtraction of algebraic fractions with linear or quadratic denominator | Adding and Multiplying Algebraic Fractions | ✓ covered |
| N6 6.6 | quadratic functions y = ax² + bx + c | Quadratic Graphs | ✓ covered |
| N6 6.7 | graphs of quadratic functions and their properties: sign of the x² coefficient, maximum and minimum points, symmetry | Quadratic Graphs, Quadratic and Cubic Graphs | ✓ covered |
| N7 7.5 | concept of equation and inequality | Inequalities | ✓ covered |
| N7 7.6 | solving simple inequalities ax + b ≤ c (all four signs), solutions on the number line | Inequalities, Two-Step Inequalities | ✓ covered |
| N7 7.7 | graphs of linear equations in two variables (ax + by = c) | y = mx + c, Coordinate Geometry | ✓ covered |
| N7 7.8 | solving simultaneous linear equations by substitution and elimination methods, and graphical method | Simultaneous by Substitution, Simultaneous by Elimination, Solving Simultaneous Equations by Scaling, Simultaneous Equations | ✓ covered |
| N7 7.9 | solving quadratic equations in one variable by factorisation | Solving by Factoring | ✓ covered |
| N7 7.10 | formulating a pair of linear equations in two variables to solve problems | Forming Equations, Simultaneous Equations | ✓ covered |
| G2 2.1–2.3 | congruent figures; similar figures; properties of similar triangles and polygons (equal corresponding angles, proportional corresponding sides) | Congruence Tests, Similar Shapes, Similarity Conditions | ✓ covered |
| G2 2.4 | enlargement and reduction of a plane figure | Enlargement with a Center, Scale Factor | ✓ covered |
| G2 2.5 | solving simple problems involving congruence and similarity | Similar Shapes, Ratio of Areas | ✓ covered |
| G4 4.1 | use of Pythagoras' theorem | Pythagoras’ Theorem, Finding a Shorter Side with Pythagoras’ Theorem, Proving Pythagoras by Dissection | ✓ covered |
| G4 4.2 | determining whether a triangle is right-angled given the lengths of three sides | The Converse of Pythagoras’ Theorem | ✓ covered |
| G4 4.3 | use of trigonometric ratios of acute angles to calculate unknown sides and angles in right-angled triangles | Sine, Cosine and Tangent, Solving Right Triangles, Finding an Angle from a Ratio | ✓ covered |
| G5 5.6 | volume and surface area of pyramid, cone and sphere | Pyramids and Cones, Spheres, Cones and Spheres, The Slant Height of a Cone | ✓ covered |
| S1 1.5 | analysis and interpretation of: dot diagrams, histograms, stem-and-leaf diagrams | Dot Diagrams, Histograms, Frequency Density, Stem and Leaf | ✓ covered |
| S1 1.6–1.7 | purposes/advantages/disadvantages; why a diagram misleads | Choosing a Chart, Misleading Graphs | ✓ covered |
| S1 1.8–1.9 | mean, mode and median as measures of central tendency; purposes and use | The Mean, Median and Mode, Measures of Central Tendency | ✓ covered |
| S1 1.10 | calculation of the mean for grouped data | Mean of Grouped Data, Averages from a Frequency Table | ✓ covered |
| S2 2.1 | probability as a measure of chance | The Probability Scale | ✓ covered |
| S2 2.2 | probability of single events (including listing all the possible outcomes) | Single-Event Probability, Sample Space, Complementary Events | ✓ covered |
4052 · Secondary Three/Four
| skill | lessons | ||
|---|---|---|---|
| N1 1.8 | use of standard form A × 10ⁿ, where n is an integer and 1 ≤ A < 10 | Standard Form, Calculating in Standard Form | ✓ covered |
| N1 1.9 | positive, negative, zero and fractional indices | Index Notation, Zero and Negative Indices, Fractional Indices | ✓ covered |
| N1 1.10 | laws of indices | Laws of Indices, The Power of a Power Rule | ✓ covered |
