Synergy Education
CAMBRIDGE O LEVEL
∫f(x)dx
MATHEMATICS
KEY POINTS
BOOKLET
Syllabus 4024 | 2025–2027
1 Number
2 Algebra & Graphs
3 Coordinate Geometry
4 Geometry
5 Mensuration
6 Trigonometry
7 Vectors & Transforms
8 Probability
x²+bx+c=0
9 Statistics
Compiled by Muzammil Abid | Synergy Education
Cambridge O Level Mathematics | Syllabus 4024 | 2025–2027
Cambridge Assessment International Education
, O Level Mathematics | Syllabus D 4024 | Key Points Booklet Synergy Education
ABOUT THIS BOOKLET
This booklet has been meticulously compiled by Muzammil Abid of Synergy Education as a
precise, exam-focused companion for students preparing for Cambridge O Level Mathematics
Syllabus D (4024). Every chapter strictly follows the official Cambridge 4024 syllabus for 2025-2027.
Compiled by Muzammil Abid
Institute Synergy Education
Syllabus Cambridge O Level Mathematics Syllabus D
Code / Year 4024 | 2025-2026-2027 (Current)
Edition v4 Final — 12 chapters, full syllabus coverage
Syllabus note Congruency, Locus, and Matrices excluded (not in 4024)
CHAPTER MAP
Ch. Topic Key Content
1 Number Types, HCF/LCM (algebraic), fractions, %, indices, bounds, surds
2 Algebra & Graphs Expressions, equations, inequalities, variation, graphs, functions
3 Coordinate Geometry Gradient, midpoint, distance, equation of line, axes concepts
4 Geometry Angles, polygons, circle theorems, tangent theorems, similarity
5 Mensuration Area, perimeter, surface area, volume (2D and 3D shapes)
6 Trigonometry SOH-CAH-TOA, sine/cosine rule, bearings, 3D trigonometry
7 Transformations & Vectors
Translation, reflection, rotation, enlargement, vectors
8 Probability Outcomes, tree diagrams, Venn diagrams, conditional probability
9 Statistics Averages, spread, histograms, cumulative frequency, box plots
10 Sequences & Patterns nth term, arithmetic, geometric, quadratic, special patterns
11 Symmetry Line symmetry, rotational symmetry, 3D planes of symmetry
12 Similarity Scale factors, area/volume ratios, similarity proofs
Muzammil Abid | Synergy Education 2 Cambridge 4024 | 2025–2027
, O Level Mathematics | Syllabus D 4024 | Key Points Booklet Synergy Education
NUMBER CHAPTER 1
1 Integers, fractions, powers, surds, percentages & more
1.1 Number Types
■ Natural numbers: 1, 2, 3, 4, …
■ Integers: …−3, −2, −1, 0, 1, 2, 3, …
■ Rational numbers: can be written as p/q (e.g. 3/4, 0.6, −2)
■ Irrational numbers: cannot be expressed as fraction (e.g. √2, π)
■ Real numbers: all rational and irrational numbers
■ Prime: exactly two factors — 1 and itself (2, 3, 5, 7, 11, …)
■ Composite: more than two factors (4, 6, 8, 9, …)
1.2 Factors, Multiples, HCF & LCM
HCF (GCD): largest factor common to two or more numbers
LCM: smallest multiple common to two or more numbers
◆ EXAMPLE
Find HCF and LCM of 12 and 18:
12 = 2^2 x 3 18 = 2 x 3^2
HCF = 2 x 3 = 6 LCM = 2^2 x 3^2 = 36
HCF & LCM of Algebraic Expressions (Variables with Powers)
star KEY POINT
HCF of algebraic terms: take LOWEST power of each COMMON factor (variable or number).
LCM of algebraic terms: take HIGHEST power of EVERY factor appearing in any term.
