MATHWITHCYE

SPM Add Maths Pro

KSSM Latest Syllabus • Form 4 & Form 5

Exam Format KBAT Strategy Full Question Bank & Marking Schemes
SPM Additional Mathematics (Kod 3472/1 & 3472/2)

Comprehensive Revision & Exam-Standard Practice

Complete curriculum covering all 10 Form 4 Chapters and 8 Form 5 Chapters. Packed with progressive worked examples, SPM Paper 1 & Paper 2 format questions, authentic examiner marking schemes, and high-impact KBAT real-world challenges.

18
Complete Chapters
100%
KSSM Latest Format
KBAT+
HOTS Modeling in Every Ch.
P1 & P2
Interactive & Print-Ready
Form 4 • Chapter 1 Paper 1 & 2

Functions

Fungsi

Composite functions $f(g(x))$, inverse functions $f^{-1}(x)$, self-inverses, domain/range constraints, and algebraic mapping modeling.

$fg(x) \neq gf(x)$ $f^{-1}(x)$ KBAT Mapping
Form 4 • Chapter 2 Paper 1 & 2

Quadratic Functions

Fungsi Kuadratik

Completing square $a(x-h)^2+k$, vertex extrema, discriminant conditions ($b^2 - 4ac \gtrless 0$), quadratic inequalities, and projectile flight.

$b^2-4ac$ Vertex $(h,k)$ KBAT Trajectory
Form 4 • Chapter 3 Paper 1 & 2

Systems of Equations

Sistem Persamaan

Simultaneous linear equations in 3 variables, one linear and one non-linear equation, substitution/elimination methods, and real-life pricing models.

3 Variables Non-linear KBAT Cost Optimization
Form 4 • Chapter 4 Paper 1 & 2

Indices, Surds & Logarithms

Indeks, Surd dan Logaritma

Laws of indices, rationalizing binomial surds with conjugates, logarithm laws, change of base formula, and exponential growth/decay models.

Surd Conjugate $\log_a b = \frac{\log_c b}{\log_c a}$ KBAT Half-Life
Form 4 • Chapter 5 Paper 1 & 2

Progressions

Janjang

Arithmetic Progression ($a, d, T_n, S_n$), Geometric Progression ($a, r, T_n, S_n$), sum to infinity $S_\infty = \frac{a}{1-r}$, and recurring loan/saving models.

AP: $T_n, S_n$ GP: $S_\infty$ KBAT Compound Savings
Form 4 • Chapter 6 Paper 2 Sec B (10m)

Linear Law

Hukum Linear

Reduction of non-linear equations to linear form $Y = mX + c$, line of best fit plotting rules, determining constants, and experimental error identification.

$Y = mX + c$ Best Fit Line KBAT Lab Data
Form 4 • Chapter 7 Paper 1 & 2

Coordinate Geometry

Geometri Koordinat

Internal division $m:n$, parallel/perpendicular lines ($m_1 m_2 = -1$), shoelace polygon area, and equation of circular/distance-ratio loci.

$m_1 m_2 = -1$ Locus $PA:PB$ KBAT Radar Beacon
Form 4 • Chapter 8 Paper 1 & 2

Vectors

Vektor

Vector addition/subtraction, collinearity condition $\vec{a} = k\vec{b}$, unit vectors $\hat{r}$, column & Cartesian forms ($x\mathbf{i} + y\mathbf{j}$), and resultant velocity navigation.

$\mathbf{i}, \mathbf{j}$ Unit Vector Collinear $\vec{AB} = \lambda \vec{BC}$ KBAT Crosswind Drift
P2 Sec C • F4 Ch 9 10 Marks Guaranteed

Solution of Triangles

Penyelesaian Segi Tiga

Sine Rule, Cosine Rule, ambiguous case of sine ($SSA$), Heron's formula, 3D triangular spatial visualization, and shortest distance from vertex to line.

Sine & Cosine Rules Ambiguous Case KBAT 3D Land Surveying
P2 Sec C • F4 Ch 10 10 Marks Guaranteed

Index Numbers

Nombor Indeks

Price index $I = \frac{Q_1}{Q_0} \times 100$, composite index $\bar{I} = \frac{\sum I_i w_i}{\sum w_i}$, chain index shifting, pie chart/bar weights, and inflation budgeting.

$\bar{I} = \frac{\sum Iw}{\sum w}$ Chain Base Shift KBAT Consumer Cost
Form 5 • Chapter 1 Paper 1 & 2

Circular Measure

Sukatan Membulat

Radian angle measure, arc length $s = r\theta$, sector area $A = \frac{1}{2}r^2\theta$, segment area, perimeter of composite figures, and pulley belt geometry.

$s = r\theta$ $A = \frac{1}{2}r^2(\theta - \sin\theta)$ KBAT Belt-Pulley
Form 5 • Chapter 2 High Weightage (P1 & P2)

Differentiation

Pembezaan

Product, quotient, and chain rules; tangents and normals ($m_1 m_2 = -1$); small changes & approximations; connected rates of change; stationary points and optimization.

