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Aga Khan University Examination Board Mathematics (SSC IX-X) Syllabus
The Mathematics (SSC IX-X) syllabus for Aga Khan University Examination Board in full: 12 chapters and 47 topics, every one listed below, plus 50 Mathematics (SSC IX-X) flashcards with answers.
Mathematics (SSC IX-X) syllabus: all 12 chapters
Expand any chapter to see its topics and sub-topics.
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Matrices and Determinants
4 topics- Types and Order of Matrices
- Addition and Multiplication of Matrices
- Determinant and Inverse of a Matrix
- Solution of Linear Equations using Matrices
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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
4 topics- Rational Expressions
- Algebraic Identities
- Surds and their Operations
- Rationalization
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Factorization
3 topics- Factorization of Algebraic Expressions
- Remainder and Factor Theorems
- Factorization of Cubic Polynomials
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Algebraic Manipulation and Equations
4 topics- HCF and LCM
- Simplification of Fractions
- Quadratic Equations
- Nature of Roots
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Sets and Functions
4 topics- Sets and Operations on Sets
- Venn Diagrams
- Ordered Pairs and Cartesian Product
- Relations and Functions
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Linear Equations and Inequalities
3 topics- Linear Equations in One Variable
- Equations Involving Absolute Value
- Linear Inequalities and their Solutions
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Coordinate Geometry
4 topics- Distance Formula
- Collinear and Non-collinear Points
- Equation of a Straight Line
- Slope and Intercepts
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Geometry and Theorems
5 topics- Congruent Triangles
- Parallelograms and Triangles
- Line Bisectors and Angle Bisectors
- Pythagoras Theorem
- Theorems Related to Circles
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Trigonometry
4 topics- Measurement of Angles (Degrees and Radians)
- Trigonometric Ratios
- Trigonometric Identities
- Angles of Elevation and Depression
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Mensuration and Statistics
4 topics- Practical Geometry of Triangles and Circles
- Frequency Distribution
- Measures of Central Tendency
- Measures of Dispersion
Aga Khan University Examination Board Mathematics (SSC IX-X) flashcards — 50 questions with answers
What is a matrix?
A matrix is a rectangular array of numbers (elements) arranged in rows and columns, enclosed in brackets.
What is meant by the order (dimension) of a matrix?
The order of a matrix 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 row matrix is a matrix that has exactly one row, i.e. order 1 x n.
What is a column matrix?
A column matrix is a matrix that has exactly one column, i.e. order m x 1.
What is a square matrix?
A square matrix is a matrix in which the number of rows equals the number of columns (order n x n).
What is a rectangular matrix?
A rectangular matrix is one in which the number of rows is not equal to the number of columns (m ≠ n).
What is a null (zero) matrix?
A null or zero matrix is a matrix in which every element is 0, denoted by O.
What is a diagonal matrix?
A diagonal matrix is a square matrix in which all non-diagonal (off-diagonal) elements are zero, and at least one diagonal element is non-zero.
What is a scalar matrix?
A scalar matrix is a diagonal matrix in which all the diagonal elements are equal (and the off-diagonal elements are zero).
What is an identity (unit) matrix?
An identity matrix is a diagonal matrix whose diagonal elements are all 1, denoted by I; for any matrix A, AI = IA = A.
What is the transpose of a matrix?
The transpose of a matrix A, written A^t, is obtained by interchanging its rows and columns; an m x n matrix becomes n x m.
When are two matrices equal?
Two matrices are equal if they have the same order and their corresponding elements are equal.
Under what condition can two matrices be added or subtracted?
Two matrices can be added or subtracted only if they have the same order; addition/subtraction is done element by element.
Is matrix addition commutative and associative?
Yes. Matrix addition is commutative (A + B = B + A) and associative ((A + B) + C = A + (B + C)).
How do you multiply a matrix by a scalar k?
Multiply every element of the matrix by k; e.g. k[a b; c d] = [ka kb; kc kd].
What is the condition for the product of two matrices AB to be defined?
The product AB is defined only when the number of columns of A equals 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.
How is each element of a matrix product AB computed?
The element in row i, column j of AB is the sum of products of corresponding entries of row i of A and column j of B (row-by-column multiplication).
Is matrix multiplication commutative?
No. In general AB ≠ BA; matrix multiplication is not commutative.
How is the determinant of a 2x2 matrix [a b; c d] calculated?
The determinant is ad − bc.
Show the other 30 Mathematics (SSC IX-X) flashcards
What is a singular matrix?
A square matrix whose determinant is zero; a singular matrix has no inverse.
What is a non-singular matrix?
A square matrix whose determinant is non-zero; only non-singular matrices have an inverse.
What is the adjoint of a 2x2 matrix [a b; c d]?
The adjoint is [d −b; −c a] (swap the main-diagonal entries and change the signs of the off-diagonal entries).