| N6 6.8 | sketching the graphs of quadratic functions given in the form y = (x − p)² + q, y = −(x − p)² + q, y = (x − a)(x − b), y = −(x − a)(x − b) | Completing the Square, Solving by Factoring, Sketching from Vertex and Factored Form | ✓ covered |
| N6 6.9 | graphs of power functions y = axⁿ, where n = −2, −1, 0, 1, 2, 3, and simple sums of not more than three of these | Quadratic and Cubic Graphs, Reciprocal Graphs, The Graphs of y = axⁿ | ✓ covered |
| N6 6.10 | graphs of exponential functions y = kaˣ, where a is a positive integer | Exponential Growth, Exponential Decay | ✓ covered |
| N6 6.11 | estimation of the gradient of a curve by drawing a tangent | Estimating a Gradient with a Drawn Tangent, The Gradient of a Curve | ✓ covered |
| N7 7.11 | solving quadratic equations by use of formula, completing the square for y = x² + px + q, and graphical method | The Quadratic Formula, Completing the Square, Quadratic Graphs | ✓ covered |
| N7 7.12 | solving fractional equations reducible to quadratic equations | Fractional Equations | ✓ covered |
| N7 7.13 | solving linear inequalities in one variable (including simultaneous inequalities), solutions on the number line | Inequalities, Two-Step Inequalities, Integer Solutions of Inequalities | ✓ covered |
| N7 7.14 | formulating a quadratic equation in one variable to solve problems | Forming Quadratic Equations | ✓ covered |
| N8 8.1–8.3 | set language and the listed notation; union and intersection of two sets; Venn diagrams | Set Notation, Complements and Subsets, Venn Diagrams, Counting a Union, Naming the Regions of a Venn Diagram | ✓ covered |
| N9 9.1–9.4 | matrices: display and interpretation, scalar product, addition/subtraction/multiplication problems | The Order of a Matrix, Adding, Subtracting and Scaling Matrices, The Matrix Product, Combining Data with a Matrix Product | ✓ covered |
| G2 2.6 | scale drawings | Map Scales, Scale Factor | ✓ covered |
| G2 2.7 | properties and construction of perpendicular bisectors of line segments and angle bisectors | Constructing a Perpendicular Bisector, Constructing an Angle Bisector | ✓ covered |
| G2 2.8 | determining whether two triangles are congruent or similar | Congruence Tests, Similarity Conditions | ✓ covered |
| G2 2.9–2.10 | ratio of areas of similar plane figures; ratio of volumes of similar solids | Ratio of Areas, Ratio of Volumes, Scaling Area and Volume | ✓ covered |
| G3 3.1 | symmetry properties of circles (equal chords equidistant; perpendicular bisector of a chord passes through the centre; equal external tangents; the line to the centre bisects the tangent angle) | Chords and the Center, Tangent Properties | ✓ covered |
| G3 3.2 | angle properties of circles (semicircle; tangent–radius; centre twice circumference; same segment; opposite segments supplementary) | Angle in a Semicircle, Angle at the Center, Angles in the Same Segment, Cyclic Quadrilaterals, Tangent Properties | ✓ covered |
| G4 4.4 | extending sine and cosine to obtuse angles | Sine and Cosine of Angles Past 90 Degrees | ✓ covered |
| G4 4.5 | use of the formula ½ab sin C for the area of a triangle | Area with Sine | ✓ covered |
| G4 4.6 | use of sine rule and cosine rule for any triangle | The Sine Rule, The Cosine Rule, Finding Angles with the Sine Rule, Finding Angles with the Cosine Rule, The Ambiguous Case of the Sine Rule | ✓ covered |
| G4 4.7 | problems in two and three dimensions including angles of elevation and depression and bearings | Elevation and Depression, Three-Figure Bearings, Back Bearings, Trigonometry in Three Dimensions | ✓ covered |
