SPM Add Maths study guide
SPM Add Maths · Work through your exam, one topic at a time.
SPM Additional Mathematics (often called Add Maths) is a Malaysian upper-secondary elective taken alongside the core SPM Mathematics paper. It is aimed at students planning to enter science, engineering, computing, accounting or actuarial pathways, and it is generally expected for those routes at pre-university level. The SPM Add Maths study guide has 12 sections and about 3,007 words.
01Functions
Functions opens the SPM Additional Mathematics syllabus and tests whether you can use function notation as a working language rather than just recite definitions. Expect composite functions, inverse functions, and questions that link the domain, the range and the graph.
296 words, about 1 min02Quadratic Equations and Quadratic Functions
Quadratic equations and quadratic functions are examined together because the algebra of roots and the geometry of the parabola are two views of one object. SPM questions ask for the nature of the roots, equations formed from given roots, completed-square form, graphs and quadratic inequalities.
328 words, about 2 min03Simultaneous Equations
Simultaneous equations in SPM Additional Mathematics almost always pair one linear equation with one non-linear equation such as a circle, parabola or hyperbola. The exam tests substitution, the link between the number of solutions and the number of intersection points, and the use of the discriminant to find an unknown constant.
267 words, about 1 min04Indices and Logarithms
Indices and logarithms test fluency with the laws of indices, the equivalence between exponential and logarithmic form, and solving equations that mix the two. SPM also expects change of base and spotting when a substitution such as y = 2ˣ turns an equation into a quadratic.
245 words, about 1 min05Coordinate Geometry
Coordinate geometry in SPM Additional Mathematics moves between algebra and the Cartesian plane: distance, midpoint, gradient, equations of straight lines, parallel and perpendicular lines, areas of polygons and loci. The exam rewards clean formula use and punishes sign slips.
237 words, about 1 min06Circular Measure
Circular measure deals with arcs, sectors, segments and chords using angles measured in radians. SPM tests the radian–degree conversion, the arc and sector formulas, and composite perimeters or areas where a triangle is subtracted from a sector.
240 words, about 1 min07Differentiation
Differentiation is the largest calculus domain in SPM Additional Mathematics. It tests the derivative concept, the standard rules, tangents and normals, stationary points and their classification, rates of change and small increments.
223 words, about 1 min08Integration
Integration reverses differentiation and, in SPM Additional Mathematics, is applied to definite integrals, areas under curves, areas between curves and volumes of revolution. The exam expects correct antiderivatives and careful handling of limits and signs.
223 words, about 1 min09Vectors
Vectors in SPM Additional Mathematics are two-dimensional. The exam tests magnitude, unit vectors, addition and subtraction, multiplication by a scalar, position vectors and collinearity.
237 words, about 1 min10Solution of Triangles
Solution of triangles covers the sine rule, the cosine rule and the area formula, plus bearings and the ambiguous case. SPM tests choosing the correct rule from the given information and interpreting obtuse angles correctly.
234 words, about 1 min11Index Numbers
Index numbers measure changes in a quantity relative to a base year and are used to build composite indices with weightages. SPM tests price and quantity indices, the interpretation of index values, and weighted composite indices.
206 words, about 1 min12Motion Along a Straight Line
Kinematics of linear motion applies differentiation and integration to displacement, velocity and acceleration along a straight line. SPM tests the relationships between s, v and a, the rest condition, maximum or minimum displacement, and total distance travelled.
271 words, about 1 min