# GCE O-Level 2024 Syllabus

## GCE 2024 O-level syllabus overview

When preparing for an important paper such as the O Level examination, it is important to understand not only the topics in the subject but also the details of the paper. Over here, we have compiled a detailed list of what a student can expect to be tested on for O Level subjects. Remember, it is never too late to start preparing! All information has been from the SEAB website.

## English

In this English Language examination, students will be assessed on their ability to:

• Listen to, read, and view a wide array of literary and informational texts critically and accurately, demonstrating an understanding and appreciation of the text.
• Analyse different types of written and multimodal texts at basic, interpretive, and evaluative levels, including understanding how language creates an impact.
• Find main ideas and details in various texts, including those with pictures or videos. Also, demonstrate the ability to compile and summarise information from different sources.
• Listen to different audio texts and demonstrate your understanding in three ways:
• Understand the basic facts.
• Make interpretations or inferences.
• Evaluate or judge the content, including being able to identify the main ideas and details.
• Be able to speak your thoughts and opinions clearly and smoothly to capture the listener's attention.
• Take part in a conversation and express your thoughts and opinions clearly.

## Maths

The O Level Mathematics syllabus is intended to provide students with fundamental mathematical knowledge and skills. The content is organised into three strands:

• Number and Algebra
• Geometry and Measurement
• Statistics and Probability

When preparing for a critical examination, students must understand and revise all the topics in a subject. Over here, we have compiled a list of all the topics tested in the subject and what to expect in the papers.

### Section 1: Numbers and algebra

#### Numbers and their operations

• Understand prime numbers and prime factorisation.
• Find the highest common factor (HCF) and lowest common multiple (LCM), squares, cubes, square roots, and cube roots using prime factorisation.
• Understand negative numbers, integers, rational numbers, real numbers, and their four operations.
• Perform calculations with a calculator.
• Represent and order numbers on the number line.
• Use symbols <, >, ⩽, ⩾ to compare numbers.
• Approximate and estimate numbers by rounding off to a required number of decimal places or significant figures and estimate results of computation.
• Use standard form A × $10^n$, where n is an integer, and 1 ⩽ A < 10.
• Understand positive, negative, zero, and fractional indices.
• Apply laws of indices to solve mathematical problems.

#### Ratio and proportion

• Understand and apply ratios involving rational numbers.
• Simplify ratios to their simplest form.
• Understand map scales for both distance and area.
• Understand and solve problems using direct and inverse proportions.

#### Percentage

• Convert one quantity to a percentage of another quantity.
• Compare two quantities by percentage.
• Understand percentages greater than 100%.
• Calculate an increase or decrease in quantity by a given percentage.
• Solve problems involving reverse percentages.

#### Rate and speed

• Understand and apply the concepts of average rate, speed, and constant speed to problem-solving.
• Convert units of measurement, such as km/h to m/s, using conversion factors.

#### Algebraic expressions and formulae

• Use letters to represent numbers and interpret notations in algebraic expressions.
• Evaluate algebraic expressions and formulae in given situations.
• Translate simple real-world situations into algebraic expressions.
• Recognise and represent patterns/relationships by finding an algebraic expression for the nth term.
• Add and subtract linear expressions and simplify linear expressions.
• Use brackets and common factors.
• Know how to factorise linear expressions of the form $ax + bx + kay + kby$.
• Expand the product of algebraic expressions.
• Change the subject of a formula.
• Find the value of an unknown quantity in a given formula using appropriate techniques.
• Use formulas such as $(a+b)^2 = a^2+2ab+b^2, (a-b)^2 = a^2-2ab+b^2$ and $a^2-b^2 = (a+b)(a-b)$ to solve problems.
• Factorise quadratic expressions such as $ax^2+bx+c$ and perform multiplication and division of simple algebraic fractions.

#### Functions and graphs

• Understand and apply Cartesian coordinates in two dimensions.
• Use a graph of ordered pairs to represent the relationship between two variables.
• Understand linear functions ($y = ax+b$) and quadratic functions ($y = ax^2+bx+c$).
• Graph linear functions and understand the gradient of a linear graph as the ratio of vertical change to horizontal change (positive and negative gradients).
• Graph quadratic functions and identify their properties, including positive or negative coefficient of $x^2$, maximum and minimum points, and symmetry.
• Sketch graphs of quadratic functions given in the form
• $y = (x - p)^2 + q$
• $y = - (x - p)^2 + q$
• $y = (x - a)(x - b)$
• $y = - (x - a)(x - b)$.
• Graph power functions of the form $y= ax^n$, where $n = -2, -1, 0, 1, 2, 3,$ and simple sums of not more than three of these.
• Graph exponential functions $y=ka^x$, where a is a positive integer.
• Estimate the gradient of a curve by drawing a tangent.