| G5 5.7 | arc length, sector area and area of a segment of a circle | Arcs and Sectors, Arc Length and Sector Area, The Area of a Segment | ✓ covered |
| G5 5.8 | use of radian measure of angle (including conversion between radians and degrees) | Radians | ✓ covered |
| G6 6.1–6.4 | gradient from two points; length of a line segment; equation of a line y = mx + c; geometric problems with coordinates | Gradient from Two Points, The Distance Between Two Points, y = mx + c, The Equation of a Line Through Two Points, Coordinate Geometry, Gradients of Parallel and Perpendicular Lines, The Midpoint of a Segment | ✓ covered |
| G7 7.1–7.8 | vectors in two dimensions: notation, directed line segments, translation, position vectors, magnitude, sum and difference, scalar multiples, geometric problems | Vectors, Column Vectors, Translation of Shapes, Position Vectors, Magnitude of a Vector, Adding Vectors, Subtracting Vectors, Scalar Multiplication, Vector Proofs with Midpoints, Collinear Vectors | ✓ covered |
| S1 1.11 | quartiles and percentiles | Percentiles, Quartiles from the Curve | ✓ covered |
| S1 1.12 | range, interquartile range and standard deviation as measures of spread | Range and IQR, Measures of Spread, Standard Deviation | ✓ covered |
| S1 1.13 | analysis and interpretation of cumulative frequency diagrams and box-and-whisker plots | Cumulative Frequency, Box and Whisker | ✓ covered |
| S1 1.14 | purposes and uses, advantages and disadvantages of the different forms of statistical representations | Choosing a Chart | ✓ covered |
| S1 1.15 | calculation of the standard deviation for a set of data (grouped and ungrouped) | Standard Deviation: Ungrouped, Standard Deviation: Grouped | ✓ covered |
| S1 1.16 | using the mean and standard deviation to compare two sets of data | Comparing Data Sets | ✓ covered |
| S2 2.3 | probability of simple combined events (including possibility diagrams and tree diagrams) | Possibility Diagrams, Tree Diagrams, Without Replacement, Multiplying Along a Tree Without Replacement | ✓ covered |
| S2 2.4 | addition and multiplication of probabilities (mutually exclusive events and independent events) | Mutually Exclusive Events, The Addition Rule for Overlapping Events, Independent Events, The Chance of At Least One | ✓ covered |
4049 · ALGEBRA
| skill | lessons | ||
|---|---|---|---|
| A1 1.1 | finding the maximum or minimum value of a quadratic function using the method of completing the square | Completing the Square | ✓ covered |
| A1 1.2 | conditions for y = ax² + bx + c to be always positive (or always negative) | Always Positive or Always Negative Quadratics | ✓ covered |
| A1 1.3 | using quadratic functions as models | Forming Quadratic Equations | ✓ covered |
| A2 2.1 | conditions for a quadratic equation to have two real / two equal / no real roots, and related conditions for a line to intersect / be tangent to / not intersect a given curve | The Discriminant and the Nature of the Roots, When a Line Meets, Touches or Misses a Curve | ✓ covered |
| A2 2.2 | solving simultaneous equations in two variables by substitution, with one of the equations being a linear equation | A Linear Equation Paired with a Quadratic, Where a Line Meets a Circle | ✓ covered |
| A2 2.3 | solving quadratic inequalities, and representing the solution on the number line | Solving a Quadratic Inequality | ✓ covered |
| A3 3.1 | four operations on surds, including rationalising the denominator | Radicals, Adding and Multiplying Radicals, Rationalizing the Denominator | ✓ covered |
| A3 3.2 | solving equations involving surds | Solving Equations with a Square Root | ✓ covered |
