EmSAT Achieve Mathematics SyllabusThis detailed syllabus outlines the topics covered in the EmSAT Achieve Mathematics exam. The exam is designed to assess students' understanding and proficiency in various mathematical concepts. Below is a breakdown of the syllabus:
1. EmSAT Achieve Polynomials- Definition and types of polynomials
- Operations with polynomials
- Polynomial factorization
- Solving polynomial equations
2. EmSAT Achieve Equations in One Variable- Linear equations
- Quadratic equations
- Rational equations
- Radical equations
- Absolute value equations
3. EmSAT Achieve Inequalities- Solving linear inequalities
- Solving quadratic inequalities
- Solving rational inequalities
- Solving absolute value inequalities
4. EmSAT Achieve System of Equations- Solving systems of linear equations
- Solving systems of quadratic equations
- Solving systems of equations using matrices
5. EmSAT Achieve Functions- Definition and properties of functions
- Function notation
- Graphing functions
- Composite and inverse functions
6. EmSAT Achieve Linear & Exponential Models- Linear models and applications
- Exponential models and applications
7. EmSAT Achieve Trigonometric Functions- Trigonometric ratios
- Trigonometric identities
- Solving trigonometric equations
8. EmSAT Achieve Exponents- Laws of exponents
- Scientific notation
- Operations with exponents
9. EmSAT Achieve Rational & Irrational Numbers- Rational numbers and operations
- Irrational numbers and their properties
- Approximating irrational numbers
10. EmSAT Achieve Complex Numbers- Complex numbers and operations
- Complex conjugates
- Complex number applications
11. EmSAT Achieve Vectors- Vector representation and operations
- Dot product and cross product of vectors
- Applications of vectors
12. EmSAT Achieve Matrices- Matrix notation and operations
- Determinants and inverses of matrices
- Applications of matrices
13. EmSAT Achieve Limits- Definition and properties of limits
- Evaluating limits
- Infinite limits and limits at infinity
14. EmSAT Achieve Differentiation- Definition and properties of derivatives
- Differentiation rules
- Applications of derivatives
15. EmSAT Achieve Integration- Indefinite and definite integrals
- Integration techniques
- Applications of integration
16. EmSAT Achieve Surface Area & Volumes- Surface area of 2D and 3D shapes
- Volume of geometric solids
17. EmSAT Achieve Geometric Theorems- Pythagorean theorem
- Similarity and congruence theorems
- Angle and side relationships in triangles and quadrilaterals
18. EmSAT Achieve Similarity Theorems- Similarity in triangles
- Similarity in circles
19. EmSAT Achieve Trigonometric Ratios & Triangles- Trigonometric ratios in right triangles
- Solving problems using trigonometry
20. EmSAT Achieve Circles- Properties of circles
- Arcs, chords, and tangents of circles
21. EmSAT Achieve Conics- Parabolas, ellipses, and hyperbolas
- Equations and properties of conic sections
22. EmSAT Achieve Statistics- Data representation and interpretation
- Measures of central tendency and dispersion
- Probability distributions
23. EmSAT Achieve Probability- Basic probability concepts
- Conditional probability
- Probability of multiple events
24. EmSAT Achieve Expressions- Simplifying algebraic expressions
- Evaluating expressions
- Solving equations and inequalities
25. EmSAT Achieve Graphs- Graphing linear equations and inequalities
- Graphing quadratic equations
- Graphing exponential and logarithmic functions
By covering these topics thoroughly, students will be well-prepared for the EmSAT Achieve Mathematics exam. It is important to study and practice each concept to ensure a strong understanding and ability to apply mathematical principles effectively.
This course is helpful for the following exams: Grade 11, Grade 12, EmSAT Achieve