#### Equations and inequalities

• Solve linear equations with one variable.
• Solve simple fractional equations that can be reduced to linear equations.
• Solve simultaneous linear equations in two variables by substitution and elimination methods and graphical methods.
• Solve quadratic equations in one unknown by factorisation, use of formula, completing the square for $y = x^2+px+q$, and graphical method.
• Solve fractional equations that can be reduced to quadratic equations.
• Formulate equations to solve problems.
• Solve linear inequalities in one variable, and represent the solution on the number line.

#### Set language and notation

• Usage of set language.
• Union and intersection of 2 sets.
• Venn diagrams.

#### Matrices

• Display of information in the form of a matrix of any order.
• Interpret the data in a given matrix.
• Calculate the product of a scalar quantity and a matrix.
• Solve problems involving the calculation of the sum and product of two matrices.

### Section 2: Geometry and measurement

#### Angles, Triangles, and Polygons

• Identify and understand right, acute, obtuse, and reflex angles.
• Recognise vertically opposite angles, angles on a straight line, and angles at a point.
• Understand angles formed by two parallel lines and a transversal: corresponding angles, alternate angles, and interior angles.
• Explore properties of triangles, special quadrilaterals, and regular polygons (pentagon, hexagon, octagon, and decagon), including symmetry properties.
• Categorise special quadrilaterals based on their properties.
• Calculate the angle total of the interior and exterior angles of any convex polygon.
• Construct simple geometrical figures from given data, including perpendicular bisectors and angle bisectors, using compasses, rulers, set squares, and protractors where appropriate.

#### Congruence and similarity

• Identify congruent figures.
• Recognise similar figures.
• Explore properties of similar triangles and polygons.
• Understand the enlargement and reduction of a plane figure.
• Interpret scale drawings.
• Examine properties and construction of perpendicular bisectors of line segments and angle bisectors.
• Determine whether two triangles are congruent or similar.
• Calculate the ratio of areas of similar plane figures.
• Determine the ratio of volumes of similar solids.
• Solve simple problems involving similarity and congruence.

#### 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 of equal length.
• The line joining an external point to the centre of the circle bisects the angle between the tangents.
• Angle properties of circles:
• An angle in a semicircle is a right angle.
• The angle between a tangent and the radius of a circle is a right angle.
• The angle at the centre is twice the angle at the circumference.
• Angles in the same segment are of equal measure.
• Angles in opposite segments are supplementary.

#### Pythagoras’ theorem and trigonometry

• Use of Pythagoras’ theorem.
• Determining whether a triangle is right-angled given the lengths of three sides.
• Use of trigonometric ratios (sine, cosine and tangent) of acute angles to calculate unknown sides and angles in right-angled triangles.
• Extending sine and cosine to obtuse angles.
• Use of the formula \begin{align}{1\over2}ab\sin C\end{align} for the area of a triangle.
• Use of sine rule and cosine rule for any triangle.
• Solve problems in two and three dimensions, including those involving angles of elevation and depression and bearings.

#### Mensuration

• Calculate the area of parallelogram and trapezium.
• Solve problems related to the perimeter and area of combined plane figures.
• Determine the volume and surface area of a cube, cuboid, prism, cylinder, pyramid, cone, and sphere.
• Convert $cm^2$ and $m^2$, as well as $cm^3$ and $m^3.$
• Solve problems related to the volume and surface area of combined solids.
• Determine the arc length, sector area, and area of a segment of a circle.
• Use radian measurement of angle, including conversion between radians and degrees.

#### Coordinate Geometry

• Determine the gradient of a straight line by using the coordinates of two points on a line.
• Ascertain the length of a line segment using the coordinates of its endpoints.
• Interpret and determine the equation of a straight-line graph in the format of y=mx+c.
• Solve geometrical problems that involve the application of coordinates.