| A4 4.1 | multiplication and division of polynomials | Expanding Two Brackets, Long Division of Polynomials | ✓ covered |
| A4 4.2 | use of remainder and factor theorems, including factorising polynomials and solving cubic equations | Factor and Remainder Theorem, Solving a Cubic Completely | ✓ covered |
| A4 4.3 | use of a³ + b³ = (a + b)(a² − ab + b²) and a³ − b³ = (a − b)(a² + ab + b²) | The Sum and Difference of Two Cubes | ✓ covered |
| A4 4.4 | partial fractions with denominator no more complicated than (ax + b)(cx + d); (ax + b)(cx + d)²; (ax + b)(x² + c²) | Integration by Partial Fractions | ✓ covered |
| A5 5.1–5.3 | Binomial Theorem for positive integer n; notations n! and nCr; the general term nCr aⁿ⁻ʳ bʳ | The Binomial Theorem, Factorials, Combinations | ✓ covered |
| A6 6.1 | exponential and logarithmic functions aˣ, eˣ, log_a x, ln x and their graphs, including laws of logarithms, equivalence of y = aˣ and x = log_a y, change of base | Exponentials and Logarithms, Logarithmic Graphs, The Natural Logarithm, The Laws of Logarithms, The Change of Base Rule | ✓ covered |
| A6 6.2 | simplifying expressions and solving simple equations involving exponential and logarithmic functions | Solving Exponential Equations, The Laws of Logarithms | ✓ covered |
| A6 6.3 | using exponential and logarithmic functions as models | Growth and Decay Problems, Exponential Growth, Exponential Decay | ✓ covered |
4049 · GEOMETRY AND TRIGONOMETRY
| skill | lessons | ||
|---|---|---|---|
| G1 1.1 | six trigonometric functions for angles of any magnitude (in degrees or radians) | Sine and Cosine of Angles Past 90 Degrees, Secant, Cosecant and Cotangent, Radians | ✓ covered |
| G1 1.2 | principal values of sin⁻¹x, cos⁻¹x, tan⁻¹x | Finding an Angle from a Ratio, The Principal Values of the Inverse Functions | ✓ covered |
| G1 1.3 | exact values of the trigonometric functions for special angles (30°, 45°, 60°) or (π/6, π/4, π/3) | Exact Sine, Cosine and Tangent at 30, 45 and 60°, Exact Trigonometric Values in Radians | ✓ covered |
| G1 1.4 | amplitude, periodicity and symmetries related to sine and cosine functions | The Graphs of Sine and Cosine, Amplitude and the Principal Axis | ✓ covered |
| G1 1.5 | graphs of y = a sin(bx) + c, y = a sin(x/b) + c, y = a cos(bx) + c, y = a cos(x/b) + c and y = a tan(bx) | The Graphs of Sine and Cosine, The Graph of Tangent, Amplitude and the Principal Axis, The Period and Phase Shift of a Wave | ✓ covered |
| G1 1.6 | use of tan A = sin A / cos A, cot A = cos A / sin A, sin²A + cos²A = 1, sec²A = 1 + tan²A, cosec²A = 1 + cot²A; the expansions of sin(A ± B), cos(A ± B), tan(A ± B); the formulae for sin 2A, cos 2A, tan 2A; the expression of a cos θ + b sin θ in the form R cos(θ ± α) or R sin(θ ± α) | Trigonometric Identities, The Identity 1 + tan²θ = sec²θ, Secant, Cosecant and Cotangent, The Compound Angle Formulas, The Double Angle Formulas, The Harmonic Form R sin(x + α), Solving a sin x + b cos x = c with the R Form | ✓ covered |
| G1 1.7 | simplification of trigonometric expressions | Trigonometric Identities, The Identity 1 + tan²θ = sec²θ | ✓ covered |
| G1 1.8 | solution of simple trigonometric equations in a given interval (excluding general solution) | Solving Simple Trigonometric Equations, Quadratic Equations in Sine, Cosine or Tangent, Trigonometric Equations with a Multiple Angle | ✓ covered |
| G1 1.9 | proofs of simple trigonometric identities | Trigonometric Identities, Proving a Trigonometric Identity | ✓ covered |
| G1 1.10 | use of trigonometric functions as models | Modeling Tides and Daylight with a Sine Function | ✓ covered |
