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.

Learn more about each O Level subject:

• English
• Maths
• A. Maths
• Physics
• Chemistry
• Biology

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.
• Add and subtract algebraic fractions with linear or quadratic denominators.

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

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

Quadratic functions

• 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
  • Radiation
• 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

Section 6: Radioactivity

• Radioactivity
  • The composition of the atom
  • Radioactive decay
  • 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

• 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

• 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

• 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

Q1: Where can I download past-year Secondary exam papers to prepare my child for O-Level 2024?