#### Vectors in two dimensions

• Use of vector notations.
• Represent a vector as a directed line segment.
• Perform translation by a vector.
• Understand position vectors.
• Calculate the magnitude of a vector.
• Use of sum and difference of two vectors to express given vectors in terms of two coplanar vectors.
• Multiply of a vector by a scalar.
• Solve geometric problems involving the use of vectors.

### Section 3: Statistics and probability

#### Data handling and analysis

• Grasp simple concepts in collecting, classifying, and tabulating data.
• Analyse and interpret various forms of statistical representations:
• Tables
• Bar graphs
• Pictograms
• Line graphs
• Pie charts
• Dot diagrams
• Histograms with equal class intervals
• Stem-and-leaf diagrams
• Cumulative frequency diagrams
• Box-and-whisker plots.
• Understand the purposes, uses, advantages, and disadvantages of different forms of statistical representations.
• Draw simple inferences from statistical diagrams.
• Explain why a given statistical diagram may lead to the misinterpretation of data.
• Understand mean, mode, and median as measures of central tendency for a set of data.
• Recognise the purposes and use of mean, mode, and median.
• Calculate the mean for grouped data.
• Understand quartiles and percentiles.
• Explore range, interquartile range, and standard deviation as measures of spread for a set of data.
• Calculate the standard deviation for a set of data (grouped and ungrouped).
• Use the mean and standard deviation to compare two sets of data.

#### Probability

• Demonstrate an understanding of probability as a measure of likelihood.
• Calculate the probability of individual events (including listing all possible outcomes in a simple probability scenario to determine likelihood).
• Determine the probability of combined events (including using possibility diagrams and tree diagrams when applicable).
• Apply addition and multiplication of probabilities (for events that are mutually exclusive or independent).

## A. Maths

The O-level Additional Mathematics syllabus is designed to equip students with fundamental mathematical knowledge for A-level H2 Mathematics. The content is organised into three strands:

• Algebra,
• Geometry and Trigonometry, and,
• Calculus.

### Section 1: Algebra

• Find the maximum or minimum value of a quadratic function using the method of completing a square.
• Understand the conditions for $y=ax^2+bx+c$ to be always positive (or always negative).
• Utilise quadratic functions as models.

#### Equations and inequalities

• Conditions for a quadratic equation to have:
• (i) two real roots, (ii) two equal roots, (iii) no real roots.
• Determine conditions for a given line to:
• (i) intersect a given curve, (ii) be tangent to a given curve, (iii) not intersect a given curve.
• Solve simultaneous equations in two variables by substitution, with one of the equations being a linear equation.
• Solve quadratic inequalities, and represent the solution on the number line.

#### Surds

• Perform the four operations on surds, including rationalising the denominator.
• Solving equations involving surds.

#### Polynomials and partial fractions

• Perform multiplication and division of polynomials.
• Apply the remainder and factor theorems, including factorising polynomials and solving cubic equations.
• Utilise the following polynomial factorisations:
• $a^3+b^3=(a+b)(a^2-ab+b^2)$
• $a^3-b^3=(a-b)(a^2+ab+b^2)$.
• Work with partial fractions with cases where the denominator is not more complicated than:
• $(ax+b)(cx+d)$
• $(ax+b)(cx+d)^2$
• $(ax+b)(x^2+c^2)$.

#### Binomial expansions

• Use of the Binomial Theorem for positive integer n.
• Use of the notations $\displaystyle n!$ and $\displaystyle \binom{n}{r}$.
• Use of the general term $\displaystyle \binom{n}{r}a^{n-r}b^r, 0\le r \le n$ (knowledge of the greatest term and properties of the coefficients is not required).

#### Exponential and logarithmic functions

• Understand exponential and logarithmic functions $a^x$ , $e^x$ , $log_{a}x$, $\ln x$ and their graphs, including:
• laws of logarithms
• equivalence of $y=a^x$and $x=\log_{a}y$
• change of base of logarithms.
• Simplify expressions and solve simple equations involving exponential and logarithmic functions.
• Use exponential and logarithmic functions as models.