| G2 2.1 | condition for two lines to be parallel or perpendicular | Gradients of Parallel and Perpendicular Lines | ✓ covered |
| G2 2.2 | midpoint of line segment | The Midpoint of a Segment | ✓ covered |
| G2 2.3 | area of rectilinear figure | The Area of a Polygon from Coordinates | ✓ covered |
| G2 2.4 | coordinate geometry of circles in the forms (x − a)² + (y − b)² = r² and x² + y² + 2gx + 2fy + c = 0 (excluding problems involving two circles) | The Equation of a Circle, Center and Radius by Completing the Square, The Tangent to a Circle at a Point, Where a Line Meets a Circle | ✓ covered |
| G2 2.5 | transformation of given relationships, including y = axⁿ and y = kbˣ, to linear form to determine the unknown constants from a straight line graph | Straightening Growth with Logarithms, Straightening a Power Law | ✓ covered |
| G3 3.1 | properties of parallel lines cut by a transversal, perpendicular and angle bisectors, triangles, special quadrilaterals and circles | Angles in Parallel Lines, Constructing a Perpendicular Bisector, Constructing an Angle Bisector, Angles in a Triangle, Special Quadrilaterals, Angle in a Semicircle | ✓ covered |
| G3 3.2 | congruent and similar triangles | Congruence Tests, Similarity Conditions | ✓ covered |
| G3 3.3 | midpoint theorem | The Midpoint Theorem | ✓ covered |
| G3 3.4 | tangent-chord theorem (alternate segment theorem) | The Alternate Segment Theorem | ✓ covered |
4049 · CALCULUS
| skill | lessons | ||
|---|---|---|---|
| C1 1.1–1.3 | derivative as gradient of the tangent; derivative as rate of change; notations f′(x), f″(x), dy/dx, d²y/dx² | The Gradient of a Curve, The Derivative As a Limit, Derivative Notation, Higher Derivatives | ✓ covered |
| C1 1.4 | derivatives of xⁿ for any rational n, sin x, cos x, tan x, eˣ and ln x, with constant multiples, sums and differences | The Power Rule, Differentiating Trigonometric Functions, Differentiating tan x and the Reciprocal Ratios, Differentiating Exponentials and Logarithms | ✓ covered |
| C1 1.5–1.6 | derivatives of products and quotients; Chain Rule | The Product Rule, The Quotient Rule, The Chain Rule | ✓ covered |
| C1 1.7–1.9 | increasing and decreasing functions; stationary points (turning points and stationary points of inflexion); second derivative test | Increasing and Decreasing Functions, Finding Stationary Points, Points of Inflection, The Second Derivative Test | ✓ covered |
| C1 1.10 | differentiation applied to gradients, tangents and normals, connected rates of change and maxima and minima problems | Tangents and Normals to Curves, Related Rates, Optimization Problems | ✓ covered |
| C1 1.11–1.13 | integration as the reverse of differentiation; integration of xⁿ, sin x, cos x, sec²x, eˣ; integration of (ax + b)ⁿ, sin(ax + b), cos(ax + b), e^(ax+b) | The Antiderivative, Integration, Integrating Powers, Integrating Trigonometric Functions, Integrating sec²x, sec x tan x and tan x, Integrating Exponentials and Logarithms, Integrating f(ax + b) | ✓ covered |
| C1 1.14–1.17 | definite integral as area; evaluation; area bounded by a curve and lines; areas below the x-axis | The Definite Integral, The Fundamental Theorem of Calculus, Area Under a Curve, Area Below the Axis | ✓ covered |
| C1 1.18 | application of differentiation and integration to displacement, velocity and acceleration of a particle moving in a straight line | Motion in a Straight Line, Velocity and Displacement by Integration | ✓ covered |
Other syllabuses: Singapore PSLE Mathematics · SAT Math · GCSE Mathematics (Higher) · Singapore A-Level H2 Mathematics