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Matric (SSC) Mathematics Syllabus
The Mathematics syllabus for Matric (SSC) in full: 15 chapters and 52 topics, every one listed below, plus 50 Mathematics flashcards with answers.
Mathematics syllabus: all 15 chapters
Expand any chapter to see its topics and sub-topics.
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Matrices and Determinants
5 topics- Types of Matrices
- Addition and Subtraction of Matrices
- Multiplication of Matrices
- Determinant and Inverse of a Matrix
- Solution of Simultaneous Linear Equations
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Real and Complex Numbers
4 topics- Real Numbers and Their Properties
- Radicals and Radicands
- Laws of Exponents
- Complex Numbers and Operations
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Logarithms
4 topics- Scientific Notation
- Common and Natural Logarithms
- Laws of Logarithms
- Application of Logarithms
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Algebraic Expressions and Formulas
3 topics- Algebraic Expressions and Rational Expressions
- Algebraic Formulas
- Surds and Their Rationalization
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Factorization
3 topics- Methods of Factorization
- Factor Theorem and Remainder Theorem
- HCF and LCM of Polynomials
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Algebraic Manipulation
3 topics- Highest Common Factor and Least Common Multiple
- Simplification of Algebraic Fractions
- Square Root of Algebraic Expressions
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Linear Equations and Inequalities
3 topics- Linear Equations
- Equations Involving Absolute Value
- Linear Inequalities and Their Solution
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Linear Graphs and Their Application
3 topics- Cartesian Plane and Coordinate Geometry
- Graphs of Linear Equations
- Graphical Solution of Equations in Two Variables
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Quadratic Equations
4 topics- Solution by Factorization and Completing the Square
- Quadratic Formula
- Nature of Roots and Discriminant
- Equations Reducible to Quadratic Form
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Introduction to Coordinate Geometry
3 topics- Distance Formula
- Collinear Points
- Midpoint Formula and Its Applications
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Algebraic Sentences and Variations
3 topics- Ratio and Proportion
- Direct and Inverse Variation
- Theorems on Proportion
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Sets and Functions
4 topics- Operations on Sets
- Venn Diagrams
- Ordered Pairs and Cartesian Product
- Binary Relations and Functions
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Basic Statistics
3 topics- Frequency Distribution
- Measures of Central Tendency
- Measures of Dispersion
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Introduction to Trigonometry
4 topics- Measurement of Angles (Degrees and Radians)
- Trigonometric Ratios
- Trigonometric Identities
- Angles of Elevation and Depression
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Theorems Related to Circles
3 topics- Chords of a Circle
- Tangents to a Circle
- Angle in a Segment
Matric (SSC) Mathematics flashcards — 50 questions with answers
What is a matrix?
A rectangular array of numbers (elements) arranged in rows and columns, enclosed in brackets.
What is the order (dimension) of a matrix?
It is written as m x n, where m is the number of rows and n is the number of columns.
What is a row matrix?
A matrix that has only one row, i.e. of order 1 x n.
What is a column matrix?
A matrix that has only one column, i.e. of order m x 1.
What is a square matrix?
A matrix in which the number of rows equals the number of columns (order n x n).
What is a rectangular matrix?
A matrix in which the number of rows is not equal to the number of columns (m not equal to n).
What is a null (zero) matrix?
A matrix in which every element is zero, denoted by O.
What is a diagonal matrix?
A square matrix in which all elements except those on the main diagonal are zero (and at least one diagonal element is non-zero).
What is a scalar matrix?
A diagonal matrix in which all the main-diagonal elements are equal.
What is an identity (unit) matrix?
A scalar matrix in which every main-diagonal element is 1; denoted by I. It acts as the multiplicative identity.
When are two matrices said to be equal?
When they have the same order and their corresponding elements are equal.
What is the transpose of a matrix A?
The matrix A^t obtained by interchanging the rows and columns of A; a matrix of order m x n becomes n x m.
What is a symmetric matrix?
A square matrix that equals its transpose, i.e. A = A^t.
What is a skew-symmetric matrix?
A square matrix for which A^t = -A; all its main-diagonal elements are zero.
What is the condition for adding or subtracting two matrices?
They must have the same order (same number of rows and columns).
How are two matrices added?
By adding their corresponding (same-position) elements.
State the commutative law for matrix addition.
A + B = B + A, i.e. matrix addition is commutative.
State the associative law for matrix addition.
(A + B) + C = A + (B + C).
What is the additive identity for matrices?
The null matrix O of the same order, since A + O = A.
What is the additive inverse of a matrix A?