Term Prime factorisation Notes
12a^3b^2 2^2 x 3 x a^3 x b^2 Factorise coefficient first
18a^2b^4c 2 x 3^2 x a^2 x b^4 x c List ALL prime and variable factors
HCF of both 2 x 3 x a^2 x b^2 = 6a^2b^2 Lowest power of each COMMON factor
LCM of both 2^2 x 3^2 x a^3 x b^4 x c = 36a^3b^4c
Highest power of EVERY factor
Muzammil Abid | Synergy Education 3 Cambridge 4024 | 2025–2027
, O Level Mathematics | Syllabus D 4024 | Key Points Booklet Synergy Education
◆ EXAMPLE
HCF and LCM of 8x^3y^2 and 12x^2y^5z:
8x^3y^2 = 2^3 x x^3 x y^2
12x^2y^5z = 2^2 x 3 x x^2 x y^5 x z
HCF = 2^2 x x^2 x y^2 = 4x^2y^2 (lowest powers of COMMON factors: 2,x,y)
LCM = 2^3 x 3 x x^3 x y^5 x z = 24x^3y^5z (highest powers of ALL factors)
Factor type HCF rule LCM rule
Numeric coefficient HCF of the numbers LCM of the numbers
Variable in BOTH terms (e.g.
Takex)LOWER power: x^min(m,n) Take HIGHER power: x^max(m,n)
Variable in ONE term onlyExclude from HCF Include in LCM
◆ EXAMPLE
HCF and LCM of x^4y^3 and x^2y^6z^2:
Common vars: x and y Unique to 2nd: z
HCF = x^min(4,2) x y^min(3,6) = x^2 y^3
LCM = x^max(4,2) x y^max(3,6) x z^2 = x^4 y^6 z^2
1.3 Fractions, Decimals & Percentages
Fraction → Decimal: divide numerator ÷ denominator
Decimal → %: multiply by 100
% change = (Change / Original) × 100
Reverse %: Original = Given amount / (1 ± rate/100)
Simple Interest: I = PRT / 100 (P=Principal, R=rate%, T=time in years)
Compound Interest: A = P(1 + r/100)■
Depreciation: V = V■ × (1 − r/100)■
★ KEY POINT
To find original before % increase/decrease: divide by (1±r/100).
Compound growth: multiply by the multiplier each period.
1.4 Indices & Standard Form
Muzammil Abid | Synergy Education 4 Cambridge 4024 | 2025–2027
CAMBRIDGE O LEVEL
∫f(x)dx
MATHEMATICS
KEY POINTS
BOOKLET
Syllabus 4024 | 2025–2027
1 Number
2 Algebra & Graphs
3 Coordinate Geometry
4 Geometry
5 Mensuration
6 Trigonometry
7 Vectors & Transforms
8 Probability
x²+bx+c=0
9 Statistics
Compiled by Muzammil Abid | Synergy Education
Cambridge O Level Mathematics | Syllabus 4024 | 2025–2027
Cambridge Assessment International Education
, O Level Mathematics | Syllabus D 4024 | Key Points Booklet Synergy Education
ABOUT THIS BOOKLET
This booklet has been meticulously compiled by Muzammil Abid of Synergy Education as a
precise, exam-focused companion for students preparing for Cambridge O Level Mathematics
Syllabus D (4024). Every chapter strictly follows the official Cambridge 4024 syllabus for 2025-2027.