### Section 2: Geometry and trigonometry

#### Trigonometric functions, identities, and equations

• Understand six trigonometric functions for angles of any magnitude (in degrees or radians).
• Determine principal values of $\displaystyle \sin^{-1}x, \cos^{-1}x, \tan^{-1}x$.
• Identify exact values of the trigonometric functions for special angles $(30^\circ, 45^\circ, 60^\circ)$ or \begin{align}\bigg(\frac{\pi}{6},\frac{\pi}{4},\frac{\pi}{3}\bigg)\end{align}
• Explore amplitude, periodicity and symmetries related to sine and cosine functions.
• Graphs of $\displaystyle y=a \sin(bx)+c, y=a \sin(\frac{x}{b})+c, y=a \cos(bx)+c, y=a \cos(\frac{x}{b})+c, y=a \tan(bx)$ where $\displaystyle {a}$ is real, $\displaystyle {b}$ is a positive integer and $\displaystyle {c}$ is an integer.
• Utilise the following trigonometric relationships:
\begin{align*} &\frac{\sin A}{\cos A} = \tan A, \frac{\cos A}{\sin A} = \cot A, \sin^2A+cos^2A=1 \\ \\ &\sec^2A=1+\tan^2A, \DeclareMathOperator\cosec{cosec}\cosec^2A=1+\cot^2A \end{align*}
• Apply the expressions of $\displaystyle \sin(A\pm B), \cos(A\pm B), \tan(A \pm B)$.
• Use the formulae for $\displaystyle \sin2A, \cos2A, \tan2A$.
• Express $\displaystyle a\cos\theta+b\sin\theta$ in the form $\displaystyle R\cos(\theta\pm\alpha) \text{ or } R\sin(\theta\pm\alpha)$
• Simplify trigonometric expressions.
• Solve simple trigonometric equations in a given interval (excluding general solution).
• Prove simple trigonometric identities.
• Use trigonometric functions as models.

#### Coordinate geometry in two dimensions

• Condition for two lines to be parallel or perpendicular.
• Midpoint of a line segment.
• Area of a rectilinear figure.
• Coordinate geometry of circles in the form:
$(x-a)^2+(y-b)^2=r^2$
$x^2+y^2+2gx+2fy+c=0$
(excluding problems involving two circles)
• Transformation of given relationships, including $y=ax^n$  and $y=kb^x$, to linear form to determine the unknown constants from a straight-line graph.

#### Proofs in plane geometry

• Understand the properties of parallel lines cut by transversal, perpendicular lines, and angle bisectors.
• Apply geometric principles to triangles, special quadrilaterals, and circles.
• Recognise congruent and similar triangles.
• Utilise the Midpoint Theorem.
• Apply the Tangent-Chord Theorem (Alternate Segment Theorem).

### Section 3: Calculus

#### Differentiation and integration

• Understand the derivative of $f(x)$ as the gradient of the tangent to the graph of $y=f(x)$ at a point.
• Recognise the derivative as the rate of change.
• Use of standard notations
• \begin{align}f'(x), f''(x), \frac{dy}{dx}, \frac{d^2y}{dx^2}\bigg[=\frac{d}{dx}(\frac{dy}{dx})\bigg]\end{align}.
• Find derivatives of $x^n$ , for any rational $n$$\sin x, \cos x, \tan x, e^x, \ln x$, together with constant multiples, sums. and differences.
• Calculate the derivatives of products and quotients of functions
• Apply the Chain Rule.
• Understand increasing and decreasing functions.
• Identify stationary points (maximum and minimum turning points and stationary points of inflexion).
• Use of the second derivative test to discriminate between maxima and minima.
• Apply differentiation to gradients, tangents and normals, connected rates of change and maxima and minima problems.
• Recognise integration as the reverse of differentiation.
• Integrate $X^n$for any rational $\displaystyle n, \sin x, \cos x, \sec^2x, e^x$ together with constant multiples, sums and differences.
• Integrate $(ax+b)^n$ + for any rational $n$, $\sin(ax+b), \cos(ax+b)$ and $e^{ax+b}$.
• Understand the definite integral as an area under a curve.
• Evaluate definite integrals.
• Find the area of a region bounded by a curve and line(s) (excluding the area of the region between 2 curves).
• Find areas of regions below the x-axis.
• Apply differentiation and integration to problems involving displacement, velocity, and acceleration of a particle moving in a straight line.