The matrix -A (each element negated), since A + (-A) = O.
Show the other 30 Mathematics flashcards
How do you multiply a matrix by a scalar k?
Multiply every element of the matrix by k.
What is the condition for the product AB of two matrices to be defined?
The number of columns of A must equal the number of rows of B.
If A is m x n and B is n x p, what is the order of AB?
The product AB has order m x p.
Is matrix multiplication commutative?
No. In general AB is not equal to BA.
How is each element of the product matrix AB obtained?
By multiplying the elements of a row of A with the corresponding elements of a column of B and adding the products (row-by-column rule).
For a 2x2 matrix A = [[a, b],[c, d]], what is its determinant?
det A = |A| = ad - bc.
What is a singular matrix?
A square matrix whose determinant is zero (|A| = 0). It has no inverse.
What is a non-singular matrix?
A square matrix whose determinant is non-zero (|A| not equal to 0). It has an inverse.
What is the adjoint of a 2x2 matrix A = [[a, b],[c, d]]?
adj A = [[d, -b],[-c, a]] — swap the main-diagonal elements and negate the other two.
What is the formula for the inverse of a non-singular 2x2 matrix A?
A^(-1) = (1/|A|) adj A, valid only when |A| is not equal to 0.
What is the key property of a matrix and its inverse?
A A^(-1) = A^(-1) A = I, the identity matrix.
Name two methods used to solve simultaneous linear equations using matrices.
The matrix-inverse method and Cramer's rule (the determinant method).
For the system ax + by = m, cx + dy = n, what is x by Cramer's rule?
x = |[[m, b],[n, d]]| / |[[a, b],[c, d]]|, i.e. the ratio of the x-determinant to the coefficient determinant.
What does it mean if the coefficient determinant of a linear system is zero?
The system has no unique solution (it is either inconsistent or has infinitely many solutions).
What are real numbers?
The set of all rational and irrational numbers, denoted by R.
What is the difference between a rational and an irrational number?
A rational number can be written as p/q (q not 0) with terminating or recurring decimals; an irrational number cannot, and its decimal is non-terminating and non-recurring.
State the closure property of real numbers under addition and multiplication.
For all real a, b: a + b and a x b are also real numbers.
State the distributive property of real numbers.
a(b + c) = ab + ac (multiplication distributes over addition).
What is the multiplicative inverse of a non-zero real number a?
1/a, since a x (1/a) = 1.
In the radical expression nth-root of a, name the parts.
n is the index (order), the symbol is the radical sign, and a is the radicand.
Express the radical nth-root of a^m in exponential (index) form.
a^(m/n).
State the product law of exponents.
a^m x a^n = a^(m+n).
State the quotient law of exponents.
a^m / a^n = a^(m-n).
What is the value of a^0 (a not equal to 0)?
a^0 = 1.
What does a negative exponent a^(-n) equal?
a^(-n) = 1 / a^n.
What is a complex number?
A number of the form a + bi, where a and b are real numbers and i = square root of -1, with i^2 = -1.
What is the conjugate of the complex number a + bi?
a - bi (the sign of the imaginary part is changed).
What is the standard form for writing a number in scientific notation?
a x 10^n, where 1 is less than or equal to a is less than 10 and n is an integer.
What is a common logarithm and a natural logarithm?
A common logarithm has base 10 (log x); a natural logarithm has base e (ln x), where e is approximately 2.718.
State the three basic laws of logarithms (product, quotient, power).
log(mn) = log m + log n; log(m/n) = log m - log n; log(m^n) = n log m.
Matric (SSC) Mathematics FAQ
What is in the Matric (SSC) Mathematics syllabus?
Matric (SSC) Mathematics is split into 15 chapters: Matrices and Determinants, Real and Complex Numbers, Logarithms, Algebraic Expressions and Formulas, Factorization, Algebraic Manipulation, Linear Equations and Inequalities, Linear Graphs and Their Application, Quadratic Equations, Introduction to Coordinate Geometry, Algebraic Sentences and Variations, Sets and Functions, Basic Statistics, Introduction to Trigonometry and Theorems Related to Circles. Together they contain 52 topics.
How many chapters are in Matric (SSC) Mathematics?
15 chapters, containing 52 topics. The largest chapter is Matrices and Determinants, with 5 topics.
Are there flashcards for Matric (SSC) Mathematics?
Yes — a 50-card Mathematics deck, printed in full in the flashcards section of this page and available in the Examius app with spaced repetition. The free plan covers one exam of your choice, including its flashcards; Examius Pro, a one-time purchase, unlocks every other exam and deck.