This is where you can study and practice, selected topics, to help you prepare for the actual test. You can review the exam objectives; prepare yourself using the study material, curated to ensure you are fully equipped to qualify the ace Exam.

You will be required to have sound knowledge of the topics listed below. The preparatory lessons have been designed to refresh your understanding of the topics, the length and depth of discussion around a particular topic reflects the weighted average of each section.

The **Number Theory and Arithmetic** section carries 7% weight of the overall exam and this section covers the following:

- Fractions (adding, subtracting and dividing fractions, fractions with different signs and mixed numbers).
- GCF and LCM
- Scientific notation
- Percentages
- Exponents
- Divisibility
- Prime and composite numbers (factorization)
- Odd and even numbers (properties, patterns)
- Order of operations
- Equalities and inequalities (multistep, compound, rational)
- Arithmetic and geometric Sequence

The **Patterns and Algebra** section carries 18% weightage and covers the following:

- Solving equations (steps, variables, expressions)
- Long and Synthetic division (polynomials)
- Factoring (quadratic, perfect squares)

- Solving system of equations
- Polynomials
- Solving inequalities
- Solving system of inequalities (graphing inequalities)

The **Geometry (2D and 3D) and Measurements** section carries 10% of the total weightage and this section covers the following topics:

- Points, lines, segments and angles
- Polygons (interior and exterior angles)
- Congruent and similar triangles
- Analytic Geometry (distance, midpoint, Pythagorean theorem, perpendicular lines)

- Perimeters, Areas, and volumes
- Metric and Imperial Units
- Transformations (multivariable, congruence)
- Units conversions
- Dilation

The next section is **Discrete Mathematics **and has 6%weightage. It covers the following:

- Basic Structures: Sets, Sequences, Sums
- Matrices
- Logic
- Permutations and Combinations
- Recursion (sequence and formula)
- Languages and Grammars
- Relations, basic definitions and properties, special types of relations
- Introduction to graph theory, basic definitions and properties, special types of graphs

The **Probability and Statistics** section carries 8% weightage and this section covers the following topics:

- Central tendency measures
- Normal Distribution
- Dispersion measures
- Data representations
- Probability
- Binomial Theorem (coefficient in binomial expansion)

The **Functions** section carries 20% weightage. This section covers the following:

- Domain and Range
- Write equation of a linear function
- Identify Functions
- Add, Subtract, Multiply, and Divide
- Functions
- Evaluate Functions
- Slope (positive and negative, slope of a line)

- Composite Functions (evaluating, recognizing)
- Linear, Quadratic Functions
- Inverse Functions
- Functions Graph
- Odd and Even Functions (connection between even and odd, symmetry of functions)
- Transformation (multivariable, congruence)
- Exponential and Logarithmic Functions

**Trigonometry **carries 14% weightage and this section explains the following:

- The 6 trigonometric Ratios
- Solving Triangles
- Law of Sine and Cosine
- Trigonometric Identities
- Sine and Cosine Functions
- Bearing
- Trigonometric Equations

The last section is **Calculus (Differentiation and Integration)** and carries 17% of overall weightage. This section will explain the following:

- Limits
- Continuity
- Derivatives (slope of curve, slope of tangent line)
- Areas and volume
- Integrals (definite integrals, anti-derivatives and indefinite integrals)
- Series and sequences (convergent and divergent sequences)
- Techniques of integration