Rates: $\frac{dy}{dt} = \frac{dy}{dx} \cdot \frac{dx}{dt}$ Max/Min $\frac{d^2y}{dx^2}$ KBAT Inverted Cone
Form 5 • Chapter 3 High Weightage (P1 & P2)

Integration

Pengamiran

Indefinite integrals, finding constant $c$, definite integrals, area between curve and axis or line, and volume of revolution generated by rotating about $x$- or $y$-axis.

Area: $\int_a^b (y_1 - y_2) dx$ Volume: $\pi \int y^2 dx$ KBAT Vase Reservoir
Form 5 • Chapter 4 Paper 1 & 2

Permutations & Combinations

Pilihatur dan Gabungan

Multiplication rule, permutations $^nP_r$, identical items, circular permutations $(n-1)!$, combinations $^nC_r$, condition restrictions (together/separated), and passcode security.

Pilihatur $^nP_r$ Gabungan $^nC_r$ KBAT Committee Assembly
Form 5 • Chapter 5 Paper 1 & 2 (High Weightage)

Probability Distribution

Taburan Kebarangkalian

Binomial Distribution $B(n, p)$, mean $\mu = np$, standard deviation $\sigma = \sqrt{npq}$, Normal Distribution $Z = \frac{X-\mu}{\sigma}$, standard normal curve symmetry, and reverse $Z$-score finding.

$P(X=r) = {^nC_r} p^r q^{n-r}$ $Z = \frac{X - \mu}{\sigma}$ KBAT Industrial QC
Form 5 • Chapter 6 Paper 1 & 2 (Trig Graph)

Trigonometric Functions

Fungsi Trigonometri

Trigonometric graphs $y = a\sin bx + c$, drawing linear superposition lines to find number of solutions, proving identities, and solving trigonometric equations within specific domains.

Identities: $\sin^2\theta + \cos^2\theta = 1$ No. of Solutions KBAT Tidal Oscillations
P2 Sec C • F5 Ch 7 10 Marks Guaranteed

Linear Programming

Pengaturcaraan Linear

Formulating inequalities from real-world constraints, graphing the feasible region $R$, and using the objective function line $ax + by = k$ to find maximum profit or minimum cost.

Constraints Modeling Objective Line $k$ KBAT Factory Profit
P2 Sec C • F5 Ch 8 10 Marks Guaranteed

Kinematics of Linear Motion

Kinematik Gerakan Linear

Displacement $s$, velocity $v = \frac{ds}{dt}$, acceleration $a = \frac{dv}{dt}$, integration $\int v\,dt = s$, initial instantaneous rest, reversing direction, and total distance traveled.

$v = \frac{ds}{dt},\; a = \frac{dv}{dt}$ Total Distance $\neq |s|$ KBAT Autonomous EV Braking
KSSM Examination Architecture

Latest SPM Additional Mathematics Exam Blueprint

Mastering both papers requires strategic time management and careful question selection in Paper 2 Section B and Section C.

Paper 1 (3472/1)

Duration: 2 Hours • Total: 80 Marks

80 Marks
A
Bahagian A (Section A) — 64 Marks

12 Compulsory Questions. Question weightage ranges between 3 to 8 marks each. Tests core mathematical concepts, algebraic precision, and standard applications.

B
Bahagian B (Section B) — 16 Marks

3 Questions given • Answer any 2 questions (8 marks each). Multi-tier analytical problem solving requiring sustained working and conceptual synthesis.

Recommended Pace: 1.5 minutes per mark. Allocate ~95 minutes for Section A, ~20 minutes for Section B, and 5 minutes for final checks.

Paper 2 (3472/2)

Duration: 2 Hours 30 Mins • Total: 100 Marks

100 Marks
A
Bahagian A (Section A) — 50 Marks

7 Compulsory Questions (6 to 8 marks each). Covers non-linear simultaneous equations, coordinate geometry, calculus, and progressions.

B
Bahagian B (Section B) — 30 Marks

4 Questions given • Answer any 3 questions (10 marks each). High-yield topics: Linear Law, Differentiation & Integration, Probability Distributions, Circular Measure.

C
Bahagian C (Section C) — 20 Marks [Application Topics]

4 Questions given • Answer any 2 questions (10 marks each): Solution of Triangles, Index Numbers, Linear Programming, Kinematics.

KBAT / HOTS Mastery Formula

How to Score Full Marks in KBAT Questions

SPM exam scripts allocate up to 35% to 40% of marks to KBAT (Higher Order Thinking Skills). To secure the full method ($K$) and answer ($N$) marks:

  • State defined algebraic variables explicitly before modeling.
  • Sketch accompanying geometric/physical boundary diagrams.
  • Always verify physical validity (e.g. reject negative distances or $r > 1$).
  • Conclude with proper context units (e.g. $\text{cm}^3/\text{s}$, RM, or hectares).