## Physics

### Section 1: Measurement

• Physical quantities, units, and measurement
• Physical quantities and SI units
• Measurement
• Scalars and vectors

### Section 2: Newtonian Mechanics

• Kinematics
• Speed, velocity, and acceleration
• Graphical analysis of motion
• Free-fall
• Dynamics
• Types of forces
• Mass, weight, and gravitational field
• Newton's laws of motion
• Effects of resistive forces of motion
• Turning effects of forces
• Moments
• Equilibrium
• Centre of gravity and stability
• Pressure
• Pressure
• Density and fluid pressure
• Energy
• Energy stores and transfers
• Work, power, and efficiency
• Energy resources

### Section 3: Thermal Physics

• Kinetic particle model of matter
• States of matter
• Kinetic particle model
• Thermal processes
• Thermal equilibrium
• Conduction
• Convection
• Thermal properties of matter
• Internal energy
• Specific heat capacity
• Melting, boiling, and evaporation
• Specific latent heat

### Section 4: Waves

• General properties of waves
• Describing wave motion
• Wave properties
• Sound
• Electromagnetic spectrum
• Properties of electromagnetic waves
• Applications of electromagnetic waves
• Effects of electromagnetic waves on cells and tissues
• Light
• Reflection of light
• Refraction of light
• Thin converging lenses

### Section 5: Electricity and magnetism

• Static electricity
• Electric charge
• Electric field
• Dangers and applications of electrostatic charging
• Current of electricity
• Conventional current and electron flow
• Electromotive force and potential difference
• Resistance
• D.C. circuits
• Circuit diagrams
• Series and parallel circuits
• Action and use of circuit components
• Practical electricity
• Electrical working, power, and energy
• Dangers of electricity
• Safe use of electricity at home
• Magnetism
• Laws of magnetism
• Magnetic properties of matter
• Magnetic field
• Electromagnetism
• Magnetic effect of a current
• Force on a current-carrying conductor
• The d.c. motor
• Electromagnetic induction
• Principles of electromagnetic induction
• The a.c. generator
• The transformer

• The composition of the atom
• Dangers and uses of radioactivity

## Chemistry

### Section 1: Matter - Structures and Properties

• Experimental chemistry
• Experimental design
• Methods of purification and analysis
• The particulate nature of matter
• Kinetic particle theory
• Atomic structure
• Chemical bonding and structure
• Ionic bonding
• Covalent bonding
• Metallic bonding
• Structure and properties of materials

### Section 2: Chemical reactions

• Chemical calculations
• Formulae and equation writing
• The mole concept and stoichiometry
• Acid-base chemistry
• Acids and bases
• Salts
• Ammonia
• Qualitative analysis
• Redox chemistry
• Oxidation and reduction
• Electrochemistry
• Patterns in the periodic table
• Periodic table trends
• Group properties
• Transition elements
• Reactivity series
• Chemical energetics
• Rate of reactions

### Section 3: Chemistry in a sustainable world

• Organic chemistry
• Fuels and crude oil
• Hydrocarbons
• Alcohols, carboxylic acids, and esters
• Polymers
• Maintaining air quality

## Biology

### Section 1: Cells and the chemistry of life

• Cell structure and organisation
• Plant and animal cells
• Cell specialisation
• Movement of substances
• Diffusion
• Osmosis
• Active transport
• Biological molecules
• Carbohydrates, fats, and proteins
• Enzymes
SECTION 2: The human body - Maintaining life
• Nutrition in humans
• Human digestive system
• Physical and chemical digestion
• Absorption and assimilation
• Transport in humans
• Parts and functions of the circulatory system
• Blood
• Heart and cardiac cycle
• Coronary heart disease
• Respiration in humans
• Human gas exchange
• Cellular respiration
• Excretion in Humans
• Structure and function of kidneys
• Kidney dialysis
• Homeostasis, co-ordination, and response in humans
• Principles of homeostasis
• Hormonal control
• Nervous control
• Infectious diseases in humans
• Organisms affecting human health
• Influenza and pneumococcal disease
• Prevention and treatment of infectious diseases
SECTION 3: Living together - Plants, Animals, and Ecosystems
• Nutrition and transport in flowering plants
• Plant structure
• Photosynthesis
• Transpiration
• Translocation
• Organisms and their environment
• Energy flow
• Food chains and food webs
• Carbon cycle and global warming
• Effects of man on the ecosystem
• Conservation
Section 4: Continuity of life
• Molecular genetics
• The structure of DNA
• From DNA to proteins
• Genetic engineering
• Reproduction
• Asexual reproduction
• Cell division
• Sexual reproduction in flowering plants
• Sexual reproduction in humans
• Sexually transmitted diseases
• Inheritance
• The passage of genetic information from parent to offspring
• Monohybrid crosses
• Variation
• Natural selection