What is the formula for the inverse of a 2x2 matrix A = [a b; c d]?
A⁻¹ = (1/(ad − bc)) [d −b; −c a], provided ad − bc ≠ 0.
What is the product of a matrix and its inverse?
A·A⁻¹ = A⁻¹·A = I, the identity matrix.
How is a system of linear equations written in matrix form?
As AX = B, where A is the coefficient matrix, X is the column matrix of variables, and B is the column matrix of constants.
Using the inverse-matrix method, how is AX = B solved?
By computing X = A⁻¹B, provided A is non-singular (det A ≠ 0).
In Cramer's rule for two equations, how is x found?
x = Dx / D, where D is the determinant of the coefficient matrix and Dx is D with the x-column replaced by the constants column.
What does it mean if the determinant of the coefficient matrix is zero?
The system has no unique solution (it is either inconsistent with no solution or has infinitely many solutions).
What is a rational number?
A number that can be written as p/q where p and q are integers and q ≠ 0; its decimal form terminates or recurs.
What is an irrational number?
A number that cannot be written as p/q with integers p, q; its decimal form is non-terminating and non-recurring, e.g. √2 and π.
What numbers make up the set of real numbers?
The real numbers consist of all rational numbers together with all irrational numbers.
State the closure, commutative and associative properties of real numbers under addition.
Closure: a + b is real; Commutative: a + b = b + a; Associative: (a + b) + c = a + (b + c).
State the distributive property of multiplication over addition for real numbers.
a(b + c) = ab + ac (and (b + c)a = ba + ca).
What are the additive and multiplicative identities of real numbers?
The additive identity is 0 (a + 0 = a); the multiplicative identity is 1 (a x 1 = a).
In the radical n√a, name the parts.
n is the index, the symbol √ is the radical sign, and a (the number under the radical) is the radicand.
What does it mean to rationalize the denominator?
It means removing the radical from the denominator, usually by multiplying numerator and denominator by a suitable surd or conjugate.
What is the conjugate of the surd a + √b?
Its conjugate is a − √b; multiplying them gives the rational number a² − b.
State the product law of exponents: aᵐ · aⁿ.
aᵐ · aⁿ = aᵐ⁺ⁿ (add the exponents when the bases are the same).
State the quotient law of exponents: aᵐ ÷ aⁿ.
aᵐ ÷ aⁿ = aᵐ⁻ⁿ (subtract the exponents, a ≠ 0).
State the power law of exponents: (aᵐ)ⁿ.
(aᵐ)ⁿ = aᵐⁿ (multiply the exponents).
What is the value of a⁰ (a ≠ 0), and the meaning of a⁻ⁿ?
a⁰ = 1, and a⁻ⁿ = 1/aⁿ (a negative exponent gives the reciprocal).
How is a fractional exponent a^(m/n) written as a radical?
a^(m/n) = n√(aᵐ) = (n√a)ᵐ.
What is a complex number and its standard form?
A complex number has the form a + bi, where a and b are real numbers and i = √(−1); a is the real part and b is the imaginary part.
What is the value of i² and the conjugate of a + bi?
i² = −1; the conjugate of a + bi is a − bi.
How do you add and multiply the complex numbers (a + bi) and (c + di)?
Add: (a + c) + (b + d)i. Multiply: (ac − bd) + (ad + bc)i (using i² = −1).
What is the standard form of scientific notation?
A number written as a x 10ⁿ, where 1 ≤ a < 10 and n is an integer.
What is a logarithm? If aˣ = y, express x as a logarithm.
A logarithm is the exponent to which a base must be raised to give a number; aˣ = y means x = logₐ y.
What are common and natural logarithms?
A common logarithm has base 10 (log₁₀, written log); a natural logarithm has base e ≈ 2.718 (written ln).
State the product, quotient and power laws of logarithms.
log(mn) = log m + log n; log(m/n) = log m − log n; log(mⁿ) = n log m.
Aga Khan University Examination Board Mathematics (SSC IX-X) FAQ
What is in the Aga Khan University Examination Board Mathematics (SSC IX-X) syllabus?
Aga Khan University Examination Board Mathematics (SSC IX-X) is split into 12 chapters: Matrices and Determinants, Real and Complex Numbers, Logarithms, Algebraic Expressions and Formulas, Factorization, Algebraic Manipulation and Equations, Sets and Functions, Linear Equations and Inequalities, Coordinate Geometry, Geometry and Theorems, Trigonometry and Mensuration and Statistics. Together they contain 47 topics.
How many chapters are in Aga Khan University Examination Board Mathematics (SSC IX-X)?
12 chapters, containing 47 topics. The largest chapter is Geometry and Theorems, with 5 topics.
Are there flashcards for Aga Khan University Examination Board Mathematics (SSC IX-X)?
Yes — a 50-card Mathematics (SSC IX-X) 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.