Compiled by Muzammil Abid
Institute Synergy Education
Syllabus Cambridge O Level Mathematics Syllabus D
Code / Year 4024 | 2025-2026-2027 (Current)
Edition v4 Final — 12 chapters, full syllabus coverage
Syllabus note Congruency, Locus, and Matrices excluded (not in 4024)
CHAPTER MAP
Ch. Topic Key Content
1 Number Types, HCF/LCM (algebraic), fractions, %, indices, bounds, surds
2 Algebra & Graphs Expressions, equations, inequalities, variation, graphs, functions
3 Coordinate Geometry Gradient, midpoint, distance, equation of line, axes concepts
4 Geometry Angles, polygons, circle theorems, tangent theorems, similarity
5 Mensuration Area, perimeter, surface area, volume (2D and 3D shapes)
6 Trigonometry SOH-CAH-TOA, sine/cosine rule, bearings, 3D trigonometry
7 Transformations & Vectors
Translation, reflection, rotation, enlargement, vectors
8 Probability Outcomes, tree diagrams, Venn diagrams, conditional probability
9 Statistics Averages, spread, histograms, cumulative frequency, box plots
10 Sequences & Patterns nth term, arithmetic, geometric, quadratic, special patterns
11 Symmetry Line symmetry, rotational symmetry, 3D planes of symmetry
12 Similarity Scale factors, area/volume ratios, similarity proofs
Muzammil Abid | Synergy Education 2 Cambridge 4024 | 2025–2027
, O Level Mathematics | Syllabus D 4024 | Key Points Booklet Synergy Education
NUMBER CHAPTER 1
1 Integers, fractions, powers, surds, percentages & more
1.1 Number Types
■ Natural numbers: 1, 2, 3, 4, …
■ Integers: …−3, −2, −1, 0, 1, 2, 3, …
■ Rational numbers: can be written as p/q (e.g. 3/4, 0.6, −2)
■ Irrational numbers: cannot be expressed as fraction (e.g. √2, π)
■ Real numbers: all rational and irrational numbers
■ Prime: exactly two factors — 1 and itself (2, 3, 5, 7, 11, …)
■ Composite: more than two factors (4, 6, 8, 9, …)
1.2 Factors, Multiples, HCF & LCM
HCF (GCD): largest factor common to two or more numbers
LCM: smallest multiple common to two or more numbers
◆ EXAMPLE
Find HCF and LCM of 12 and 18:
12 = 2^2 x 3 18 = 2 x 3^2
HCF = 2 x 3 = 6 LCM = 2^2 x 3^2 = 36
HCF & LCM of Algebraic Expressions (Variables with Powers)
star KEY POINT
HCF of algebraic terms: take LOWEST power of each COMMON factor (variable or number).
LCM of algebraic terms: take HIGHEST power of EVERY factor appearing in any term.
Term Prime factorisation Notes
12a^3b^2 2^2 x 3 x a^3 x b^2 Factorise coefficient first
18a^2b^4c 2 x 3^2 x a^2 x b^4 x c List ALL prime and variable factors
HCF of both 2 x 3 x a^2 x b^2 = 6a^2b^2 Lowest power of each COMMON factor
LCM of both 2^2 x 3^2 x a^3 x b^4 x c = 36a^3b^4c
Highest power of EVERY factor
Muzammil Abid | Synergy Education 3 Cambridge 4024 | 2025–2027
, O Level Mathematics | Syllabus D 4024 | Key Points Booklet Synergy Education
◆ EXAMPLE
HCF and LCM of 8x^3y^2 and 12x^2y^5z:
8x^3y^2 = 2^3 x x^3 x y^2
12x^2y^5z = 2^2 x 3 x x^2 x y^5 x z
HCF = 2^2 x x^2 x y^2 = 4x^2y^2 (lowest powers of COMMON factors: 2,x,y)
LCM = 2^3 x 3 x x^3 x y^5 x z = 24x^3y^5z (highest powers of ALL factors)
Factor type HCF rule LCM rule
Numeric coefficient HCF of the numbers LCM of the numbers
Variable in BOTH terms (e.g.
Takex)LOWER power: x^min(m,n) Take HIGHER power: x^max(m,n)
Variable in ONE term onlyExclude from HCF Include in LCM
◆ EXAMPLE
HCF and LCM of x^4y^3 and x^2y^6z^2:
Common vars: x and y Unique to 2nd: z
HCF = x^min(4,2) x y^min(3,6) = x^2 y^3
LCM = x^max(4,2) x y^max(3,6) x z^2 = x^4 y^6 z^2
1.3 Fractions, Decimals & Percentages
Fraction → Decimal: divide numerator ÷ denominator
Decimal → %: multiply by 100
% change = (Change / Original) × 100
Reverse %: Original = Given amount / (1 ± rate/100)
Simple Interest: I = PRT / 100 (P=Principal, R=rate%, T=time in years)
Compound Interest: A = P(1 + r/100)■
Depreciation: V = V■ × (1 − r/100)■
★ KEY POINT
To find original before % increase/decrease: divide by (1±r/100).
Compound growth: multiply by the multiplier each period.
1.4 Indices & Standard Form
Muzammil Abid | Synergy Education 4 Cambridge 4024 | 2025–2027
